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 185 173 178 178 197 169 O Height (cm) of Main Opponent 179 186 180 182 179 187 a. Use the sample data with a 0.01 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, ji4 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? Hpipg = 0 cm Hitpg > 0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t= -0.40 (Round to two decimal places as needed.) Identify the P-value. P-value=| |(Round to three decimal places as needed.)