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.
A. 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.
B. The marketing team for a nation-wide travel agency wants to know if adults with high school, associates, bachelors, masters, and doctoral degrees differ in terms of the amount of money they spend on travel annually.
C. A professor wants to know if students' knowledge of statistics increases on average from the beginning to the end of an introductory statistics course. The professor gives students the same exam during the first week of class and last week of class.
D. A biology student wants to know if there is a relationship between biological sex (male/female) and eye color (blue, brown, green, other).
E. An educational researcher wants to compare the effectiveness of three different instructional methods. Students are randomly assigned to receive one of the three instructional methods. After four weeks of instruction their knowledge is measured using an exam worth up to 100 points.
2. Open the dataset SUMMER16STDATA.MTW. Assume this sample is representative of the population of all World Campus STAT 200 students. We want to conduct a one-way ANOVA to see if students who prefer swimming, running, and volleyball differ in terms of the number of hours they exercise weekly.
A. Why is a one-way ANOVA an appropriate statistical procedure for this scenario?
B. Has the assumption of equal variances been met? Explain how you checked for this.
C. Use the five-step hypothesis testing procedure to determine if there is evidence that the mean number of hours spent exercising weekly is different for students who prefer swimming, running, and volleyball. Use the five-step hypothesis testing procedure.
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D. Make all possible pairwise comparisons using Tukey's Honestly Significant Differences Test. Which pairs are different?
E. How would you explain these results to a friend who has no knowledge of statistics?
3. Open the dataset SUMMER16STDATA.MTW. Assume this sample is representative of the population of all World Campus STAT 200 students. We want to know if there is a relationship between the flavor of cupcake that individuals prefer and the flavor of ice cream they prefer. (35 points)
A. Construct a contingency table to display these variables.
B. What proportion of people who prefer vanilla cupcakes also prefer vanillaice cream?
C. If preferred flavor of cupcake and preferred flavor of ice cream are independent of one another, how many people in this sample would you have expected to prefer vanillacupcakes and vanillaice cream?
D. Conduct a chi-square test of independence to determine if there is a statistically significant relationship between preferred cupcake flavor and preferred ice cream flavor in the population. Use the five-step hypothesis testing procedure.
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4. According to https://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%.
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?