14. Heights of Winners and Runners-Up Listed below are the heights of candidates who won presidential elections and the heights of the candidates with the next highest number of popular votes. The data are in chronological order, so the corresponding heights from the two lists are matched. For candidates who won more than once, only the heights from the first election are included, and no elections before 1900 are included.

a. A well-known theory is that winning candidates tend to be taller than the corresponding losing candidates. Use a 0.05 significance level to test that theory. Does height appear to be an important factor in winning the presidency?

b. If you plan to test the claim in part

(a) by using a confidence interval, what confidence level should be used? Construct a confidence interval using that confidence level, then interpret the result.

Won Presidency Runner-Up 71 74.5 74 73 69.5 71.5 75 72 73 74 68 69.5 72 71 72 71.5 70.5 69 74 70 71 72 70 67 70 68 71 72 70 72 72 72 492 Chapter 9 Inferences from Two Samples