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. Overall, the 53 Football Bowl Subdivision (FBS) games (the highest division) had a mean spread (winning score minus losing score) of 16.189 in a particular week, with a standard deviation of 12.128. We took a sample of 4 games that were played that week in the next-highest league, the Football Championship Subdivision (FCS), to see if the mean spread was different; one of the many leagues within the FCS, the Patriot League, played 4 games that weekend. 

a. List the independent variable and the 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.