Question

hw 9 # 16

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights​ (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts​ (a) and​ (b) below.

Height left parenthesis cm right parenthesis of PresidentHeight (cm) of President	186	169	166	177	183	177
Height left parenthesis cm right parenthesis of Main OpponentHeight (cm) of Main Opponent	162	185	175	183	187	177

a. Use the sample data with a

0.05 significance level to test the claim that for the population of heights for presidents and their main​ opponents, the differences have a mean greater than 0 cm.In this​ example,

mu Subscript dμd

is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ president's height minus their main​ opponent's height.

What are the null and alternative hypotheses for the hypothesis​ test?

b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Answer 1

Conclusion :

There is not sufficient evidence to support the claim that the mean heights of presidents are larger than the mean heights of their opponents.