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 180 181 171 176 197 166   Height (cm) of Main Opponent 168 184 174 170 197 186   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 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?   H0​: μd equals=   00 cm H1​: μd greater than>   00 cm ​(Type integers or decimals. Do not​ round.) Identify the test statistic.   t=nothing ​(Round to two 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
181
171
176
197
166
 
Height (cm) of Main Opponent
168
184
174
170
197
186
 
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 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?
 
H0​:
μd
equals=
 
00
cm
H1​:
μd
greater than>
 
00
cm
​(Type integers or decimals. Do not​ round.)
Identify the test statistic.
 
t=nothing
​(Round to two decimal places as​ needed.)
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