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 162 188 175 168 189 176 187 180 172 177 196 172 O 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 mean greater than 0 cm, In this example, H, 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? Ho: Hd = 0 cm H: Hd > 0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)

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b) What is the P Value?

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 162 188
187 180 172 177 196
172
175 168 189 176
.....
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, µ, 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?
Ho: Hd
0 cm
0 cm
H1: Hd
(Type integers or decimals. Do not round.)
>
Identify the test statistic.
t=
(Round to two decimal places as needed.)
Transcribed Image Text: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 162 188 187 180 172 177 196 172 175 168 189 176 ..... 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, µ, 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? Ho: Hd 0 cm 0 cm H1: Hd (Type integers or decimals. Do not round.) > Identify the test statistic. t= (Round to two decimal places as needed.)
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