MATH 225N: Statistical Reasoning for the Health Sciences – CU Entire Course Solution

MATH 225N: Statistical Reasoning for the Health Sciences

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MATH 225N Week 1 Assignment: Comparing Sampling Methods

1. Question: In order to study the shoe sizes in his town. Billy sample the population by dividing the residents by age and randomly selecting the proportionate number of residents of each age group. Which type of sampling is used.
2. Question: When is sampling stratified sampling appropriate.
3. Question: In reference to different sampling methods, Is the following statement true or false?
4. Question: A town planner is interested is getting some demographic data about the household in the city. The city has four wards with the following numbers of households, ward a has 2107, ward B 903, Ward C ha 1505 and Ward D has 1490. The budget for the project allows the planner to survey 100households. She plans to use as stratified sampling method. What number of households should be chosen from Ward B. Enter whole number?
5. Question: To study the mean blood pressure of all people in her state. Christine samples the population by dividing the residents by towns and randomly selecting 9 of the towns. She then collects data from all the residents in the selected town. Which type of sampling is used.?
6. Question: When considering different sampling methods, cluster sampling the steps_____
7. Question: The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that would be required to select flights by each proposed method. Which of the following would be reasonable methods of stratified sampling? Select all that apply.
8. Question: An executive for a large national restaurant chain with multiple locations in each of 513 counties wants to personally sample the cleanliness of the chain’s restaurants throughout the country by visiting restaurants. The executive wants a good quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would be most appropriate?

MATH 225N Week 1 Assignment: Evidence, Claims, and Types

1. Question: A large manufacturing firm is interested in the effect of the temperature of the manufacturing floor on worker productivity. Over the course of a year. The firm randomly samples its 103 sites and records the temperature and the quantity of items produced on that day. Is this an experiment or an observational study?
2. Question: In a study to add a new feature to a software program, the programmer introduced two categories, men and women, in the survey she conducted. Is the study observational or experimental? What is the controlled factor?
3. Question: A biology student is interested in the relationship between temperature and germination time to soy beans. The student gets sample seeds from multiple sources and randomly selects 180 seeds from them. Then he sets up three growing stations. On at 20C, one at 15C, and one at 25C. he divides the seeds into three groups of 60 and plants the seeds from each group in a growing station. He records the germination time of each side. Is this an observation study or an experiment? if it is an experiment, what is controlled factor.?
4. Question: A study was conducted among school students on the relationship between getting up late and getting to school late. Is this an example of an observational study? If it is an experiment, what is the controlled factor?
5. Question: In a study to support drug discovery for patients with lung cancer, patients were divided into 3 groups based on the severity of the disease. Smoking and alcohol consumption habits for all 3groups. Is this an example of an observational study of experimental study?
6. Question: An opinion poll was conducted to know whether parents play n role in shaping a career for their children. Respondents were asked to vote “yes” if they think parents have a role to play and “No” if they think parents have no role to play in shaping the career of their children. Is the study observational or experiment, what is the controlled factor.?
7. Question: Is an online poll asking the preferred mobile phone type used by school children an observational study or experimental study? If it is an experiment, what is controlled factor?
8. Question: A biologist is interested in finding the relationship between the amount of sunlight and the growth rate of sunflowers. Would an experimental of observational study design be more appropriate?

STA 4322: Introduction to Statistics Theory – Entire Course Solution

MATH 225N Week 1 Assignment: Variables and Measures of Data

1. Question: A climate scientist keeps track of the daily temperature, in degrees Fahrenheit, of a take over the course of six weeks. What is the level of measurement of the data?
2. Question: Patricia is collecting data on favorite ice cream. What type of data is this?
3. Question: Continuous data is the type of quantitative data that is the result of counting?
4. Question: Margaret is investigating if gender ha any effect on political party association. What is the response variable?
5. Question: Which of the following best describes the term explanatory variable?
6. Question: At a comic convention, a researcher asks attendees what their favorite comic book is. What is the level of measurement of the data?
7. Question: An explanatory variable is a value or component of the independent variable applied in an experiment?
8. Question: A response variable is a variable that has an effect on a study even though it is neither as independent nor a dependent variable?
9. Question: Given that Angelina is collecting data on commute distance. What type of data is she working with?
10. Question: Patrick is collecting data on shoe size. What type if data is this?
11. Question: Timothy is collecting data on number of dental cavities. What type of data is this?
12. Question: Given that Justin is collecting data on reaction time. What type of data is he working with?
13. Question: A track runner keeps track how long it takes her to run 200meter dash. What is the level of measurement of the data?
14. Question: A new mother keeps track of time when her baby wakes up each morning. What is the level of measurement of the data?

MATH 225N Week 1 Discussion: Basic Statistics Data Used in Everyday Life

Initial Post Instructions:

1. Present two different types of data, or variables, used in the health field. Examples could be blood pressure, temperature, pH, pain rating scales, pulse oximetry, % hematocrit, minute respiration, gender, age, ethnicity, etc.
2. Classify each of your variables as qualitative or quantitative and explain why they fall into the category that you chose.
3. Also, classify each of the variables as to their level of measurement–nominal, ordinal, interval or ratio—and justify your classifications.
4. Which type of sampling could you use to gather your data? (stratified, cluster, systematic, and convenience sampling).

MATH 225N Week 2 Assignment: Frequency Tables

1. Question:  A small startup company wishes to know how many hours, per week, that its employees spend commuting to and from work. The number of hours for each employee are shown below. Construct a frequency table for grouped data using four classes; 9, 18, 18, 14, 13, 4, 12, 9, 13, 10, 20, 12, 19, 20, 13, 3, 5, 20, 17, 1
2. Question:  An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct the table for the instructor using six classes…. 48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
3. Question: Sixteen people were asked how many miles (to the nearestmile) theycommute to work each day. The data are as follows: 2,5,7,3,2,10,18,5,10,10,5,7,13,12,2,5
4. Question: The following data represents the average number of emergency doctor visits per day in a small city: 3,4,4,8,7,2,3,8,3,9,9.
5. Question:  The frequency table below shows the number of goals Real Madrid scored in each of their soccer games in April and May of 2015.  Determine the total number of data values represented in the table.
6. Question:  The ages of 30 students in a class are given below. Construct a frequency table for grouped data using 6 classes. For convenience, the data has been ordered from smallest to largest 15,17,18,19,25,25,27,28,29,30,30,32,33,36,38,45,45,48,49,50,52,53,55,56,57,58,59,59,63,68
7. Question:  The ages of the students in an art class at the community center are listed below. 8,10,15,15,18,19,20,22,22,25,42,42,49,50,56

MATH 225N Week 2 Assignment; Frequency Tables and Histograms

1. Question: The speed (in mph) of randomly selected bicyclists were measured as they were approaching a hill. The results are presented in the following histogram.How many of those bicyclists were traveling at least 8.5 and less than 11.5mph as they were approaching the hill?

5. Question: Describe the shape of the given histogram.
6. Question: Describe the shape of the given histogram.
7. Question: The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The results were tallied and are presented in the following histogram. How many of those students held their breath greater than 12.5 and less than 15.5 seconds?
8. Question: Several people were asked to report the number of hours of sleep they average per night. The results are shown in the histogram below. How many of those people average greater than 4.5 and less than 6.5hours of sleep per night?
9. Question: Given the following histogram for a set of data, how many values in the data set are greater than 5.5 but less than 8.5?
10. Question: Given the following histogram for a set of data, how many values in the data set are greater than 10.5 and less than 12.5?
11. Question: A professor gave students a test, and the distribution of the scores of the students is shown in the histogram below. What shape does the distribution have?
12. Question: Describe the shape of the given histogram.
13. Question: A professor gave students a test that was easier than usual. The distribution of the scores of the students is shown in the histogram below. What shape does the distribution have?
14. Question: Describe the shape of the given histogram.
15. Question: A restaurant is open for both lunch and dinner. One day, the owner kept track of the number of occupied tables in the dining area and created a histogram showing the results for each half hour of the day. What shape does the distribution have?
16. Question: The histogram shows the income of the families of the students in a statistics class. What is the shape of the histogram?
17. Question: A student surveys his class and creates a histogram showing the number of pets in each student’s house. What is the shape of the distribution?
18. Question: The histogram below represents the prices of digital SLR camera models at a store. Describe the shape of the distribution.
19. Question: A professor created a histogram showing the birth month of the students in one of her classes. What is the shape of the histogram?
20. Question: A bookstore took an inventory of the prices of its books and created a histogram to show the results. What shape does the distribution have?
21. Question: Describe the shape of the given histogram.
22. Question: Describe the shape of the given histogram.

MATH 225N Week 2 Assignment: Line and Bar Graphs

2. Question: A travel agency is conducting research on how many times families went on vacation during the last year. The following table shows the number of times sampled families went on vacation. Create the corresponding bar graph to represent this data below. Drag the dots on the top of the bar graph to create the chart.
3. Question: According to the given data, what can the travel agency conclude about the sampled families?
4. Question: Josslyn is a car salesperson who keeps track of her sales over time. The line graph below shows how many cars she sells per week. What was the change in cars sold from week 2 to 6? Do not include the unit in your
5. Question: Marc is keeping track of the total number of movies he has watched over time. The line graph below shows the data where the number of movies corresponds to the number of movies that had been watched at the beginning of the week shown on the horizontal axis. How many movies did Marc watch between the beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.
6. Question: The data listed below represents the distance from a city taxi depot (to the nearest mile) by the number of hours since a taxi left the depot to pick up passengers. Create the corresponding line graph to represent this data below.
7. Question: According to the information above, which of the following is an appropriate analysis of the taxi’s distance?
8. Question: The bar graph below shows the number of men and women in different clubs. What is the total number of women across all the clubs shown? Do not include the units in your answer.
9. Question: The bar graph below shows the number of men and women in different classes. How many total students are in the Chemistry class? Do not include the units in your answer.
10. Question: The data listed below represents the number of vacation days taken in the span of one year by the number of employees. Create the corresponding line graph to represent this data below.
11. Question: According to the information above, which of the following is an appropriate analysis of the vacation takes taken by employees?
12. Question: Horace is trying to improve at golf. So, he keeps track of the number of the total rounds he has played over time. The line graph below shows the data.
13. Question: Alice is keeping track of the total number of books she has read over time. The line graph below shows the data. How many books did Alice read from month 2 to 3? Do not include the unit in your
14. Question: The data listed below represents the number of TVs in a house by family size. Create the corresponding line graph to represent this data below.
15. Question: According to the information above, what family sizes have 6 TVs in their household?
16. Question: The data listed below represents the number of minutes spent texting on a Friday night by age (in years). Create the corresponding line graph to represent this data below.
17. Question: According to the information above, which of the following is an appropriate analysis of texting?
18. Question: The data listed below represents the number of trees planted by the number of benches in a park. Create the corresponding line graph to represent this data below.
19. Question: According to the information above, which of the following is an appropriate analysis of the trees planted?

MATH 225N Week 2 Assignment: Stem and Leaf plots

1.      Question: A set of data is summarized by the stem and leaf plot below.

2.      Question: A set of data is summarized by the stem and leaf plot below.

MATH 225N Week 3 Assignment: Distribution Shape

1. Question: If the median of a data set is 13 and the mean is 13, which of the following is most likely?
2. Question: Which of the following box-and-whisker plots shows a skewed data set? Select all answers that apply.

