content area top Part 1 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 left parenthesis cm right parenthesis of President 188 183 182 178 183 169 Height left parenthesis cm right parenthesis of Main Opponent 178 172 167 173 180 181 Question content area bottom Part 1 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, mu Subscript 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? Upper H 0: mu Subscript d equals 0 cm Upper H 1: mu Subscript d greater than 0 cm (Type integers or decimals. Do not round.) Part 2 Identify the test statistic. tequals 1.37 (Round to two decimal places as needed.) Part 3 Identify the P-value. P-valueequals 0.114 (Round to three decimal places as needed.) Part 4 The confidence interval is enter your response here cmless thanmu Subscript dless than enter your response here cm