According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 27 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, u, is now less than 27 kilometers. The administrator chooses a random sample of 78 visitors. The mean distance hiked for the sample is 25.6 kilometers. Assume the population standard deviation is 7.1 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 27 kilometers? Perform a hypothesis test, using the 0.05 level of significance,

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According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 27 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, u, is now less than 27 kilometers. The administrator chooses a random sample of 78 visitors. The mean distance hiked for the sample is 25.6
kilometers. Assume the population standard deviation is 7.1 kilometers.
Can the administrator conclude that the mean distance hiked by each visitor is now less than 27 kilometers? Perform a hypothesis test, using the 0.05 level of
significance.
(a) State the null hypothesis H, and the alternative hypothesis H,.
O<O O$O D>O
H:
D=D D<O
(b) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
Transcribed Image Text:According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 27 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, u, is now less than 27 kilometers. The administrator chooses a random sample of 78 visitors. The mean distance hiked for the sample is 25.6 kilometers. Assume the population standard deviation is 7.1 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 27 kilometers? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. O<O O$O D>O H: D=D D<O (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test.
V Enter the p-value.
(Kound to 3 decimal places.)
-3
-2
-1
1.
(c) Based on your answer to part (b), choose what the administrator can conclude, at the 0.05 level of significance.
LEGO
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 27 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 27 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 27 kilometers.
O 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 27 kilometers.
3.
2.
Transcribed Image Text:V Enter the p-value. (Kound to 3 decimal places.) -3 -2 -1 1. (c) Based on your answer to part (b), choose what the administrator can conclude, at the 0.05 level of significance. LEGO 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 27 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 27 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 27 kilometers. O 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 27 kilometers. 3. 2.
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