• A horizontal box-and-whisker plot is above a horizontal axis labeled from 0 to 16 in increments of 2. The box-and-whisker plot has the following five-number summary: 1, 3, 4, 6, and 15. All values are approximate. The part of the box at point 4 is represented with a dotted line.
• A horizontal box-and-whisker plot is above a horizontal axis labeled from 0 to 20 in increments of 5. The box-and-whisker plot has the following five-number summary: 4, 14, 16, 19, and 20. All values are approximate. The part of the box at point 16 is represented with a dotted line.

3. Question: Which of the following box-and-whisker plots shows a skewed data set? Select all answers that apply.

• A horizontal box-and-whisker plot is above a horizontal axis labeled from 0 to 20 in increments of 5. The box-and-whisker plot has the following five-number summary: 4, 14, 16, 19, and 20. All values are approximate. The part of the box at point 16 is represented with a dotted line.

4. Question: Which of the following histograms shows a skewed data set? A histogram has a horizontal axis labeled Values from negative 2 to 10 in increments of 2 and a vertical axis labeled Frequency from 0 to 300 in increments of 50. The histogram has vertical bars of width 1, starting at the horizontal axis value of negative 0.5. The approximate heights of the bars are as follows, where the horizontal axis label is listed first and the approximate height is listed second: negative 0.5, 40; 0.5, 140; 1.5, 225; 2.5, 270; 3.5, 175; 4.5, 95; 5.5, 35; 6.5, 20.

5. Question: Which of the following frequency tables show a skewed data set? Select all answers that apply.
6. Question: If the median of a data set is 13 and the mean is 23, which of the following is most likely?
7. Question: Which of the following frequency tables shows a skewed data set? Select all answers that apply.
8. Question: Which of the following lists of data has the smallest standard deviation?
9. Question: Which of the data sets represented by the following histograms has the smallest standard deviation?
10. Question: The following dataset represents the salaries for all six employees at a small start-up company.Find the mean, variance, and standard deviation for this dataset of salaries (expressed in thousands of dollars): 55, 59, 63, 67, 71, 75
11. Question: A company is interested to know the variation in yearly sales amount for all 5 salespeople in the company. The dataset shown below is the sales amount sold by the 5 salespeople in the company (expressed in thousands of dollars): 40,60,65,70,80

• Find the variance for this dataset.

• Find the sample variance of the following set of data:
  10, 3, 10, 3, 9.

12. Question: The International Shark Attack File recorded the number of shark attacks between 1837 and 2016. Below are the total number of shark attacks for 8 U.S. states. Find the sample variance.
13. Question: For the following data set, you are interested to determine the “spread” of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this data set:

• Final Exam scores for a group of 10 students in a Statistics course with an enrollment of 30 students.

14. Question: Find the sample variance of the following set of data: 11, 4, 4, 6, 10…… Round the final answer to one decimal place.

MATH 225N Week 3 Assignment: Understanding Measures of Central Tendency

1. Question: Given the following box-and-whisker plot, decide if the data is skewed or symmetrical. Select the correct answer below:
2. Question: Which of the following frequency tables show a skewed data set? Select all answers that apply. Select the correct answer below:
3. Question: Which of the following frequency tables show a skewed data set? Select all answers that apply.
4. Question: Which of the following frequency tables shows a skewed data set? Select all answers that apply.
5. Question: For the following dataset, you are interested to determine the “spread” of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this data set: Ages of all students in a Statistics course with an enrollment of 30 students.
6. Question: Which of the data sets represented by the following histograms has the smallest standard deviation?
7. Question: A company is interested to know the variation in yearly sales amount for all 5 salespeople in the company.
8. Question: Which of the data sets represented by the following histograms has the smallest standard deviation?
9. Question: The data set shown below is the sales amount sold by the 5 salespeople in the company (expressed in thousands of dollars): 40,60,65,70,80 Find the variance for this dataset.
10. Question: The data below are the monthly average high temperatures for November, December, January, and February in New York City from the Country Studies/Area Handbook Series sponsored by the U.S. Department of the Army between 1986 and 1998. What is the sample standard deviation? 54,42,40,40 Round the final answer to one decimal place.
11. Question: The following data values represent the daily amount spent by a family during a 7 day summer vacation. Find the sample standard deviation of this dataset: $96, $125, $80, $110, $75, $100, $121 Round the final answer to one decimal place.
12. Question: Which of the following lists of data has the smallest standard deviation?
13. Question: Which of the following lists of data has the smallest standard deviation?
14. Question: Find the median of the following set of miles per gallon for randomly selected sports cars 36,22,24,30,44,13,21,34,18
15. Question: Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year 2,5,6,12,14,12,6,2,5,3,14,5
16. Question: Laura runs at the park after school and wants to know the mean number of miles she runs. The numbers for the miles run each day so far are listed below: 8,9,7,13,3,9,14. Find the mean number of miles she runs daily.
17. Question: An art collector bought 20paintings at an art fair, and wants to know the average price of her new paintings. She adds the prices of all the paintings and divides this number by 20 to find an average price of $350 . Is this price a sample mean or a population mean, and which symbol would be used to denote it?
18. Question: Given the following list of the number of pens randomly selected students purchased in the last semester, find the median 13,7,8,37,32,19,17,32,12,26
19. Question: Find the mode of the following amounts of exercise (in hours) randomly selected runners completed during a weekend 2,14,14,4,2,4,1,14,4,4,8
20. Question: Find the mode of the following list of points earned on a 16 point quiz given during a finance class. 7,7,3,2,7,16,12,16,12
21. Question: Find the median of the following set of data. 35,43,18,35,29,27,19,19 Give your answer as a number only. For example, if you found the median was 34, you would enter 34.
22. Question: Each person in a group shuffles a deck of cards and keeps selecting a card until an ace appears. Find the mode of the following number of cards drawn from a deck until an ace appears. 14,10,7,14,9,9,10,12,9,7,12
23. Question: A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren are given in inches by 63,71,60,59,74,60,60,75,58.
24. Question: What is the population mean of the height of his grandchildren in inches? Round your answer to the nearest tenth of an inch and do not include units.
25. Question: Given the following list of the number of pencils randomly selected students used in a school year, find the median; 10,22,6,7,19,5,27
26. Question: A teacher randomly selects 10 out of her 30 students and finds that the mean height of those 10 students is 5′2″. Is this a sample mean or a population mean, and which symbol would be used to denote it?
27. Question: A data set lists the number of strikes scored per team during a bowling league championship. For this data set, the minimum is 2, the first quartile is 3, the median is 5, the third quartile is 7, and the maximum is 14. Construct a box-and-whisker plot that shows the number of strikes scored.
28. Question: Given the following frequency table of data, what is the potential outlier?
29. Question: Given the following frequency table of data, what is the potential outlier?
30. Question: A data set lists the number of extra credit points awarded on midterm scores of 15 students taking a statistics course. For this data set, the minimum is 3, the median is 15, the third quartile is 16, the interquartile range is 4, and the maximum is 19. Construct a box-and-whisker plot that shows the extra credit points awarded.
31. Question: Given the following list of data, what is the five-number summary? 10, 12, 14, 14, 14, 16, 17, 17, 17, 19, 19
32. Question: The following frequency table summarizes a set of data. What is the five-number summary?
33. Question: The following frequency table summarizes a set of data. What is the five-number summary?
34. Question: The following frequency table summarizes a set of data. What is the five-number summary?
35. Question: Given the following frequency table of data, what is the potential outlier?
36. Question: The five number summary for a set of data is given below. What is the interquartile range of the set of data? Enter just the number as your answer. For example, if you found that the interquartile range was 25, you would enter 25.
37. Question: The five number summary for a set of data is given below. Using the interquartile range, which of the following are outliers? Select all correct answers.
38. Question: Given the following frequency table of data, what is the potential outlier?
39. Question: The five number summary for a set of data is given below….. What is the interquartile range of the set of data?
40. Question: The five number summary for a set of data is given below……Using the interquartile range, which of the following are outliers? Select all correct answers.
41. Question: A data set lists the number of hours each student, from a finance class, studied for a midterm. For this data set, the minimum is 3, the median is 6, the third quartile is 9, the interquartile range is 5, and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours studied. Begin by first placing the middle dot on the median. Then work on placing the rest of the points starting with the ones closest to the median.
42. Question: A data set lists the number of hours waiters worked at a restaurant every Friday during the last year. For this data set, the minimum is 1, the median is 5, the third quartile is 8, the interquartile range is 4, and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours worked on a Friday.
43. Question: The following dataset represents the favorite color reported by young children at a birthday party: Blue, Green, Red, Blue, Blue, Yellow, Pink, Yellow, Red, Red, Blue, Blue, Blue, Green, Blue. Which of the following would be best to describe a typical value in the dataset?
44. Question: The following histogram shows the monthly rents reported in a survey of university students. Which of the following would be a reasonable measure of central tendency for this dataset? Select all that apply.
45. Question: The following dataset represents the dollar amounts of donations collected at the entrance to a free museum during one hour. Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?
46. Question: The following dataset represents the math test scores for a class of 20 students; 90, 60, 85, 100, 100, 90, 100, 75, 100, 95, 95, 85, 30, 100, 40, 15, 100, 90, 70, 80 Identify the best measure of central tendency for this dataset.
47. Question: The following is a dataset of salaries for a company (in thousands). Find the mean and median and determine if the mean or median is the better measure of central tendency 11,87,85,95,92,93,97
48. Question: The following dataset represents the math test scores for a class of 20 students 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 Would the mode be a good measure of central tendency for this dataset?
49. Question: The following histogram shows menu prices of entrees at a local restaurant. Identify the best measure of central tendency for this dataset
50. Question: The following dataset represents the math test scores for a class of 20 students; 90, 85, 95, 100, 100, 90, 100, 70, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75. How many outliers are in this dataset?
51. Question: A trainer would like to find the mean number of sports drinks the people in her class had in the last week. She collects data from 26 participants in her aerobics class. The graph shows the frequency for the number of sports drinks. Find the mean number of sports drinks consumed by the 26 participants, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
52. Question: A student at a fashion school would like to find the mean number of hats his fellow students own. He collects data from 25 students in his fashion design course. The graph shows the frequency for the number of hats owned by his fellow classmates. Find the mean number of hats owned by the 25 students, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
53. Question: Given the frequency table below, which equation shows the mean of the set of data?
54. Question: For the grouped frequency table shown below which shows salaries at a company (expressed in thousands), find the midpoint for the second row in the table:
55. Question: Given the frequency table below, what is the estimated mean? Round your answer to two decimal places.
56. Question: A manager at a shoe factory would like to find the mean number of breaks taken by employees on a particular Friday. He collects data from 15 fellow coworkers in the factory. The graph shows the frequency for the number of breaks taken during this time period. Find the mean number of breaks for the 15 coworkers, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
57. Question: A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65 homes in the area. The graph shows the frequency for the number of people living in the homes.
58. Question: Find the mean number of people living in the 65 homes, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean. A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65 homes in the area. The graph shows the frequency for the number of people living in the homes. Find the mean number of people living in the 65 homes, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
59. Question: Find the mode of the following amounts (in thousands of dollars) in checking accounts of randomly selected people aged 20-25  2,4,4,7,2,9,9,2,4,4,11
60. Question: Find the mode of the following number of states randomly selected travelers at a service plaza visited in the past three years 18,13,8,8,13,10,13,10,9,18
61. Question: The following is a dataset of the average weekly number of cups of coffee consumed by employees in an office. Find the mean and median and determine if the mean or median is the better measure of central tendency 5,0,5,2,0,10,7,8,10,21,5,8,2,5,3,5
62. Question: The following histogram shows the dollar amounts of donations collected by a charitable organization over the course of a month. Identify the best measure of central tendency for this dataset.
63. Question: The following dataset represents the math test scores for a class of 20students:90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75: Suppose that the last value, 75, was mistakenly recorded as 5. What measure(s) of the typical value in a dataset would be affected by this error? Select all that apply.

