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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. 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. 1 2 3 135 120 128 108 111 100 Weather Station January April USE SALT Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d January - April.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho H0; H₁: Mg> 0; right-tailed Ho: Mg0; H₂: Mg < 0; left-tailed Ho: Hg = 0; H₂ H * 0; two-tailed Hoi Ha> 0; H₁: Mg0; right-tailed 4 5 64 78 88 61 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.

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. 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. 1 2 3 135 120 128 108 111 100 Weather Station January April USE SALT Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d January - April.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho H0; H₁: Mg> 0; right-tailed Ho: Mg0; H₂: Mg < 0; left-tailed Ho: Hg = 0; H₂ H * 0; two-tailed Hoi Ha> 0; H₁: Mg0; right-tailed 4 5 64 78 88 61 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.

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. 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. 3 4 5 128 64 78 88 61 Weather Station January April LUSE SALT 1 2 135 120 111 100 108 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d January - April.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: MgO; H₁: Mg> 0; right-tailed Ho: Mg = 0; M₁: Mg < 0; left-tailed Ho: Mg0; H₂: Mg0; two-tailed Hoi Ha> 0; H₁: Mg0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. OP-value> > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < 0.025 O OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. ^ ^
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. 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. 3 4 5 128 64 78 88 61 Weather Station January April LUSE SALT 1 2 135 120 111 100 108 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d January - April.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: MgO; H₁: Mg> 0; right-tailed Ho: Mg = 0; M₁: Mg < 0; left-tailed Ho: Mg0; H₂: Mg0; two-tailed Hoi Ha> 0; H₁: Mg0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. OP-value> > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < 0.025 O OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. ^ ^
Sketch the sampling distribution and show the area corresponding to the P-value. O-4 A s (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State 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 sufficient 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 Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. O-4 A s (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State 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 sufficient 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 Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January
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