Question

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	1	2	3	4	5
January	138	128	130	64	78
April	107	112	112	88	61

Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 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?

H₀: μ_d = 0; H₁: μ_d < 0; left-tailedH₀: μ_d > 0; H₁: μ_d = 0; right-tailed    H₀: μ_d = 0; H₁: μ_d > 0; right-tailedH₀: μ_d = 0; H₁: μ_d ≠ 0; two-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately uniform distribution.    The standard normal. We assume that d has an approximately normal distribution.The Student's t. 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.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

(a) the level of significance is 0.01
the null and alternate hypotheses.

H0: μd > 0; H1: μd = 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that d has an approximately normal distribution.

using minitab>stat>basic stat>paired t test

we have

Paired T-Test and CI: january, april

Paired T for january - april

N Mean StDev SE Mean
january 5 107.6 34.0 15.2
april 5 96.0 21.9 9.8
Difference 5 11.60 20.82 9.31

99% lower bound for mean difference: -23.28
T-Test of mean difference = 0 (vs > 0): T-Value = 1.246 P-Value = 0.1404

the value of the sample test statistic is 1.246


(c) the P-value. is 0.1404