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

190

182

180

181

187

172

Height (cm) of Main Opponent 

180

187

176

182

186

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, Ha 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?

Họ: Ha

Hy: Ha

(Type integers or decimals. Do not round.)

Identify the test statistic.

+= (Round to two decimal places as needed.)

Identify the P-value.

P-value = (Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

Since the P-value is opponents.

the significance level,

the null hypothesis. There

sufficient evidence to support the claim that presidents tend to be taller than their

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)?