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

6. A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (cm) of presidents (see data set 15 Presidents) Height (cm) of the President 188 183 188 188 185 177 Height of Main Opponent 175 185 188 173 177 183

a. Use the sample data with a 0.10 significance level to test the claim that for the population of heights of presidents and their main opponents, the differences have mean great than 0 cm.

b. Construct a 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)?