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. ^ ^
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 4CA
Related questions
Question
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.
^
^
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