MATH 225N Week 3 Discussion: Measure of Central Tendency and Variation

Required Resources

Read/review the following resources for this activity:

• OpenStax Textbook: Chapter 2 Lesson
• Minimum of 1 scholarly source
• In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).

Initial Post Instructions

For this Discussion, you will examine central tendency and variability in terms of pulse rate.

Find and record the pulse rate of 10 different people where you work. Tell us a little about the population from which you drew your data. Describe your findings in terms of central tendency and variability.

Consider using some of the following to help you form your initial discussion post:

• What are your measures of central tendency (i.e., mean, median, and mode)? Which might be the better measure for central tendency and why?
• What is the standard deviation of your data? How variable are the data (range)?
• Are there any outliers? Investigate possible reasons for these outliers, and things that might limit them if further study were to be carried out.
• What are some variables that should be considered in discussing your measures of central tendency and variation? Is there any skewness in your measured data?
• How would you describe this data (i.e. what insights did you gain from this data)?

MATH225N – Statistical Reasoning for the Health Sciences

Follow-Up Post Instructions

Respond to at least two peers or one peer and the instructor. Further the dialogue by providing more information and clarification.

MATH 225N Week 3 Lab Assignment: Frequency Distribution

Steps to Complete Week 3 Lab

Step 1: Go to the Chamberlain Library at: https://library.chamberlain.edu (Links to an external site.) .

Step 2: Click Databases in the Search the Library block. Then choose ProQuest Nursing and Allied Health Database in the dropdown menu.

Database Search Example

Step 3: Below, you will find the titles of six articles from the ProQuest database that show a frequency distribution within the article. CHOOSE ONE OF THE ARTICLES FROM THE LIST BELOW. You will perform two searches using this article.

(1) For our first broad-based search, use the underlined words in your chosen article to search and see how many articles from the database contain these underlined words (see the example below the article list for an example search on post-partum depression).

Article Titles

1. Oral manifestations in diabetic patients under treatment for ischemic heart diseases: A comparative observational study
2. Systolic blood pressure , diastolic blood pressure, and pulse pressure: An evaluation of their joint effect on mortality
3. The Relationship Between Body Mass Index (BMI) and Menstrual Disorders at Different Ages of Menarche and Sex Hormones
4. Adolescents’ first tobacco products: Associations with current multiple tobacco product use
5. Association of lifestyle modification and pharmacological adherence on blood pressure control among patients with hypertension at Kenyatta National Hospital, Kenya: A crosssectional study
6. Demographic, parental, and personal factors and youth athletes’ concussion -related knowledge and beliefs

Example of search on post partum depression

Make sure to checkmark Full Text and Peer Reviewed, and choose Last 12 Months from the drop down list. Also, choose English under the language section.

This will yield a list of articles about the topic that you chose. Look to see how many results were found.

(2) For our second more narrow search, go back and search for the title of the article that you chose originally. Type A PORTION of the article title into the search bar and find the full PDF for that article.

Step 4: Complete your lab by taking the following steps

1. Copy and paste, or post a screen shot of the frequency distribution from the article you chose at the top of your Word document.
2. On your first search, what terms did you use, and what other things did you mark on the search page before conducting your search? Why did you choose the article that you did? How many articles were found with these search terms? Give the full APA reference of the article you are using for this lab.
3. What data are shown in the frequency distribution and why might it be of interest? Include the size of the classes, noting if they are of a consistent size or not. Also include a conclusion that could be made from the frequency distribution. (1 to 2 paragraphs)
4. How else might these data have been displayed? Discuss pros and cons of 2 other presentation options, such as tables or different graphical displays (1 to 2 paragraphs)

Step 5: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 3: Lab

MATH 225N Week 3 Lab Assignment: Statistical Data Presentation Pain and Heart Rate

Steps to Complete Week 3 Lab

Step 1: Go to the Chamberlain Library at: https://library.chamberlain.edu (Links to an external site.).

Step 2: Click Databases in the Search the Library block. Then choose ProQuest Nursing and Allied Health Database in the dropdown menu.

Database Search Example

Step 3: Below, you will find the titles of six articles from the ProQuest database that show a frequency distribution within the article. CHOOSE ONE OF THE ARTICLES FROM THE LIST BELOW. You will perform two searches using this article.

(1) For our first broad-based search, use the underlined words in your chosen article to search and see how many articles from the database contain these underlined words (see the example below the article list for an example search on post-partum depression).

Article Titles

1. Oral manifestations in diabetic patients under treatment for ischemic heart diseases: A comparative observational study
2. Systolic blood pressure , diastolic blood pressure, and pulse pressure: An evaluation of their joint effect on mortality
3. The Relationship Between Body Mass Index (BMI) and Menstrual Disorders at Different Ages of Menarche and Sex Hormones
4. Adolescents’ first tobacco products: Associations with current multiple tobacco product use
5. Association of lifestyle modification and pharmacological adherence on blood pressure control among patients with hypertension at Kenyatta National Hospital, Kenya: A crosssectional study
6. Demographic, parental, and personal factors and youth athletes’ concussion -related knowledge and beliefs

Example of search on post partum depression

Make sure to checkmark Full Text and Peer Reviewed, and choose Last 12 Months from the drop down list. Also, choose English under the language section.

This will yield a list of articles about the topic that you chose. Look to see how many results were found.

(2) For our second more narrow search, go back and search for the title of the article that you chose originally. Type A PORTION of the article title into the search bar and find the full PDF for that article.

Step 4: Complete your lab by taking the following steps

1. Copy and paste, or post a screen shot of the frequency distribution from the article you chose at the top of your Word document.
2. On your first search, what terms did you use, and what other things did you mark on the search page before conducting your search? Why did you choose the article that you did? How many articles were found with these search terms? Give the full APA reference of the article you are using for this lab.
3. What data are shown in the frequency distribution and why might it be of interest? Include the size of the classes, noting if they are of a consistent size or not. Also include a conclusion that could be made from the frequency distribution. (1 to 2 paragraphs)
4. How else might these data have been displayed? Discuss pros and cons of 2 other presentation options, such as tables or different graphical displays (1 to 2 paragraphs)

Step 5: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 3: Lab”.

MATH 225N Week 4 Assignment: Evaluating Probability With The Binomial Distribution

