Heights of winners and runners-up
Assume that the paired sample data
are simple random samples and that the differences have a distribution that is
approximately normal.
Heights of Winners and Runners-up
Listed below are the heights (in
inches) of candidates who won presidential elections and the heights 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 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; – 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.
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