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	191	182	179	183	200	174
Height (cm)of Main Opponent	183	185	178	181	184	176

a. Use the sample data with a 0.01
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?

Identify the test statistic.

t=

Identify the​ P-value.

​P-value =

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<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