Question: Heights of winners and runners up: Listed below are the heights of candidates who won presidential elections and the heights of candidates with the next highest number of votes. The data are in chronological order, so the corresponding heights 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 corresponding losing candidates. Use a 0.05 significance level to test that theory. Does height appear top 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, and then interpret the result.

Won Presidency Lost

71 73
74.5 74
74 68
73 69.5
69.5 72
71.5 71
75 72
72 71.5
70.5 70
69 68
74 71
70 72
71 70
72 72
70 72
67 72