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In this problem, assume thất the distribution of differences is approximately normal. Note: For degrees of freedom d.r. not in the Student's t table, use the closest d.r. that is smaller. In some situations, this choice of d.r. may Increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 January April 3 122 5 78 61 4 130 105 127 64 97 108 88 Does this information indicate that the peak wind gusts are higher in January than in April? Use a - 0.01. Solve the problem using the critical region method of testing. (Let d- January - April. Round your answers to three decimal places.) test statistic - critical value = Interpret your conclusion in the context of the application. O Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? O The conclusions obtained by using both methods are the same. O we reject the null hypothesis using the critical region method, but fail to reject using the P-value method. O we reject the null hypothesis using the P-value method, but fail to reject using the critical region method.

In this problem, assume thất the distribution of differences is approximately normal. Note: For degrees of freedom d.r. not in the Student's t table, use the closest d.r. that is smaller. In some situations, this choice of d.r. may Increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 January April 3 122 5 78 61 4 130 105 127 64 97 108 88 Does this information indicate that the peak wind gusts are higher in January than in April? Use a - 0.01. Solve the problem using the critical region method of testing. (Let d- January - April. Round your answers to three decimal places.) test statistic - critical value = Interpret your conclusion in the context of the application. O Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? O The conclusions obtained by using both methods are the same. O we reject the null hypothesis using the critical region method, but fail to reject using the P-value method. O we reject the null hypothesis using the P-value method, but fail to reject using the critical region method.

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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In this problem, assume that the distribution of differences is approximately normal. **Note**: For degrees of freedom *d.f.* not in the Student’s t table, use the closest *d.f.* that is smaller. In some situations, this choice of *d.f.* may increase the *P*-value by a small amount and therefore produce a slightly more “conservative” answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. | Wilderness District | 1 | 2 | 3 | 4 | 5 | |---------------------|-----|-----|-----|-----|-----| | January | 130 | 127 | 122 | 64 | 78 | | April | 105 | 97 | 108 | 88 | 61 | Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) - test statistic = ______ - critical value = ______ Interpret your conclusion in the context of the application. - ○ Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. - ○ Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. - ○ Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. - ○ Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the *P*-value method. Are they the same? - ○ The conclusions obtained by using both methods are the same. - ○ We reject the null hypothesis using the critical region method, but fail to reject using the *P*-value method. - ○ We reject the null hypothesis using the *P*-value method, but fail to reject using the critical region method.
Transcribed Image Text:In this problem, assume that the distribution of differences is approximately normal. **Note**: For degrees of freedom *d.f.* not in the Student’s t table, use the closest *d.f.* that is smaller. In some situations, this choice of *d.f.* may increase the *P*-value by a small amount and therefore produce a slightly more “conservative” answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. | Wilderness District | 1 | 2 | 3 | 4 | 5 | |---------------------|-----|-----|-----|-----|-----| | January | 130 | 127 | 122 | 64 | 78 | | April | 105 | 97 | 108 | 88 | 61 | Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) - test statistic = ______ - critical value = ______ Interpret your conclusion in the context of the application. - ○ Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. - ○ Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. - ○ Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. - ○ Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the *P*-value method. Are they the same? - ○ The conclusions obtained by using both methods are the same. - ○ We reject the null hypothesis using the critical region method, but fail to reject using the *P*-value method. - ○ We reject the null hypothesis using the *P*-value method, but fail to reject using the critical region method.
Expert Solution
Step 1

Solution:

January  April  d= jan  - April (d-d) (d-d)2
130 105 25 12.6 158.76
127 97 30 17.6 309.76
122 108 14 1.6 2.56
64 88 -24 -36.4 1324.96
78 61 17 4.6 21.16

n= 5 Sample size 

∑d= 62d = ∑dn=625= 12.4  Difference of sample mean ∑(d-d)2=1817.2sd=∑(d-d)2n-1sd=1817.24sd = 454.3sd = 21.3143   Difference of sample standard deviation α=0.01 Level of significance 

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