1. Question: Which of the pairs of events below is dependent? Select the correct answer below:
2. Question: Identify the option below that represents dependent events. Select the correct answer below:
3. Question: Which shows mutually exclusive events? Select the correct answer below:
4. Question: Which of the pairs of events below is mutually exclusive? Select the correct answer below:
5. Question: A deck of cards contains RED cards numbered 1,2,3,4,5,6, BLUE cards numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is … at random, what is the probability that the card has an ODD number?
6. Question: Hector is a baseball fan but wants to watch something different. There are 5basketball games, 2 football games, and 4hockey games that he can choose to watch. If Hector randomly chooses a game, what is the probability that it is a basketball game?
7. Question: There are 26 cards in a hat, each of them containing a different letter of the alphabet. If one card is chosen at random, what is the probability that it is not between the letters L and P, inclusive?
8. Question: A spinner contains the numbers 1 through 80. What is the probability that the spinner will land on a number that is not a multiple of 12?
9. Question: An art collector wants to purchase a new piece of art. She is interested in 5 paintings, 6 vases, and 2 statues. If she chooses the piece at random, what is the probability that she selects a painting?
10. Question: Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high-difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is the probability that Boris is assigned a moderate-difficulty question first?
11. Question: A spinner contains the numbers 1 through 40. What is the probability that the spinner will land on a number that is not a multiple of 6? Give your answer as a fraction.
12. Question: A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 4?
13. Question: Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
14. Question: A weighted coin has a 55 probability of landing on heads. If you toss the coin 14 times, what is the probability of getting heads exactly 9 times? (Round your answer to 3 decimal places if necessary.)
15. Question: Identify the parameter pin the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 546 and without a popcorn coupon is 0.454. If you buy 27 movie tickets, we want to know the probability that exactly 15 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)
16. Question: A softball pitcher has a 64 probability of throwing a strike for each pitch. If the softball pitcher throws 20 pitches, what is the probability that exactly 13 of them are strikes?
17. Question: Identify the parameter n in the following binomial distribution scenario. A basketball player has a 429 probability of making a free throw and a 0.571 probability of missing. If the player shoots 20 free throws, we want to know the probability that he makes no more than 12 of them. (Consider made free throws as successes in the binomial distribution.)
18. Question: Give the numerical value of the parameter pin the following binomial distribution scenario. A softball pitcher has a 675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes. Consider strikes as successes in the binomial distribution. Do not include p= in your answer.
19. Question: Identify the parameters p and n in the following binomial distribution scenario. Jack, a bowler, has a 38 probability of throwing a strike and a 0.62 probability of not throwing a strike. Jack bowls 20 times (Consider that throwing a strike is a success.). The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6 matches. What is the mean for the number of matches that they win in the tournament?
20. Question: Using the same scenario, what is the standard deviation for the number of matches that they win in the tournament?
21. Question: The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6
22. Question: Identify the parameter n in the following binomial distribution scenario. A weighted coin has a 441 probability of landing on heads and a 0.559 probability of landing on tails. If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)
23. Question: Give the numerical value of the parameter n, the number of trials, in the following binomial distribution scenario.
    A weighted coin has a 486 probability of landing on heads and a 0.514 probability of landing on tails. If you toss the coin 27 times, we want to know the probability of getting heads exactly 11 times.
    Consider a toss of heads as success in the binomial distribution.
24. Question: The probability of winning on an arcade game is 659. If you play the arcade game 30 times, what is the probability of winning exactly 21 times?
25. Question: The probability of buying a movie ticket with a popcorn coupon is 526. If you buy 26 movie tickets, what is the probability that exactly 15 of the tickets have popcorn coupons?
26. Question: The probability of buying a movie ticket with a popcorn coupon is 608. If you buy 10 movie tickets, what is the probability that more than 3 of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)
27. Question: A softball pitcher has a 507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes? (Round your answer to 3 decimal places if necessary.)
28. Question: A 2014 study by researchers at the University College Antwerp and the University of Leuven showed that e-cigarettes are effective at reducing cigarette craving. Participants were separated into two groups. One group was … e-cigarettes and the other was told to not smoke e-cigarettes. Two months later, researchers observed how many participants had stopped smoking cigarettes. The following table shows approximate numbers. According to the table, what is the probability that a randomly … participant did not stop smoking, … that the participant received an e-cigarette?
29. Question: Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the relative risk of flying for those birds that have long beaks? … decimal places.
30. Question: Given the contingency table below, determine the marginal distribution of breakfast and lunch. Round your answer(s) to the nearest whole number. Select all that apply.
31. Question: 155 fitness center members were asked if they run and if they lift weights. The results are shown in the table below. Given that a randomly selected survey participant does not run, what is the probability that the participant lifts weights?
32. Question: Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
33. Question: Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the odds ratio for birds that fly having long beaks against birds that do not fly having long beaks? Round your answer to two decimal places. Fill in the following contingency table and find the number of students who both watch comedies AND watch dramas.
34. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are shown in the contingency table below. What is the odds ratio for married people having children against unmarried people having children? Round your answer to two decimal places.
35. Question: Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
36. Question: A group of college freshman are targeted with a voter registration advertisement. Another group of freshman are not targeted. The table below shows how many of these freshman registered to vote. What is the odds ratio for freshman targeted with the advertisement registering to vote against freshman not targeted with the advertisement registering to vote? Does the advertisement appear to have been successful? Round to two decimal places.
37. Question: Researchers__to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of? Round your answer to two decimal places.
38. Question: Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked them whether or not they had a fear of flying and whether or not they had a fear of heights. The data are … in the contingency table below. What is the relative risk of being afraid of flying for those who are afraid of heights? Round your answer to two decimal places.
39. Question: A study of drivers with speeding violations in the last year and drivers who use cell phones produced the following fictional data: Find the probability that a randomly chosen person takes public transit to work given that the person does not support the environmental bill.
40. Question: Fill in the following contingency table and find the number of students who both do not go to the beach AND do not go to the mountains.
41. Question: Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
42. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people having children to married against people not having children to … married? Round your answer to two decimal places.
43. Question: Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people wearing cotton clothes being depressed against people not wearing cotton clothes … depressed? Round your answer to two decimal places.
44. Question: Review the flu vaccine data below. What is the odds ratio of not catching the flu for those who receive the new vaccine?
45. Question: Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
46. Question: In a recent survey, a group of people were asked if they were happy or unhappy with the state of the country. The data are … in the contingency table below, organized by political party. What is the odds ratio for people unhappy with the state of the country to be republicans against people happy with the state of the country to__ republicans? __ two decimal places.
47. Question: Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of being married for those who have children? Round your answer to two decimal places.
48. Question: Kelsey, a basketball player, hits 3-point shots on 1%of her attempts. If she takes 14 attempts at 3-point shots in a game, what is the probability that she hits exactly six of them? Use Excel to find the probability.
49. Question: A computer graphics card manufacturer is testing an improvement to its production process. If a sample of 100 graphics cards manufactured using the new process has a less than 10% chance of having 3 or more defective graphics cards, then the manufacturer will switch to the new process. Otherwise, the manufacturer will stay with its existing process. If the probability of a defective graphics card using the new process is 9%, will the manufacturer switch to the new production process?
50. Question: In a large city’s recent mayoral election, 126, 519 out of 283,143 registered voters actually turned out to vote. If 20 registered voters are randomly selected, find the probability that exactly 8 of them voted in the mayoral election. Use Excel to find the probability.
51. Question: Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.
52. Question: A certain cold remedy has an 88%rate of success of reducing symptoms within 24 Find the probability that in a random sample of 45 people who took the remedy, 40 of them had a reduction of symptoms within a day.
53. Question: Kevin works for a company that manufactures solar panels. In a large batch of solar panels, about 1in 200 is defective. Suppose that Kevin selects a random sample of six solar panels from this batch. What is the probability that none of the solar panels are defective? Use Excel to find the probability.
54. Question: A database system assigns a 32-character ID to each record, where each character is either a number from 0to 9 or a letter from A to F. Assume that each number or letter … is equally … Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.
55. Question: A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will … spun 5 If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?
56. Question: A poll is conducted to determine if political party has any association with whether a person is for or against a certain bill. In the poll, 214 out of 432 Democrats and 246 out of 421 Republicans are in favor of the bill. Assuming political party has no association, the probability of these results being by chance is calculated to … 01. Interpret the results of the calculation.
57. Question: Arianna will roll a standard die 10 times in which she will record the value of each roll. What is a trial of this experiment?
58. Question: A health survey determined the mean weight of a sample of 762men between the ages of 26 and 31 to 173 pounds, while the mean weight of a sample of 1,561 men between the ages of 67 and 72 was 162 The difference between the mean weights is significant at the 0.05 level. Determine the meaning of this significance level.
59. Question: The mean body temperature of a human is 60F. In a study, the body temperature of 127 individuals.
60. chance is less than 0.01. Interpret the results of the calculation.
61. Question: Which of the following events seem like they would unlikely to occur by chance?
62. Question: Before a college professor gave an exam, he held a review session, where 30o f his 150 students attended the review. The mean score of the students who attended was 86%, whereas the mean score of the students who didn’t attend the review was 79%. The difference in the mean scores is significant at the 05 level, assuming the review session does not associate with a higher exam score. Determine the meaning of this significance level.
63. Question: According to a recent poll, 5% of people aged 25 years or older in the state of Massachusetts have a bachelor’s degree or higher. The poll also reported that 30.0% of people aged 25 years or older in the state of Delaware have a bachelor’s degree or higher. The poll sampled 354 residents of Massachusetts and 210 residents of Delaware. The data was … at the 0.013 level. Determine the meaning of this significance level.
64. Question: A survey was conducted to see whether age has an association with the belief that a master’s degree or higher provides an advantage in one’s career. Of the 524 adults between the ages of 22 and 25 surveyed, 56% believed that a master’s degree has value in a person’s career path. Of the 458 adults surveyed between the ages of 40 and 45, 52% also believed that a master’s degree has value in a person’s career path. Assuming age is not … with this belief, the probability of the data being the result of chance is … 21. Interpret this calculation.
65. Question: A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are shown in his orchard and determines the average mass per apple to … 98g. The results are shown at the 01 level. What is the correct interpretation of this calculation?
66. Question: Paul will roll two standard dice simultaneously. If Event A = both dice are odd and Event B = at least one die is even, which of the following best describes events A and B?
67. Question: Patricia will draw 8 cards from a standard 52-card deck with replacement. Which of the following are not events in this experiment?
68. Question: Which of the following gives the definition of event?
69. Question: Which of the following gives the definition of trial?
70. Question: Beth is performing an experiment to check if a die is fair. She rolls the die 5times and records the sequence of numbers she gets.
71. Question: Which of the following pairs of events are independent?
72. Question: Is the statement below true or false? Mutually exclusive is the property of events in which none can occur at the same time.
73. Question: Trial best fits which of the following descriptions?
74. Question: Jacqueline will spin a fair spinner with the numbers 0, 1, 2, 3, and 4a total of 3 If Event A = spinner lands on numbers all greater than 2 and Event B = total sum of 9, which of the following best describes events A and B?

MATH 225N Week 4 Discussion: Probability

Initial Post Instructions

Probability plays a major role in the medical community. Diagnoses are based on probabilities. They are really questions or “what if’s”, and are answered by the probability that the treatment will be the best for the ailment.

Let’s look at probability in terms of both the real world and the medical community.

1. Survey 30 people to find out if they are left-handed or right-handed, and use the following chart to create a contingency table with the information.

Left handed Right handed Total Female Male Total

1. Answer the following questions about the information in your contingency table:
   1. If a person is randomly selected from the survey participants, what is the probability that the person will be left-handed?
   2. If you randomly choose a female from the people you surveyed, what is the probability that she is left-handed?
   3. What is the odds ratio of choosing a left-handed female?
   4. What is the relative risk of choosing a left-handed female?

STA 4321: Introduction to Probability – Full Course Solution

MATH 225N Week 5 Assignment; Applications of the Normal Distribution – Excel

1. Question: Sugar canes have lengths, X, that are normally distributed with mean 365.45 centimeters and standard deviation 4.9 centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters? Round your answer to four decimal places.
2. Question: The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50 miles.
3. Question: A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and variance 9. Calculate the probability that a component is at least 12 centimeters long.
4. Question: The average speed of a car on the highway is 85 kmph with a standard deviation of 5 kmph. Assume the speed of the car, X, is normally distributed. Find the probability that the speed is less than 80 kmph.
5. Question: The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.
6. Question: The average number of acres burned by forest and range fires in a county is 4,500 acres per year, with a standard deviation of 780 acres. The distribution of the number of acres burned is normal. What is the probability that between 3,000 and 4,800 acres will be burned in any given year? Round your answer to four decimal places.
7. Question: Suppose that the weight, X, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate P(X<185).
8. Question: Suppose that the weight, X , in pounds, of a 40 -year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate P(120≤X≤153) .
9. Question: A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and standard deviation 3 centimeters. Calculate the probability that the length of a component lies between 19 and 21 centimeters.
10. Question: A firm’s marketing manager believes that total sales for next year will follow the normal distribution, with a mean of $3.2 million and a standard deviation of $250,000. Determine the sales level that has only a 3% chance of being exceeded next year.
11. Question: Suppose that the weight of navel oranges is normally distributed with a mean of μ=6 ounces and a standard deviation of σ=0.8 ounces. Find the weight below that one can find the lightest 90% of all navel oranges.
12. Question: A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3,000 miles. What mileage would correspond to the the highest 3% of the tires?
13. Question: The average credit card debt owed by Americans is $6375, with a standard deviation of $1200. Suppose a random sample of 36 Americans is selected. Identify each of the following:
14. Question: The heights of all basketball players are normally distributed with a mean of 72 inches and a population standard deviation of 1.5 inches.  If a sample of 15 players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
15. Question: After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean 85 points and standard deviation 3 points. Use the Empirical Rule to find the probability that a randomly selected student’s score is greater than 76 points. Provide the final answer as a percent rounded to two decimal places.
16. Question: After collecting the data, Christopher finds that the total snowfall per year in Reamstown is normally distributed with mean 94 inches and standard deviation 14 inches. Which of the following gives the probability that in a randomly selected year, the snowfall was greater than 52 inches? Use the empirical rule
17. Question: The College Board conducted research studies to estimate the mean SAT score in 2016 and its standard deviation. The estimated mean was 1020 points out of 1600 possible points, and the estimated standard deviation was 192 points. Assume SAT scores follow a normal distribution. Using the Empirical Rule, about 95% of the scores lie between which two values?
18. Question: After collecting the data, Kenneth finds that the body weights of the forty students in a class are normally distributed with mean 140 pounds and standard deviation 9 pounds. Use the Empirical Rule to find the probability that a randomly selected student has a body weight of greater than 113 pounds. Provide the final answer as a percent rounded to two decimal places.
19. Question: Mrs. Miller’s science test scores are normally distributed with a mean score of 77 (μ) and a standard deviation of 3 (σ). Using the Empirical Rule, about 68% of the scores lie between which two values?
20. Question: Brenda has collected data to find that the finishing times for cyclists in a race has a normal distribution. What is the probability that a randomly selected race participant had a finishing time of greater than 154 minutes if the mean is 143 minutes and the standard deviation is 11 minutes? Use the empirical rule.
21. Question: Suppose X∼N(20,2), and x=26. Find and interpret the z-score of the standardized normal random variable.
22. Question: Isabella averages 17 points per basketball game with a standard deviation of 4 points. Suppose Isabella’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(17,4).
23. Question: Suppose X∼N(6.5,1.5), and x=3.5. Find and interpret the z-score of the standardized normal random variable.
24. Question: Suppose X∼N(5.5,2), and x=7.5. Find and interpret the z-score of the standardized normal random variable.
25. Question: Jerome averages 16 points a game with a standard deviation of 4 points. Suppose Jerome’s points per game are normally distributed. Let X = the number of points per game. Then X∼N(16,4).
26. Question: Josslyn was told that her score on an aptitude test was 3 standard deviations above the mean. If test scores were approximately normal with μ=79 and σ=9, what was Josslyn’s score? Do not include units in your answer. For example, if you found that the score was 79 points, you would enter 79.
27. Question: Marc’s points per game of bowling are normally distributed with a standard deviation of 13 points. If Marc scores 231 points, and the z-score of this value is 4, then what is his mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 150 points, you would enter 150.
28. Question: Floretta’s points per basketball game are normally distributed with a standard deviation of 4 points. If Floretta scores 10 points, and the z-score of this value is −4, then what is her mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 33 points, you would enter 33.
29. Question: Jamie was told that her score on an aptitude test was 3 standard deviations below the mean. If test scores were approximately normal with μ=94 and σ=6, what was Jamie’s score? Do not include units in your answer. For example, if you found that the score was 94 points, you would enter 94.
30. Question: A normal distribution is observed from the number of points per game for a certain basketball player. If the mean is 16 points and the standard deviation is 2 points, what is the probability that in a randomly selected game, the player scored between 12 and 20 points? Use the empirical rule
31. Question: A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles.  Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles.
32. Question: A random sample of lobster tail lengths has a sample mean of x¯=4.7 inches and sample standard deviation of s=0.4 inches.  Use the Empirical Rule to determine the approximate percentage of lobster tail lengths that lie between 4.3 and 5.1 inches.
33. Question: A random sample of SAT scores has a sample mean of x¯=1060 and sample standard deviation of s=195.  Use the Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
34. Question: The number of pages per book on a bookshelf is normally distributed with mean 248 pages and standard deviation 21 pages. Using the empirical rule, what is the probability that a randomly selected book has less than 206 pages?
35. Question: Mr. Karly’s math test scores are normally distributed with a mean score of 87 (μ) and a standard deviation of 4 (σ). Using the Empirical Rule, about 99.7% of the data values lie between which two values?
36. Question: In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches. Suppose X, height in inches of adult women, follows a normal distribution. Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?
37. Question: A normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points. Use the empirical rule for normal distributions to estimate the probability that in a randomly selected game the player scored less than 26 points.
38. Question: A normal distribution is observed from the number of points per game for a certain basketball player. If the mean is 15 points and the standard deviation is 3 points, what is the probability that in a randomly selected game, the player scored greater than 24 points? Use the empirical rule
39. Question: The College Board conducted research studies to estimate the mean SAT score in 2016 and its standard deviation. The estimated mean was 1020 points out of 1600 possible points, and the estimated standard deviation was 192 points. Assume SAT scores follow a normal distribution. Using the Empirical Rule, about 95% of the scores lie between which two values?
40. Question: The typing speeds for the students in a typing class is normally distributed with mean 44 words per minute and standard deviation 6 words per minute. What is the probability that a randomly selected student has a typing speed of less than 38 words per minute? Use the empirical rule
41. Question: Nick has collected data to find that the body weights of the forty students in a class has a normal distribution. What is the probability that a randomly selected student has a body weight of greater than 169 pounds if the mean is 142 pounds and the standard deviation is 9 pounds? Use the empirical rule.
42. Question: The times to complete an obstacle course is normally distributed with mean 73 seconds and standard deviation 9 seconds. What is the probability using the Empirical Rule that a randomly selected finishing time is less than 100 seconds?
43. Question: After collecting the data, Douglas finds that the finishing times for cyclists in a race is normally distributed with mean 149 minutes and standard deviation 16 minutes. What is the probability that a randomly selected race participant had a finishing time of less than 165 minutes? Use the empirical rule
44. Question: Charles has collected data to find that the total snowfall per year in Reamstown has a normal distribution. Using the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 87 inches if the mean is 72 inches and the standard deviation is 15 inches?
45. Question: Christopher has collected data to find that the total snowfall per year in Laytonville has a normal distribution. What is the probability that in a randomly selected year, the snowfall was greater than 53 inches if the mean is 92 inches and the standard deviation is 13 inches? Use the empirical rule
46. Question: The times to complete an obstacle course is normally distributed with mean 87 seconds and standard deviation 7 seconds. What is the probability that a randomly selected finishing time is greater than 80 seconds? Use the empirical rule
47. Question: Sugar canes have lengths, X, that are normally distributed with mean 365.45 centimeters and standard deviation 4.9 centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters?
48. Question: On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
49. Question: In a survey of men aged 20-29 in a country, the mean height was 73.4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 10% of heights.
50. Question: Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean of μ=81 points and a standard deviation of σ=4 points. The middle 50% of the exam scores are between what two values?

