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 194 175 167 180 183 168 Height (cm) of Main Opponent 185 173 174 182 196 174 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? Ho Hd = 0 cm H₁ Hd 0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.3: Measures Of Spread
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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
194 175 167 180 183 168
Height (cm) of Main Opponent 185 173 174 182 196 174
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?
Ho Hd = 0 cm
H₁ Hd
0 cm
(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 194 175 167 180 183 168 Height (cm) of Main Opponent 185 173 174 182 196 174 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? Ho Hd = 0 cm H₁ 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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