Question: Suppose your friend in problem arranged for three more cars, labeled the 9 cars A-I, changed a to .05, and conducted the "quiet" test. The results are shown in the accompanying table. Perform a Mann-Whitney U test and write a conclusion.
Problem: A friend of yours is trying to convince a mutual friend that the ride is quieter in an automobile built by [Toyota or Honda (you choose)] than one built by [Honda or Toyota (no choice this time; you had just 1 degree of freedom-once the first choice was made, the second was determined)]. This friend has arranged to borrow six fairly new cars-three made by each company-and to drive your blindfolded mutual friend around in the six cars (labeled A-F) until a stable ranking for quietness is achieved. So convinced is your friend that he insists on adopting a = .01, "so that only the recalcitrant will not be convinced.
As the statistician in the group, you decide that a Mann-Whitney U test is appropriate. However, being the type who thinks through the statistics before gathering experimental data, you look at the appropriate subtable in Table H and find that the experiment, as designed, is doomed to retain the null hypothesis. Write an explanation of why the experiment must be redesigned.