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According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 30 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, µ, is now less than 30 kilometers. The administrator chooses a random sample of 45 visitors. The mean distance hiked for the sample is 29.5 kilometers. Assume the population standard deviation is 9.9 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. OI O=0 H: µ < 30 ?

According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 30 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, µ, is now less than 30 kilometers. The administrator chooses a random sample of 45 visitors. The mean distance hiked for the sample is 29.5 kilometers. Assume the population standard deviation is 9.9 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. OI O=0 H: µ < 30 ?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 30 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, µ, is now less than 30 kilometers. The administrator chooses a random sample of 45 visitors. The mean distance hiked for the sample is 29.5 kilometers. Assume the population standard deviation is 9.9 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. O<O OSO Ho: µ = 30 >[ D=0 H: µ < 30 ? (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 1 – x • 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 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.339 0.2+ Step 3: Shade the area represented by the p-value. 0.1+ Step 4: Enter the p-value. (Round to 3 decimal places.) 0.367 2= 0.339
Transcribed Image Text:According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 30 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, µ, is now less than 30 kilometers. The administrator chooses a random sample of 45 visitors. The mean distance hiked for the sample is 29.5 kilometers. Assume the population standard deviation is 9.9 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. O<O OSO Ho: µ = 30 >[ D=0 H: µ < 30 ? (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 1 – x • 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 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.339 0.2+ Step 3: Shade the area represented by the p-value. 0.1+ Step 4: Enter the p-value. (Round to 3 decimal places.) 0.367 2= 0.339
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