STAT 200 Lesson 11 Associations between Categorical Variables complete solutions correct answers key

STAT 200 Lesson 11 Associations between Categorical Variables complete solutions correct answers key  

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. 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).

B. 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).

C. 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).

D. 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: