Homework Help is Here – Start Your Trial Now!
Math
Statistics
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in th 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 Januar and April are recorded below. Weather Station 1 2 3 4. January April 139 120 126 64 78 104 111 100 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d = January A (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? OH: H 0; Hi Hg = 0; right-tailed O H: H= 0; H,: < 0; left-tailed O H: = 0; H,: 4# 0; two-tailed O H,: H = 0; H: H> 0; 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 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. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in th 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 Januar and April are recorded below. Weather Station 1 2 3 4. January April 139 120 126 64 78 104 111 100 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. (Let d = January A (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? OH: H 0; Hi Hg = 0; right-tailed O H: H= 0; H,: < 0; left-tailed O H: = 0; H,: 4# 0; two-tailed O H,: H = 0; H: H> 0; 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 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. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
icon
Concept explainers
Topic Video
Question
13)
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. Weather Station 2 4 January April 139 120 126 64 78 104 111 100 88 61 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? OH:H>0; H,H = 0; right-tailed O H: = 0; H,:< 0; left-tailed %3D O H: = 0; H,: # 0; two-tailed O H,: K = 0; H,: H> 0; 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 Student's t. We assume that d has an approximately uniform distribution. I O The standard normal. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.)
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. Weather Station 2 4 January April 139 120 126 64 78 104 111 100 88 61 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? OH:H>0; H,H = 0; right-tailed O H: = 0; H,:< 0; left-tailed %3D O H: = 0; H,: # 0; two-tailed O H,: K = 0; H,: H> 0; 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 Student's t. We assume that d has an approximately uniform distribution. I O The standard normal. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.)
Ga -2 O-4 (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 fail to reject the null hypothesis and conclude the data are 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. (e) State your conclusion in the context of the application. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in Januany. 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 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. Need Help? Read It Watch it
Transcribed Image Text:Ga -2 O-4 (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 fail to reject the null hypothesis and conclude the data are 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. (e) State your conclusion in the context of the application. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in Januany. 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 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. Need Help? Read It Watch it
Expert Solution
Step 1
Jan Apr d  
139 104 35  
120 111 9  
126 100 26  
64 88 -24  
78 61 17  
    12.6 Mean
    22.6561 Stdev
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Angles, Arcs, and Chords and Tangents
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
SEE MORE TEXTBOOKS