MATH 225N Week 5 Assignment: Central Limit Theorem for Means

1. Question: A family of statisticians is trying to decide if they can afford for their child to play youth baseball. The cost of joining a team is normally distributed with a mean of $750 and a standard deviation of $185. If a sample of 40 teams is selected at random from the population, select the expected mean and standard deviation of the sampling distribution below.
2. Question: A cupcake baker is planning a supplies order and needs to know how much flour he needs. He knows that his recipes use an average of 100 grams of flour, normally distributed, with a population standard deviation of 15 grams. If he is consulting a sample size of 30recipes, select the mean and standard deviation of the sampling distribution to help him order his supplies from the options below.
3. Question: A head librarian for a large city is looking at the overdue fees per user system-wide to determine if the library should extend its lending period. The average library user has $19.67in fees, with a standard deviation of $7.02. The data is normally distributed and a sample of 72 library users is selected at random from the population. Select the expected mean and standard deviation of the sampling distribution from the options below.
4. Question: A well known social media company is looking to expand their online presence by creating another platform. They know that they current average 2,500,000 users each day, with a standard deviation of 625,000 users. If they randomly sample 50 days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary:
5. Question: A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected.
6. Question: The average time it takes a certain brand of ibuprofen to start working is 25 minutes, with a standard deviation of 13 minutes, distributed normally. A pharmacist randomly samples 20 pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary:
7. Question: Major league baseball recruiters are analyzing college players as potential draft choices. In a survey of college baseball players, the recruiters found that they hit an average of  13 home runs per season, with a standard deviation of 5.  Suppose a random sample of 45 baseball players is selected. Identify each of the following and remember to round to the nearest whole number:
8. Question: The average credit card debt owed by Americans is $6375, with a standard deviation of $1200. Suppose a random sample of 36 Americans is selected. Identify each of the following:
9. Question: The heights of all basketball players are normally distributed with a mean of 72 inches and a population standard deviation of 1.5 inches.  If a sample of 15 players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
10. Question: The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans,  with a standard deviation of 450 people. Suppose a random sample of 10 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
11. Question: The Washington Wheat Farmers Club is studying the impact of rising grain prices on their members’ planting habits. The club members produce an average of 150 million bushels of wheat per year, with a standard deviation of 18 million bushels. The club takes a random sample of 35 years to create a statistical study. Identify each of the following, rounding to the nearest hundredth when necessary:
12. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers…… A curve labeled A rises to a maximum near the left of the horizontal axis and the falls. Another curve labeled B rises to a maximum to the right of and below curve A and falls.
13. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest standard deviation. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the right, curve Upper B is tall and skinny, and curve Upper C is farthest to the left.
14. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. A figure consists of two curves labeled Upper A and Upper B. The curve Upper A is tall and evenly spread out from the center and the curve Upper is B is shorter and more spread out than A.
15. Question: Which of the following lists of data has the smallest standard deviation?
16. Question: Which of the following lists of data has the smallest standard deviation?
17. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is shorter and more spread out than curve Upper B, and the curve Upper B is taller and farther to the right than curve Upper A.
18. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is evenly spread out, curve Upper B is tall and the least spread out, and curve Upper C is short and more evenly spread out from the center.
19. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the left from the center, curve Upper B is evenly spread out to the right from the center, and curve Upper C is tall and the least spread out.
20. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean. A curve labeled B rises to a maximum and then falls. A curve labeled A rises to a maximum below and to the right of A and then falls. A curve labeled C rises to a maximum to the right of and below the maximum of A.
21. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the left, curve Upper B is farthest to the right, and curve Upper C is tall and skinny.
22. Question: A head football coach is concerned about the weight gain of some of his players. He finds that the weight of all football players is normally distributed with a mean of 250 pounds and a population standard deviation of 54 pounds. If the coach selects a random sample of 10 players from the population, identify the expected mean and the standard deviation of the sampling distribution below.
23. Question: A businesswoman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary.

MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions

1. Question: A dental student is conducting a study on the number of people who visit their dentist regularly. Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=60.
2. Question: From recent census data, it is discovered that the proportion of the adults in the United States who are first generation Americans is 14%.  For a random sample of size 500, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
3. Question: From recent survey data, a car buying business finds that 12.5% of the proportion of adults in a city would be likely to use their services. For a random sample of 115 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
4. Question: From recent survey data, its known that the proportion of adults in the United States who are smokers is 18%. For a random sample of size 150, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
5. Question: A small community college has a population of 986 students, 252 of whom them are considered non-traditional students.
6. Question: A marketing team is targeting people who might buy a hybrid car. In their city, with a population of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=121.
7. Question: A brokerage company is analyzing its retirement accounts for its clients nearing retirement. From recent survey data, the proportion of adults in the United States who say they are financially ready for retirement is 31%. For a random sample of size 85, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
8. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. B has the larger mean. A has the larger standard deviation.
9. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. The means of A and B are equal. A has the larger standard deviation.
10. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest standard deviation.
11. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. B has the larger mean. A has the larger standard deviation.
12. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean. Remember that the mean of a normal distribution is the x-value of its central point (the top of the “hill”). Therefore, a distribution with a larger mean will be centered farther to the right than a distribution with a smaller mean.
13. Question: Which of the data sets represented by the following histograms has the smallest standard deviation?…. An untitled histogram has a horizontal axis labeled from 0 to 150 in increments of 50 and vertical axis labeled from 0 to 140 in increments of 20. The histogram contains vertical bars of width 6, starting at the horizontal axis value of 75. The approximate heights of the bars as follows, where the horizontal axis label is listed first and the approximate height is listed second: 75, 6; 82, 18; 88, 70; 76, 115; 82, 150; 88, 103; 95, 70; 102, 20; 108, 8.
14. Question: Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?
15. Question: Suppose that you are conducting a survey on how many pets each employee has in his or her household. The mean number of pets is 4 per household, and the standard deviation is 2. Rob only owns cats, and he has 10 cats. (Which of the following statements is true?). The number of pets owned by Rob is 3 standard deviations to the right of the mean.          If the number of pets owned by Rob is 6 standard deviations to the right of the mean, then Rob should have 4+6×2=16  pets.
16. Question: A math instructor is teaching an algebra course, statistics course and calculus course… After the final exams are completed the instructor would like to know which class had most consistent scores on the final exam and which class had the greatest variation in scores on the final exam. The results from the final exam for these three classes are shown below: Based on these results, which class had most consistent scores on the final exam and which class had the greatest variation in scores on the final exam.
17. Question: Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?
18. Question: Which of the following lists of data has the largest standard deviation?
19. Question: Which of the following lists of data has the largest standard deviation? 24, 15, 21, 23, 9, 22, 12, 21, 20, 13
20. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean
21. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers: A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is evenly spread out from the center, and curve Upper B is farther to the right than A and more evenly spread out.
22. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.
23. Question: An obstetrician is researching postpartum programs for new mothers. From recent census data, it is known that the proportion of women in the United States who are of child bearing age is 17%. For a random sample of size 250, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
24. Question: A youth director for a city’s parks and recreations department is planning for next year’s program. From a a survey of city residents, the director knows that 35% of the population participate in the parks and recreations programs. For a random sample of 40 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
25. Question: From recent survey data, its known that the proportion of adults in the United States who are smokers is 18%. For a random sample of size 150, what is standard deviation for the sampling distribution of the sample proportions.
26. Question: A small community college has a population of 986 students, 252 of whom them are considered non-traditional students. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=40.
27. Question: Economists are analyzing the effects of new tax policies on population growth. From recent census data, it is known that the proportion of families in the United States who have more than 3 children in the household is 26%. For a random sample of 50 families, what is the standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places? Given the population proportion p=26%=0.26 and a sample size of n=50, the standard deviation of the sampling distribution of sample proportions is
28. Question: Of the 459,000 people living in Miami, 68%indicated on a recent, city-wide survey that they were employed. For a random sample of size 490 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places? Given the population proportion p=68%=0.68 and a sample size of n=490, the standard deviation of the sampling distribution of sample proportions is
29. Question: The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean. A curve labeled A rises to a maximum near the left of the horizontal axis and falls, a curve labeled B rises to a maximum near the right of the horizontal axis and falls, a curve labeled C rises to a maximum near the center of the horizontal axis and falls.
30. Question: A credit card company surveys its customers to determine the number of times they use the card each month. There are 5,500 customers and 2,756 indicate that they use the card at least twice each month. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=70 customers.
31. Question: A horse racing track knows that the proportion of its gamblers that report winning is 15%. For a random sample of 64 gamblers, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places? Given the population proportion p=15%=0.15 and a sample size of n=64, the standard deviation of the sampling distribution of sample proportions is
32. Question: Of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. The bank president would like to increase her institution’s marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=400.
33. Question: A baseball team calls itself “America’s Favorite Team,” because it has 90,000 fans on social media out of 2,210,000 social media users. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=1,000.
34. Question: A study by doctors of children attending a certain elementary school finds that, of 812 students, 245 watch more than 2 hours of television each day. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=100 students
35. Question: Pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. A small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=180
36. Question: A dental student is conducting a study on the number of people who visit their dentist regularly. Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=60.
37. Question: From recent survey data, its known that the proportion of adults in the United States who are smokers is 18%. For a random sample of size 150, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

