Refer to the Chance (Summer 2009) investigation into "topsy-turvy" college football seasons, Exercise. Recall that statisticians created a formula for determining a weekly "topsy-turvy" (TT) index, designed to measure the degree to which the top 25 ranked teams changed from the previous week. The greater the TT index, the greater the changes in the ranked teams. The statisticians calculated the TT index each week of the 15-week college football season for 6 recent seasons. In order to determine whether any of the 15 weeks in a season tend to be more or less topsy-turvy than others, the statisticians conducted an analysis of variance on the data using a randomized block design, where the 15 weeks were considered the treatments and the 6 seasons were the blocks.
a. Suppose the data (TT index values) are not normally distributed. How would this impact the ANOVA con ducted in Exercise 10.67? Explain.
b. Give the null and alternative hypotheses for the Friedman test applied to the data.
c. Find the rejection region for the Friedman test using α = .01.
d. Explain how you would calculate the Friedman test statistic for this data set.
e. Give a p -value of the test that would lead you to conclude that no one week is any more "topsy-turvy" than any other week.