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?

Answer 1

x=no. of presidents who were taller than their opponents=13

$n=20,~\hat{p}=13/20= 0.65.~Now,~n\hat{p}=13>5,~n(1-\hat{p})=7>5,~so~we\\ use~normal~approximation~to~find~confidence~interval~for~true~proportion,~p.\\ 95\%~C.I.~for~p~is\\ \left(\hat{p}-Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},~\hat{p}+Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right )=( 0.4,~0.9)$