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A popular theory is that presidential candidates have an advantage if they are taller than their...

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

187

181

184

191

179

Height (cm) of Main Opponent

182

173

172

173

184

176

  1. 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.

B. Identify the test statistic.

C. Identify the​ P-value.

D. What is the conclusion based on the hypothesis​ test?

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

Since the confidence interval contains ____________     ____________the null hypothesis.

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