MATH 225N Week 5 Assignment; Understanding Normal Distribution

1. Question: Lexie averages 149 points per bowling game with a standard deviation of 14 Suppose Lexie’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(149,14).
2. Question: Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable.
3. Question: Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.
4. Isabella averages 17points per basketball game with a standard deviation of 4 Suppose Isabella’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(17,4).
5. Question: Suppose X∼N(13.5,1.5), and x=9. Find and interpret the z-score of the standardized normal random variable
6. Question: Suppose X∼N(10,0.5), and x=11.5. Find and interpret the z-score of the standardized normal random variable.
7. Question: Annie averages 23 points per basketball game with a standard deviation of 4 Suppose Annie’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(23,4).
8. Question: Suppose X∼N(9,1.5), and x=13.5. Find and interpret the z-score of the standardized normal random variable.
9. Question: Rosetta averages 148 points per bowling game with a standard deviation of 14 Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14).
10. Question: Suppose X∼N(5.5,2), and x=7.5.
11. Question: Jerome averages 16 points a game with a standard deviation of 4 points. Suppose Jerome’s points per game are normally distributed. Let X = the number of points per game. Then X∼N(16,4).
12. Question: John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,11).
13. Question: Suppose X∼N(16.5,0.5), and x=16.
14. Question: Gail averages 64 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose Gail’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(64,9.5).
15. Question: William averages 58 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose William’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,10.5).
16. Question: Hugo averages 22 points per basketball game with a standard deviation of 4 Suppose Hugo’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(22,4).
17. Question: In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 Suppose X, height in inches of adult women, follows a normal distribution. Let x=68, the height of a woman who is 5′ 8″ tall. Find and interpret the z-score of the standardized normal random variable.
18. Question: Suppose X∼N(16.5,2), and x=18.5.
19. Question: Suppose X∼N(6.5,1.5), and x=3.5.
20. Question: Suppose X∼N(20,2), and x=26.
21. Question: Isabella averages 152 points per bowling game with a standard deviation of 5 points. Suppose Isabella’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5).

MATH 225N Week 5 Assignment: Understanding the Empirical Rule

1. Question: A random sample of CO2 levels in a school has a sample mean of x¯=598.4 ppm and sample standard deviation of s=86.7 ppm.  Use the Empirical Rule to determine the approximate percentage of CO2 levels that lie between 338.3 and 858.5 ppm.
2. Question: Suppose that a random sample of redwood trees has a sample mean diameter of x¯=24.1 feet, with a sample standard deviation of s=3.7 feet. Since the diameters of redwood trees are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two diameters are approximately 68% of the data?
3. Question: Suppose a random sample of monthly rainfalls in a given area has a sample mean of x¯=22.2 inches, with a sample standard deviation of s=3.5 inches. Since rainfall amounts in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two amounts are approximately 99.7% of the data?
4. Question: Suppose a random sample of adult women has a sample mean height of x¯=64.3 inches, with a sample standard deviation of s=2.4 inches. Since height distribution are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two heights are approximately 99.7% of the data?
5. Question: For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches,  use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
6. Question: Returning to the sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to estimate the percentage of heights that are less than 61.9 inches.
7. Question: A random sample of males has a sample mean blood volume of x¯=5.2 liters, with a sample standard deviation of s=0.2 liters. Since blood volumes in males are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two volumes are approximately 95% of the data?
8. Question: A random sample of men’s weights have a sample mean of x¯=182.3 pounds and sample standard deviation of s=12.7 pounds.   Use the Empirical Rule to determine the approximate percentage of men’s weights that lie between 156.9 and 207.7 pounds.
9. Question: A random sample of waiting times at a bus stop has a sample mean time of x¯=214.6 seconds, with a sample standard deviation of s=29.4 seconds. Since waiting times at this bus stop are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two waiting times are approximately 95% of the data?
10. Question: Suppose a random sample of monthly temperatures in a given area has a sample mean of x¯=83.2∘F, with a sample standard deviation of s=1.5∘F. Since temperatures in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two temperatures are approximately 99.7% of the data?
11. Question: A random sample of small business stock prices has a sample mean of x¯=$54.82 and sample standard deviation of s=$8.95.  Use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81.

MATH 225N Week 6 Assignment: Confidence Interval for Mean

1. Question: Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90% confident that the sample mean is within 1 day of the true population mean?
2. Question: The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 442 words and an unknown population mean. If a random sample of 24 essays is taken and results in a sample mean of 1330 words, find a 99% confidence interval for the population mean.
3. Question: The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches. Identify the parameters needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

4. Question: The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches. What is the correct interpretation of the confidence interval?

5. Question: Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 2points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean?
6. Question: The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds. Identify the parameters needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.

7. Question: The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds. What is the correct interpretation of the confidence interval?

8. Question: Suppose heights of dogs, in inches, in a city are normally distributed and have a known population standard deviation of 7 inches and an unknown population mean. A random sample of 15 dogs is taken and gives a sample mean of 34 Find the confidence interval for the population mean with a 99% confidence level.
9. Question: The germination periods, in days, for grass seed are normally distributed with a population standard deviation of 5 days and an unknown population mean. If a random sample of 17 types of grass seed is taken and results in a sample mean of 52 days, find a 80% confidence interval for the population mean.
10. Question: Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 6 points and an unknown population mean. A random sample of 22 scores is taken and gives a sample mean of 92 points. Identify the parameters needed to calculate a confidence interval at the 98% confidence level. Then find the confidence interval.

11. Question: Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 6 points and an unknown population mean. A random sample of 22 scores is taken and gives a sample mean of 92 points. What is the correct interpretation of the 95% confidence interval?

12. Question: Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean?
13. Question: The population standard deviation for the scores of a standardized test is 4 If we want to be 90%confident that the sample mean is within 1 point of the true population mean, what is the minimum sample size that should be taken?
14. Question: The population standard deviation for the total snowfalls per year in a city is 13 If we want to be 95%confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size that should be taken?
15. Question: The population standard deviation for the lengths, in seconds, of the songs in an online database is 15 If we want to be 90% confident that the sample mean is within 4 seconds of the true population mean, what is the minimum sample size that should be taken?
16. Question: The population standard deviation for the number of corn kernels on an ear of corn is 94 If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean, what is the minimum sample size that should be taken?
17. Question: Suppose the weights, in pounds, of the dogs in a city are normally distributed. If the population standard deviation is 3 pounds, what minimum sample size is needed to be 95% confident that the sample mean is within 1 pound of the true population mean?
18. Question: Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean?
19. Question: Suppose the speeds of vehicles traveling on a highway are normally distributed. If the population standard deviation is 2 miles per hour, what minimum sample size is needed to be 90% confident that the sample mean is within 1 mile per hour of the true population mean?
20. Question: A College Board sample estimated the standard deviation of 2016 SAT scores to be 194 You are researching the average SAT score. You want to know how many people you should survey if you want to know, at a 98%confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score. What value for z should you use in the sample size formula?
21. Question: You are researching the average SAT score, and you want to know how many people you should survey if you want to know, at a 98%confidence level, that the sample mean score is within 50 points of the true population mean. From above, we know that the population standard deviation is 194, and z01=2.326. What is the minimum sample size that should be surveyed? ​
22. Question: A television network wants to estimate the average number of hours of TV watched each week by viewers.  The network decides to create a 95%confidence interval for the average number of hours of TV watched each week.  How large of a sample size of viewers should be used to create this confidence interval if the television network wants to be 95% confident that the sample mean is within 1 hour of the population mean?  Assume the standard deviation for the number of hours of TV watched each week is 5. 97 viewers
23. Question: Suppose the number of square feet per house is normally distributed. If the population standard deviation is 155 square feet, what minimum sample size is needed to be 90% confident that the sample mean is within 47 square feet of the true population mean?
24. Question: The population standard deviation for the typing speeds for secretaries is 4 words per minute. If we want to be 90% confident that the sample mean is within 1 word per minute of the true population mean, what is the minimum sample size that should be taken?
25. Question: The population standard deviation for the body weights of the employees of a company is 10 If we want to be 95%confident that the sample mean is within 3 pounds of the true population mean, what is the minimum sample size that should be taken?
26. Question: The population standard deviation for the scores of a standardized test is 5 If we want to be 95%confident that the sample mean is within 2 points of the true population mean, what is the minimum sample size that should be taken?
27. Question: Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 4 points, what minimum sample size is needed to be 95% confident that the sample mean is within 1 point of the true population mean?
28. Question: The population standard deviation for the lengths, in words, of the essays written for a contest is 542 If we want to be 90%confident that the sample mean is within 141 words of the true population mean, what is the minimum sample size that should be taken?
29. Question: Suppose the total snowfalls per year in a city are normally distributed. If the population standard deviation is 13 inches, what minimum sample size is needed to be 95% confident that the sample mean is within 4 inches of the true population mean?
30. Question: Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?
31. Question: The population standard deviation for the number of pills in a supplement bottle is 16 If we want to be 95%confident that the sample mean is within 5 pills of the true population mean, what is the minimum sample size that should be taken?

MATH 225N Week 6 Assignment: Confidence Intervals-Empirical Rule

1. Question: The average number of onions needed to make French onion soup from a population of recipes is unknown. A random sample of recipes yields a sample mean of x¯=8.2 onions. Assume the sampling distribution of the mean has a standard deviation of σx¯=2.3 onions. Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions.
2. Question: In a random sample of 30 young bears, the average weight at the age of breeding is 312 Assuming the population ages are normally distributed with a population standard deviation is 30 pounds, use the Empirical Rule to construct a 68% confidence interval for the population average of young bears at the age of breeding. Do not round intermediate calculations. Round only the final answer to the nearest pound. Remember to enter the smaller value first, then the larger number.
3. Question: A random sample of garter snakes were measured and the proportion of snakes that were longer than 20 inches in length recorded. The measurements resulted in a sample proportion of p′=0.25, with a sampling standard deviation of σp′=0.05. Write a 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length
4. Question: The average height of a population is unknown. A random sample from the population yields a sample mean of x¯=66.3 inches. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.8 inches. Use the Empirical Rule to construct a 95% confidence interval for the true population mean height.

