# STAT 200 Lesson 11: Associations between Categorical Variables

Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. For all tests use an alpha level of .05 unless otherwise specified.

1. For each scenario, which statistical procedure is most appropriate (one sample mean, one sample proportion, two independent proportions, two independent means, two paired/dependent means, one-way ANOVA, chi-square test of independence)? Explain why. (24 points)

A. The honors college at one large university wants to know if their accepted students have an average IQ that is higher than the known national average of 100.

B. A team of World Campus advisors wants to know if there is a relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.

C. A group of political science students wants to know if there is a relationship between whether someone is registered to vote or not and their level of education. They take a sample of 200 people and ask if they are registered to vote (yes or no) and ask for their level of education (no college degree, college degree).

D. A preschool teacher wants to know if four-year-old boys and girls differ in terms of whether or not they like superheroes. He takes a representative sample of 30 preschool students, records each child’s gender, and asks if they like superheroes (yes/no).

E. Food scientists want to know if there is a relationship between whether or not a child likes licorice and whether or not the child’s mother likes licorice. They take a sample of 50 child-mother pairs and ask each individual if they like licorice (yes/no).

F. A team of sleep scientists wants to know if there is a relationship between biological sex and whether or not an individual has sleep apnea. They take a sample of 500 individuals and record their biological sex (male/female) and if they have sleep apnea (yes/no).

G. An admissions counselor at a technical college wants to know if there is a relationship between gender (man/woman) and students’ intended major area (computer science, automotive mechanics, culinary arts, cosmetology).

H. A group of psychology students wants to compare the anxiety levels of test takers who are given a dog, cat, or teddy bear to pet. They take a sample of 120 introductory psychology students. Participants are randomly assigned to one of the three treatment conditions (dog, cat, teddy bear). After the testing sessions the experimenters administer an anxiety survey to each participant. Scores on the anxiety scale are quantitative.

2. According to http://espn.go.com/college-football/team/fpi/_/id/213/penn-state-nittany-lions (as of November 3, 2015) the probability that Penn State will win the football game against Michigan is 39.4%. The probability that Penn State will win the football game against Michigan State is 23.0%. (16 points)

A. What are the odds that Penn State will beat Michigan?

B. What are the odds that Penn State will beat Michigan State?

C. What is the odds ratio for Penn State beating Michigan compared to beating Michigan State?

D. How would you explain the odds ratio that you calculated in part C to a friend with no knowledge of statistics?

3. Use the file SP16STUDENTDATA.MTW to answer the following questions. (30 points)

A. Construct a contingency table of biological sex and preferred winter sport.

B. What proportion of females prefer figure skating.

C. What proportion of males prefer figure skating?

D. What is the “relative risk” of preferring figure skating for females compared to males?

E. How would you interpret the value that you computed in part D for a friend with no knowledge of statistics?

F. Conduct a chi-square test of independence to determine if there is evidence of a relationship between biological sex and preferred winter sport in the population. Assume that this sample is representative of the population of all World Campus students. Use the five-step hypothesis testing procedure labeling each of your steps.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

4. Use the file SP16STUDENTDATA.MTW to answer the following questions. Assume that this sample is representative of the population of all World Campus students. A team of researchers wants to know if there is a relationship between biological sex and dieting in the population of World Campus students. (30 points)

A. Conduct a chi-square test of independence to determine if there is a statistically significant relationship between biological sex and dieting in the population. Use the five-step hypothesis testing procedure labeling each of your steps.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

B. What proportion of females in this sample were dieting?

C. What proportion of males in this sample were dieting?

D. Compute a relative risk ratio comparing females to males in terms of dieting.

E. Pretend that you are writing a report for the team that is conducting this research. Using your results from parts A through D, write a paragraph that explains your findings. Discuss both your inferential findings from part A and your descriptive findings from parts B, C, and D. It is expected that you will need 60-100 words to do this well.

1. For each scenario, which statistical procedure is most appropriate (one sample mean, one sample proportion, two independent proportions, two independent means, two paired/dependent means, one-way ANOVA, chi-square test of independence)? Explain why. (24 points)

A. The honors college at one large university wants to know if their accepted students have an average IQ that is higher than the known national average of 100.

B. A team of World Campus advisors wants to know if there is a relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.

C. A group of political science students wants to know if there is a relationship between whether someone is registered to vote or not and their level of education. They take a sample of 200 people and ask if they are registered to vote (yes or no) and ask for their level of education (no college degree, college degree).

D. A preschool teacher wants to know if four-year-old boys and girls differ in terms of whether or not they like superheroes. He takes a representative sample of 30 preschool students, records each child’s gender, and asks if they like superheroes (yes/no).

E. Food scientists want to know if there is a relationship between whether or not a child likes licorice and whether or not the child’s mother likes licorice. They take a sample of 50 child-mother pairs and ask each individual if they like licorice (yes/no).

F. A team of sleep scientists wants to know if there is a relationship between biological sex and whether or not an individual has sleep apnea. They take a sample of 500 individuals and record their biological sex (male/female) and if they have sleep apnea (yes/no).

G. An admissions counselor at a technical college wants to know if there is a relationship between gender (man/woman) and students’ intended major area (computer science, automotive mechanics, culinary arts, cosmetology).

H. A group of psychology students wants to compare the anxiety levels of test takers who are given a dog, cat, or teddy bear to pet. They take a sample of 120 introductory psychology students. Participants are randomly assigned to one of the three treatment conditions (dog, cat, teddy bear). After the testing sessions the experimenters administer an anxiety survey to each participant. Scores on the anxiety scale are quantitative.

2. According to http://espn.go.com/college-football/team/fpi/_/id/213/penn-state-nittany-lions (as of November 3, 2015) the probability that Penn State will win the football game against Michigan is 39.4%. The probability that Penn State will win the football game against Michigan State is 23.0%. (16 points)

A. What are the odds that Penn State will beat Michigan?

B. What are the odds that Penn State will beat Michigan State?

C. What is the odds ratio for Penn State beating Michigan compared to beating Michigan State?

D. How would you explain the odds ratio that you calculated in part C to a friend with no knowledge of statistics?

3. Use the file SP16STUDENTDATA.MTW to answer the following questions. (30 points)

A. Construct a contingency table of biological sex and preferred winter sport.

B. What proportion of females prefer figure skating.

C. What proportion of males prefer figure skating?

D. What is the “relative risk” of preferring figure skating for females compared to males?

E. How would you interpret the value that you computed in part D for a friend with no knowledge of statistics?

F. Conduct a chi-square test of independence to determine if there is evidence of a relationship between biological sex and preferred winter sport in the population. Assume that this sample is representative of the population of all World Campus students. Use the five-step hypothesis testing procedure labeling each of your steps.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

4. Use the file SP16STUDENTDATA.MTW to answer the following questions. Assume that this sample is representative of the population of all World Campus students. A team of researchers wants to know if there is a relationship between biological sex and dieting in the population of World Campus students. (30 points)

A. Conduct a chi-square test of independence to determine if there is a statistically significant relationship between biological sex and dieting in the population. Use the five-step hypothesis testing procedure labeling each of your steps.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

B. What proportion of females in this sample were dieting?

C. What proportion of males in this sample were dieting?

D. Compute a relative risk ratio comparing females to males in terms of dieting.

E. Pretend that you are writing a report for the team that is conducting this research. Using your results from parts A through D, write a paragraph that explains your findings. Discuss both your inferential findings from part A and your descriptive findings from parts B, C, and D. It is expected that you will need 60-100 words to do this well.

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