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)ofPresident

177

174

179

177

190

166

Height(cm)ofMainOpponent

164

171

169

182

196

185

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 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?