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 178 186 167 181 196 168 Height (cm) of Main Opponent 170 179 180 171 192 180 a. 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. In this example, d 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 Hd = 0 cm H: Hd > 0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)