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 180 184 182 178 187 181   Height (cm) of Main Opponent 165 181 182 168 188 183   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, μd 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?   ​P-value=nothing ​(Round to three decimal places as​ needed.)

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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
180
184
182
178
187
181
 
Height (cm) of Main Opponent
165
181
182
168
188
183
 
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,
μd
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?
 
​P-value=nothing
​(Round to three decimal places as​ needed.)
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