Question: Let's consider whether U.S. college football teams are more likely or less likely to be mismatched in the upper National Collegiate Athletic Association (NCAA) divisions. The highest division, Division I (technically, Division I-A), includes such vaunted teams as the Ohio State University Buckeyes and the University of Michigan Wolverines. During week 11 of the fall 2006 college football season, Ohio State beat Illinois by 7 points and Michigan beat Ball State by 8. Overall, however, the 53 Division I games had a mean spread (winning score minus losing score) of 16.189 that week, with a standard deviation of 12.128. We took a sample of four games that were played that week in the next-highest league, Division I-AA, to see if the spread was different; one of the many leagues within Division I-AA, the Patriot League, played four games that weekend.
a. List the independent variable and dependent variable in this example.
b. Did we use random selection? Explain.
c. Identify the populations of interest in this example.
d. State the comparison distribution.
e. Check the assumptions for this test.