MATH 225N Week 6 Assignment: Estimating Sample Size for a Population Proportion

1. Question: Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 90%confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
2. Question: Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 90%confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males?
3. Question: Deborah wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 90%confidence interval which has an error bound of at most 3%. How many people should be polled to create the confidence interval?
4. Question: Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 95%confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
5. Question: Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are over the age of forty?
6. Question: Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 90%confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
7. Question: Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 98%confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males?
8. Question: Virginia wants to estimate the percentage of students who live more than three miles from the school. She wants to create a 95%confidence interval which has an error bound of at most 5%. How many students should be polled to create the confidence interval?
9. Question: Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 95%confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
10. Question: Emma wants to estimate the percentage of people who use public transportation. She surveys 140 individuals and finds that 100 use public transportation. What is the sample proportion for successes, p′?
11. Question: Emma wants to estimate the percentage of people who use public transportation. She surveys 140 individuals and finds that 100 use public transportation. What are the sample proportion for failures, q′?
12. Question: Using the information from above, with p′=0.714, q′=0.286, and n=140, what is the 90% confidence interval for the proportion of the population who use public transportation?
13. Question: The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded “yes” when asked if they use Facebook. What is the value of p′, the estimate proportion of Facebook users in this research study?
14. Question: The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded “yes” when asked if they use Facebook. From the question above, we know that p′=0.71. What is the error bound for proportions (EBP) of a confidence interval with a 99% confidence level?
15. Question: The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded “yes” when asked if they use Facebook.  What is the confidence interval, at the 99% confidence level, for the proportion of the population of internet users that use facebook?
16. Question: Daniel wants to estimate the percentage of people who play sports. He surveys 360 individuals and finds that 75 play sports. What is the sample proportion for successes, p′?  p′=xn=75/360=0.208
17. Question: Daniel wants to estimate the percentage of people who play sports. He surveys 360 individuals and finds that 75 play sports. What is the sample proportion for failures, q′?

Since p′+q′=1, we can solve for q′.

q′=1−p′=1−0.208=0.792

18. Question: Using the information from above, with p′=0.208, q′=0.792, and n=360, what is the 95% confidence interval for the proportion of the population who play sports?
19. Question: The population mean of a set of data is unknown. The sample mean is 29, and the error bound for the mean is 4, at a 68%confidence level. (So, x¯=29 and EBM = 4.) Find and interpret the confidence interval estimate.
20. Question: Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 92%confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who are males?
21. Question: Billy wants to estimate the percentage of students who live more than three miles from the school. He wants to create a 95%confidence interval which has an error bound of at most 3%. How many students should be polled to create the confidence interval?
22. Question: Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 98%confident that the estimated proportion is within 5 percentage points of the true population proportion of customers who click on ads on their smartphones?
23. Question: Jason wants to estimate the percentage of people who sleep for at least seven hours each night. He wants to create a 92%confidence interval which has an error bound of at most 3%. How many people should be polled to create the confidence interval?
24. Question: Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 98%confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who are over the age of forty?
25. Question: Ariana wants to estimate the percentage of people who play a musical instrument. She surveys 380 individuals and finds that 260 play a musical instrument. What is the sample proportion for successes, p′?
26. Question: Ariana wants to estimate the percentage of people who play a musical instrument. She surveys 380 individuals and finds that 260 play a musical instrument. What is the sample proportion for failures, q′?
27. Question: Using the information from above, with p′=0.684, q′=0.316, and n=380, what is the 90% confidence interval for the proportion of the population who play a musical instrument?
28. Question: Suppose a pizza company wants to determine the current percentage of customers who eat pizza more than twice a month. How many customers should the company survey in order to be 98%confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who eat pizza more than twice a month?
29. Question: Brenda wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 95%confidence interval which has an error bound of at most 2%. How many people should be polled to create the confidence interval?

STA 3100: Programming with Data – UF Complete Course Solution

MATH 225N Week 6 Assignment: Understanding Confidence Intervals

1. Question: In a random sample of 350 attendees of a minor league baseball game, 184 said that they bought food from the concession stand. Create a 95% confidence interval for the proportion of fans who bought food from the concession stand. Use Excel to create the confidence interval, rounding to four decimal places.
2. Question: Alison, the owner of a regional chain of pizza stores, is trying to decide whether to add calzones to the menu. She conducts a survey of 700 people in the region and asks whether they would order calzones if they were on the menu. 46 people responded “yes.” Create a 90% confidence interval for the proportion of people in the region who would order calzones if they were on the menu. Round your answer to four decimal places.
3. Question: A company wants to determine a confidence interval for the average CPU time of its teleprocessing transactions. A sample of 70 random transactions in milliseconds is given below. Assume that the transaction times follow a normal distribution with a standard deviation of 600 milliseconds. Use Excel to determine a 98% confidence interval for the average CPU time in milliseconds. Round your answers to the nearest integer and use ascending order.
4. Question: A sample of 22 test-tubes tested for number of times they can be heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct a 99% confidence interval for μ. Round your answers to two decimal places and use increasing order.
5. Question: Suppose that the scores of bowlers in a particular league follow a normal distribution such that the standard deviation of the population is 12. Find the 95% confidence interval of the mean score for all bowlers in this league using the accompanying data set of 40 random scores. Round your answers to two decimal places and use ascending order.
6. Question: Suppose scores on exams in statistics are normally distributed with an unknown population mean. A sample of 26 scores is given below. Use Excel to find a 90% confidence interval for the true mean of statistics exam scores.
7. Question: In a random sample of 2,282 college students, 356 reported getting 8 or more hours of sleep per night. Create a 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night.
8. Question: A restaurant is reviewing customer complaints. In a sample of 227 complaints, 57 complaints were about the slow speed of the service. Create a 95% confidence interval for the proportion of complaints that were about the slow speed of the service.
9. Question: The number of hours worked per year per adult in a state is normally distributed with a standard deviation of 37. A sample of 115 adults is selected at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98% confidence interval for the mean hours worked per year for adults in this state
10. Question: Suppose the weights of tight ends in a football league are normally distributed such that σ2=1,369. A sample of 49 tight ends was randomly selected, and the weights are given below. Use Excel to calculate the 95% confidence interval for the mean weight of all tight ends in this league.
11. Question: In a city, 22 coffee shops are randomly selected, and the temperature of the coffee sold at each shop is noted. Use Excel to find the 90% confidence interval for the population mean temperature. Assume the temperatures are approximately normally distributed.
12. Question: An automobile shop manager timed 27 employees and recorded the time, in minutes, it took them to change a water pump. Assuming normality, use Excel to find the 99% confidence interval for the true mean.
13. Question: A tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a survey ten years ago, a sample of 28 property tax bills is given below. Assume the property tax bills are approximately normally distributed. Use Excel to construct a 95% confidence interval for the population mean property tax bill.
14. Question: A study was conducted to estimate the mean age when people buy their first new car. The ages of purchase for 22 randomly selected people are given below. Assume the ages are approximately normally distributed. Use Excel to determine the 99% confidence interval for the mean.

MATH 225N Week 7 Assignment: Conduct a Hypothesis Test for Proportion; P-Value Approach

1. Question: A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam.
2. Question: A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation.
3. Question: A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors.
4. Question: A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime.
5. Question: A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam. Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

6. Question: A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000. Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

7. Question: A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors.
8. Question: A business owner claims that the proportion of online orders is greater than 75%. To test this claim, the owner checks the next 1,000 orders and determines that 745 orders are online orders.
9. Question: A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000.
10. Question: A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 478 people have Internet access.
11. Question: A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors.
12. Question: A researcher claims that the proportion of people who are right-handed is 70%. To test this claim, a random sample of 600 people is taken and its determined that 397 people are right handed.
13. Question: A college administrator claims that the proportion of students that are female is 62%. To test this claim, a random sample of 300 students is taken and its determined that 211 students are female.
14. Question: A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 61 people are unemployed. Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

15. Question: A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders. Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

17. Question: An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car   Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle. Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
18. Question: A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%.  To test this claim, a survey asked 500 randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service.
19. Question: A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts.
20. Question: A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime.

MATH 225N Week 7 Assignment: Construct Hypothesis Test for Proportions – Excel

1. Question: Steve listens to his favorite streaming music service when he works out. He wonders whether the service’s algorithm does a good job of finding random songs that he will like more often than not. To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them. Use Excel to test whether Steve will like a randomly selected song more often than not, and then draw a conclusion in the context of the problem. Use α=0.05.
2. Question: A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested two types of batteries and claimed that the batteries from Company A outperformed the batteries from Company B. A representative from Company B asked for the exact data from the study. The author of the article told the representative from Company B that in 200 tests, a battery from Company A outperformed a battery from Company B in 108 of the tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name.
3. Question: A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 45 defective ballots. Use Excel to test if the candidate’s claim is true and that more than 5.8% of the ballots were defective. Identify the p-value, rounding to three decimal places.

4. Question: Dmitry suspected that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.
5. Question: Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times. Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%.

1. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
2. Use Excel to test whether the true proportion of odds is different from 50%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

6. Question: Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.

7. Question: Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.

MATH 225N Week 7 Assignment: Hypothesis Test for the Mean – Population Standard Deviation Known

1. Question: .Jamie, a bowler, claims that her bowling score is less than 168 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She bowls 17 games. The mean score of the sample games is 155 points. Jamie knows from experience that the standard deviation for her bowling score is 19 points.

H0: μ≥168; Ha: μ<168

α=0.01 (significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

2. Question: Which of the following results in a null hypothesis p≤0.61and alternative hypothesis p>0.61?
3. Question: Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points.

H0: μ≤140; Ha: μ>140

α=0.05 (significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

4. Question: Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less.
5. Question: Which of the following results in a null hypothesis p=0.3 and alternative hypothesis p≠0.3?
6. Question: Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are not up to the current electric codes.
7. Question: Which graph below corresponds to the following hypothesis test?
   H0:μ≥5.9, Ha:μ<5.9
8. Question: Which graph below corresponds to the following hypothesis test?
   H0:p≤8.1, Ha:p>8.1
9. Question: Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario?
10. Question: Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65%of college students will graduate with debt.
11. Question: Which graph below corresponds to the following hypothesis test?
    H0:μ≤16.9, Ha:μ>16.9
12. Question: Which of the hypothesis tests listed below is a left-tailed test? Select all correct answers.
13. Question: Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65%of college students will graduate with debt.
14. Question: A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative hypothesis, Ha, is that the seat belt can hold less than 5000 pounds of force. What is a Type II error in this scenario?
15. Question: Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario?
16. Question: Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80%of the time. Which of the following gives β, the probability of a Type II error?
17. Question: A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does not think this is accurate, and so he wants to show that the percentage of people who follow a normal maintenance schedule is not equal to 68%. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.H0: p=0.68; Ha: p≠0.68

18. Question: Which of the following results in a null hypothesis p≤0.62 and alternative hypothesis p>0.62?
19. Question: Which of the following results in a null hypothesis μ≥31 and alternative hypothesis μ<31?
20. Question: Which of the following results in a null hypothesis μ≤7 and alternative hypothesis μ>7?
21. Question: Which of the following answers give valid null and alternative hypotheses for a hypothesis test?
22. Question: A mattress store advertises that their beds last at least 5 years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test….. If μdenotes the average time, in years, that the mattresses last, what are the null and alternative hypotheses in this situation?
23. Question: Which of the following results in a null hypothesis p≥0.44 and alternative hypothesis p<0.44?
24. Question: Which of the following results in a null hypothesis p≥0.44 and alternative hypothesis p<0.44?
25. Question: Suppose a pitcher claims that her pitch speed is not equal to 45 miles per hour, on average. Several of her teammates do not believe her, so the pitcher decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 21 pitches. The mean speed of the sample pitches is 46 miles per hour. The pitcher knows from experience that the standard deviation for her pitch speed is 6 miles per hour.

