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According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 21 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, H, is now less than 21 kilometers. The administrator chooses a random sample of 85 visitors. The mean distance hiked for the sample is 20.5 kilometers. Assume the population standard deviation is 8.3 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 21 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H.. H: 0 D20 D-O D-0 ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by • The prvalue is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) 02 Step 3: Shade the area represented by the pvalue. Step 4: Enter the pvalue. (Round to 3 decimal places.) ? (e) Based on your answer to part (b), choose what the administrator can conclude, at the 0.10 level of significance. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. O Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. • Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough

According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 21 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, H, is now less than 21 kilometers. The administrator chooses a random sample of 85 visitors. The mean distance hiked for the sample is 20.5 kilometers. Assume the population standard deviation is 8.3 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 21 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H.. H: 0 D20 D-O D-0 ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by • The prvalue is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) 02 Step 3: Shade the area represented by the pvalue. Step 4: Enter the pvalue. (Round to 3 decimal places.) ? (e) Based on your answer to part (b), choose what the administrator can conclude, at the 0.10 level of significance. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. O Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. • Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 21 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, H, is now less than 21 kilometers. The administrator chooses a random sample of 85 visitors. The mean distance hiked for the sample is 20.5 kilometers. Assume the population standard deviation is 8.3 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 21 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H. OSO D-O ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) 02 Step 3: Shade the aren represented by the pvalue. Step 4: Enter the p-value. (Round to 3 decimal places.) ? (c) Based on your answer to part (b), choose what the administrator can conclude, at the 0.10 level of significance. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 klometers. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers.
Transcribed Image Text:According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 21 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, H, is now less than 21 kilometers. The administrator chooses a random sample of 85 visitors. The mean distance hiked for the sample is 20.5 kilometers. Assume the population standard deviation is 8.3 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 21 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H. OSO D-O ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) 02 Step 3: Shade the aren represented by the pvalue. Step 4: Enter the p-value. (Round to 3 decimal places.) ? (c) Based on your answer to part (b), choose what the administrator can conclude, at the 0.10 level of significance. O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 klometers. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 21 kilometers.
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