Question

Refer to the data set of 20 randomly selected presidents given below. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a 95% confidence interval estimate of the population percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not? Click the icon to view the table of heights. Construct a 95% confidence interval estimate of the percentage of presidents who were taller than their opponents %<p [% (Round to one decimal place as needed.) If greater height was an advantage, then taller candidates should have won 50% of the elections. In this case, greater height to be an advantage for presidential candidates because the confidence interval include 50% President and Opponent Height - X PRESIDENT Polk McKinley Cleveland Harrison Johnson J. Q. Adams Carter GH. W. Bush G. W. Bush Eisenhower Harding Truman Taft Nixon Wilson Coolidge Harrison Jackson Lincoln Reagan HEIGHT 173 170 180 173 192 171 177 188 183 179 183 175 182 182 180 178 168 185 193 185 HEIGHT OPP 185 178 180 168 180 191 183 173 185 178 178 173 178 180 182 180 180 171 188 177 Print Done

Answer 1

Number were taller then their X = 11 of president who opponents n=20 0.55 95% confidence interval estimate of the percentage of president who taller than their opponent is were ê - Zah P (1-ê 2 < p e Ŕ + 22 ľ (1-P 0.55 1.96 0.55 X 0.45 20 C 0.55 71.96 0.55x0.45 0.55 2 p s 0.55 +0.22 0.22 0.33 0.3 0.77 2p 0.8 If won of the the greater height advantage, then taller candidates should have more than 50% elections In this case, greater height does not appears to be advantage for for presidential candidates, because the confidence interval includes 50 %