Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal
Listed below are the heights of candidates who won presidential elections and the heights (in inches) of the candidates who were runners up. The data are in chronological order, so the corresponding heights from the two lists are matched. For candidates who wonmore than once, only the heights from the first election are included, and no elections before 1900 are included.
Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal.
Won Presidency: 71, 74.5, 74, 73, 69.5, 71.5, 75, 72, 70.5, 69, 74, 70, 71, 72, 70, 67
Runner-Up: 73, 74, 68, 69.5, 72, 71, 72, 71.5, 70, 68, 71, 72, 70, 72, 72, 72
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.