A popular theory is that presidential candidates have an advantage if they are taller than their main opponents, Listed are haights (in contimotors) of randomly selected presidents along with the heights of their main opponents, Complete parts (a) and (b) bolow. Height (cm] of President 179 184 179 177 192 177 8 Height (cm] of Main Opponent 174 175 187 176 197 185 a. Use the sample data with a 0.06 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, jug 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? Ho: Ma am (Type intogors or decimals, Do not round ) 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)? Use this information to draw an appropriate conclusion about the claim that presidents are generally taller than their main opponents