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 (>,≠,=,<) ___ cm H1: μd (>,≠,=,<) ___ 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? Since the P-value is (less than or equal to, greater than) the significance level, (fail to reject, reject) the null hypothesis. There (is, is not) sufficient 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)?
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 (>,≠,=,<) ___ cm H1: μd (>,≠,=,<) ___ 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? Since the P-value is (less than or equal to, greater than) the significance level, (fail to reject, reject) the null hypothesis. There (is, is not) sufficient 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)?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 6E
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Question
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
|
181
|
172
|
174
|
177
|
187
|
172
|
|
---|---|---|---|---|---|---|---|
Height (cm) of Main Opponent
|
166
|
182
|
171
|
169
|
188
|
169
|
|
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 (>,≠,=,<) ___ cm
H1: μd (>,≠,=,<) ___ 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?
Since the P-value is (less than or equal to, greater than)
the significance level, (fail to reject, reject)
the null hypothesis. There (is, is not) sufficient evidence to support the claim that presidents tend to be taller than their opponents.
the significance level, (fail to reject, reject)
the null hypothesis. There (is, is not) sufficient 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<μd<______cm.
(Round to one decimal place as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
Since the confidence interval contains (zero, only negative numbers, only positive numbers)
(reject, fail to reject) the null hypothesis.
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