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 Height (cm) of Main Opponent 183 175 178 181 176 181 188 181 194 197 182 170

. Use the sample data with a

0.05

significance level to test the claim that for the population of heights for presidents and their mainopponents, the differences have a mean greater than 0 cm.In thisexample,

d

is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as thepresident's height minus their mainopponent's height. What are the null and alternative hypotheses for the hypothesistest?