A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (cm) of presidents along with the heights of their main opponents (from Data Set 15

"Presidents").
a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0 cm.
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)?

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BMI SEPT 22.02 19.70 24.09 26.97 21.51 252 WT SEPT WT APRIL 59 86 69 BMI APRIL 18.14 17.44 22.43 25.57 20.10 72 74 93 68 64 173 178 183 193 178 175 185 188 Height (cm) of President Height (cm) of Main Opponent 171 175 180 173