nts (in centimeters) of randomly selected presidents along with the heights of their main opponents. C elow. Height (cm) of President Height (cm) of Main Opponent 175 177 170 173 184 170 193 173 168 184 196 173 se the sample data with a 0.05 significance level to test the claim that for the population of heights fo n opponents, the differences have a mean greater than 0 cm. is example, ua is the mean value of the differences d for the population of all pairs of data, where ea ant's height minus tbeir main opponent's height WVhat are the null and alternativ

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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
Height (cm) of Main Opponent 175 177 170 173 184
193 173 168
184 196 173
170
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, µg 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
cm
Hy: Hd
cm
(Type integers or decimals. Do not round.)
Identify the test statistic.
t =
(Round to two decimal places as needed.)
Identify the P-value.
P-value =
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
sufficient
V the significance level,
the null hypothesis. There
Since the P-value is
evidence to support the claim that presidents tend to be taller than their opponents.
b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the
confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is
cm < Hd <
cm.
(Round to one decimal place as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
the null hypothesis.
Since the confidence interval contains
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 175 177 170 173 184 193 173 168 184 196 173 170 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, µg 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 cm Hy: Hd cm (Type integers or decimals. Do not round.) Identify the test statistic. t = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? sufficient V the significance level, the null hypothesis. There Since the P-value is evidence to support the claim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is cm < Hd < cm. (Round to one decimal place as needed.) What feature of the confidence interval leads to the same conclusion reached in part (a)? the null hypothesis. Since the confidence interval contains
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