Question

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 (cm) of President	Height (cm) of Main Opponent
193	177
180	174
183	164
180	181
185	197
173	186

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,μd 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?

t = ??? ( round to two decimal places

P-value = ???? (round to three decimals)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is ________ the significance​ level,______ the null hypothesis. There ________ sufficient evidence to support the claim that presidents tend to be taller than their opponents.

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)?

The confidence interval is _____ cm < −5.3 μd < ____ cm

What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Since the confidence interval contains _______ ________   the null hypothesis.

Answer 1