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 177 172 180 184 189 181 Height (cm) of Main Opponent 162 189 165 176 181 173 a. Use the sample data with a 0.05significance 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? Identify the test statistic. Identify the P-value. 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.
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 177 172 180 184 189 181 Height (cm) of Main Opponent 162 189 165 176 181 173 a. Use the sample data with a 0.05significance 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? Identify the test statistic. Identify the P-value. 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.
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 5E
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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
|
177
|
172
|
180
|
184
|
189
|
181
|
|
---|---|---|---|---|---|---|---|
Height (cm) of Main Opponent
|
162
|
189
|
165
|
176
|
181
|
173
|
|
a. Use the sample data with a 0.05significance 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?
Identify the test statistic.
Identify the P-value.
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.
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