Heights of Presidential Winners and Losers The accompanying table shows the heights of presidents matched with the heights of the candidates they beat. All heights are in inches, and only the second-place candidates are included. Use a 0.05 significance level for the following.

a. Use the linear correlation coefficient r to test for a significant linear correlation between the heights of the winners and the heights of the candidates they beat. (See Section 9-2.) Does there appear to be a correlation?

b. Use the rank correlation coefficient rs to test for a significant linear correlation between the heights of the winners and the heights of the candidates they beat. (See Section 12-6.) Does there appear to be a correlation?

c. Use the sign test to test the claim that there is a difference between the heights of the winning candidates and the heights of the losing candidates.

d. Use the Wilcoxon signed-ranks test to test the claim that there is a difference between the heights of the winning candidates and the heights of the corresponding losing candidates.

e. Use the parametric t test (see Section 8-4) to test the claim that there is a difference between the heights of the winning candidates and the heights of the corresponding losing candidates.

f. What do the preceding results suggest about the heights of winning presidential candidates and the heights of the corresponding losing presidential candidates?

Winner 76 66 70 70 74 71.5 73 74 Runner-up 64 71 72 72 68 71 69.5 74