H0: μ=45; Ha: μ≠45

α=0.01 (significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

26. Question: Suppose a bowler claims that her bowling score is less than 116 points, on average. Several of her teammates do not believe her, so the bowler decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 25 games. The mean score of the sample games is 103 points. The bowler knows from experience that the standard deviation for her bowling score is 19 points.

H0: μ≥116; Ha: μ<116

α=0.05 (significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

27. Question: Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 What is the Type II error in this scenario?
28. Question: Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800 pounds and less. What is the Type I error in this scenario?
29. Question: Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80%of the time. What is the Type I error in this scenario?
30. Question: A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, H0, is that the rack can hold at least 100 pounds of force. The alternative hypothesis, Ha, is that the rack can hold less than 100 pounds of force. What is a Type I error in this scenario?
31. Question: What is β, the probability of a Type II error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are not up to the current electric codes. the probability that the electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, more than 10% of the homes are not up to the current electric codes
32. Question: Determine the Type I error if the null hypothesis, H0, is: Carmin believes that her chemistry exam will only cover material from chapters four and five.

MATH 225N Week 8 Assignment: Coefficient of Determination

1. Question: A medical experiment on tumor growth gives the following data table……… The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 3922.8 and the sum of squares of regression (SSR) was 3789.0. Calculate R2, rounded to three decimal places.
2. Question: A scientific study on mesothelioma caused by asbestos gives the following data table……. Using technology, it was determined that the total sum of squares (SST) was 1421.2 and the sum of squares due to error (SSE) was 903.51. Calculate R2 and determine its meaning. Round your answer to four decimal places.
3. Question: A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened……. A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 278.0 and the sum of squares of regression (SSR) was 274.3. Use these values to calculate the coefficient of determination. Round your answer to three decimal places.
4. Question: A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened

Days (since opening) # of dump truck loads

6 54

9 78

14 92

17 86

21 121

A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 2349 and the sum of squares of error (SSE) was 329. Use these values to calculate the coefficient of determination. Round your answer to three decimal places.

MATH 225N Week 8 Assignment: Correlation and Causation

Question: True or False: The more samples taken in a scientific study, the longer the amount of time it will take to complete the research on the samples. Although there are other factors that affect study time, such as experience and equipment, increasing the number of samples will cause an increase in research time.

Question: Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.)

Question: Which of the following situations could have a regression line with a negative y-intercept? Select all that apply:

Question: Which of the following data sets or plots could have a regression line with a negative slope? Select all that apply.

Question: Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.

Question: An experiment finds that runners with the longest legs complete a mile run in less time.Identify the relation between leg length and time of a mile run.Leg length and time of a mile run are negatively correlated. A longer leg length is associated with a lower time of a mile run, which implies a negative relationship. There would need to be more evidence to prove causation.

Question: Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply.

Question: Which of the following situations could produce data sets or plots would have a regression line with a negative slope? Select all that apply.

MATH 225N Week 8 Assignment: Linear Regression Equations

1. Question: Annie owns a tutoring service. For each tutoring session, she charges $75 plus $35 per hour of work. A linear equation that expresses the total amount of money Annie earns per tutoring session is y=75+35x. What are the independent and dependent variables? What is the y-intercept and the slope?
2. Question: George is an avid plant lover and is concerned about the lack of daffodils that grow in his backyard. He finds the growth of the daffodils, G, is dependent on the percent of aluminum measured in the soil, x, and can be modeled by the function …. G(x)=16−4x….. Draw the graph of the growth function by plotting its G-intercept and another point.

So, (7,−12)is another point on the graph of G(x).

3. Question: What percent of aluminum in the soil must there be for the daffodils to grow only by 5 centimeters? …. Round your final answer to the nearest whole number….. 03 percent$3\ \text{percent}$3 percent​
4. Question: The scatter plot below shows data relating competitive chess players’ ratings and their IQ. Which of the following patterns does the scatter plot show?
5. Question: The scatter plot below shows data relating total income and the number of children a family has. Which of the following patterns does the scatter plot show?
6. Question: The number of quetions marked incorrect on a statistics midterm, y, is dependent on the pages of notes a student wrote over the semester, x, and can be modeled by the function y(x)=30−3.5x. Draw the graph of the function by plotting its y-intercept and another point.

7. Question: How many pages of notes did a student take if they had 12 problems marked incorrect on the statistics midterm?
8. Question: A shoe designer explored the relationship between the percent of defects and the percent of new machines at various production facilities throughout the state. The designer collects information from 6of their facilities, shown in the table below.
9. Question: Using the linear relationship graphed above, estimate the percent of new machines if there is12%defects in the shoes at various production facilities.
10. Question: A department store manager explored the relationship between the percent of customers that wait more than 7 minutes in line and the percent of customers that purchase last minute items at checkout. The manager collects information from 5 checkout lines, shown in the table below. Use the graph below to plot the points and develop a linear relationship between the percent of waiting customers and the percent of last minute purchases.

11. Question: Using the linear relationship graphed above, estimate the percent of last minute purchases if 40%of the customers wait more than 7 minutes in line.
12. Question: A government agency explored the relationship between the percent of public colleges and the percent of freshmen that stay home during college. The researcher collects information from 5 states, shown in the table below. Use the graph below to plot the points and develop a linear relationship between the percent of public colleges and the percent of freshmen that stay home during college.

18. Question: Using the linear relationship graphed above, estimate the percent of freshmen that stay in-state if there are 45%public colleges
19. Question: Describe the relationship between the independent variable, x, and the dependent variable, y, if the correlation is positive.
20. Question: Which of the following patterns does the scatter plot show?
21. Question: Horace keeps track of the amount of time he studies and the score he gets on his quiz. The data are shown in the table below. Which of the scatter plots below accurately records the data?
22. Question: An owner of multiple online clothing stores explored the relationship between the percent of on-call service representatives and the percent of purchases over $75 at the same stores. The owner collects information from 6 of their online stores, shown in the table below. Use the graph below to plot the points and develop a linear relationship between the percent of on-call service representatives and the percent of purchases over $75.
23. Question: Using the linear relationship graphed above, estimate the percent of over $75purchases if there are 40% on-call service representatives.

MATH 225N Week 8 Assignment: Performing Linear Regressions with Technology

1. Question: An economist is studying the link between the total value of a country’s exports and that country’s gross domestic product, or GDP. The economist recorded the GDP and Export value (in millions of $’s) for 30 nations for the same fiscal year. This sample data is provided below.
2. Question: An economist is trying to understand whether there is a strong link between CEO pay ratio and corporate revenue. The economist gathered data including the CEO pay ratio and corporate revenue for 30 companies for a particular year. The pay ratio data is reported by the companies and represents the ratio of CEO compensation to the median employee salary. The data are provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
3. Question: The table below shows data on annual expenditure, x (in dollars), on recreation and annual income, y (in dollars), of 20 families. Use Excel to find the best fit linear regression equation. Round the slope and intercept to the nearest integer.
4. Question: The table below gives the average weight (in kilograms) of certain people ages 1–20. Use Excel to find the best fit linear regression equation, where age is the explanatory variable. Round the slope and intercept to two decimal places.
5. Question: In the following table, the age (in years) of the respondents is given as the x value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places.
6. Question: The heights (in inches) and weights (in pounds) of 25 baseball players are given below. Use Excel to find the best fit linear regression equation, where height is the explanatory variable. Round the slope and intercept to two decimal places
7. Question: A market researcher looked at the quarterly sales revenue for a large e-commerce store and for a large brick-and-mortar retailer over the same period. The researcher recorded the revenue in millions of dollars for 30 quarters. The data are provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
8. Question: An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the absolute magnitude or MV and stellar mass or M for 30 stars. The absolute magnitude of a star is the intensity of light that would be observed from the star at a distance of 10 parsecs from the star. This is measured in terms of a particular band of the light spectrum, indicated by the subscript letter, which in this case is V for the visual light spectrum. The scale is logarithmic and an MV that is 1 less than another comes from a star that is 10 times more luminous than the other. The stellar mass of a star is how many times the sun’s mass it has. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.

MATH 225N Week 8 Assignment: Predictions Using Linear Regression

1. Question: The table shows data collected on the relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is yˆ=0.16x+36.2. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

Studying (Minutes) 50, 70,90,110 Reading (Minutes) 44,48,50,54

According to the line of best fit, what would be the predicted number of minutes spent reading for someone who spent 67 minutes studying? Round your answer to two decimal places.

2. Question: The table shows data collected on the relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is yˆ=0.16x+36.2.

Studying (Minutes) 507090110 Reading (Minutes) 44485054

According to the line of best fit, the predicted number of minutes spent reading for someone who spent 67 minutes studying is 46.92.

Is it reasonable to use this line of best fit to make the above prediction?

3. Question: Michelle is studying the relationship between the hours worked (per week) and time spent reading (per day) and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.79x+98.8. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

Hours Worked (per week) 30405060 Minutes Reading (per day) 75685852

According to the line of best fit, what would be the predicted number of minutes spent reading for a person who works 27 hours (per week)? Round your answer to two decimal places, as needed.

4. Question: Michelle is studying the relationship between the hours worked (per week) and time spent reading (per day) and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.79x+98.8.
5. Hours Worked (per week) 30405060Minutes Reading (per day) 75685852

According to the line of best fit, the predicted number of minutes spent reading for a person who works 27 hours (per week) is 77.47.

Is it reasonable to use this line of best fit to make the above prediction?

MATH 225N Week 8 Assignment: Understand the Difference Between Correlation and Causation

Question: How to Determine the Significance of the Correlation Coefficient

Given the R-value and the size of the sample, n,

1. Find the degrees of freedom (df). df=n−2, where n is the sample size.

2. Find the critical values in the table (using the degrees of freedom).
3. Compare r to the appropriate critical value in the table to make a conclusion.
   – If r is not between the positive and negative critical values, then the correlation coefficient is significant, meaning we can trust its validity and use the line for prediction.
   – If r is between the positive and negative critical values, then the correlation coefficient is not significant, and we should not use the line for prediction.
4. Question:Suppose you computed r=0.801 using n=10 data points. Using the critical values table below, determine if the value of r is significant or not.

MATH 225N Week 8 Interpret the Slope and Y-Intercept of the Least Squares Regression Line

1. Question:  A scientific study on gerbil population growth results in the data below. The least squares regression line modeling this data is given by yˆ=13.3+5.567x. What is the intercept of the regression line? Round your answer to one decimal place.
2. Question:  True or False: The more mangoes you eat, the more rashes you get.
3. Question:  Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better). Identify what can be concluded based on this information.
4. Question:  True or false: The larger the truck, the larger the load it can fit.
5. Question:  An observational study shows a moderate negative correlation between the price of the car a person owns and the happiness of that person. Answer the following question based only on this information. True or false: It can be concluded that in general, owning a more expensive car makes people less happy.
6. Question:  True or False: The larger the number of cavities, the older the person.
7. Question:  True or false: Increases in height cause increases in shoe size.
8. Question:  Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information. True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are.