In this problem, assume that the distribution of differences is approximately no
ID: 3156856 • Letter: I
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 124 129 121 64 78 April 98 104 113 88 61
Does this information indicate that the peak wind gusts are higher in January than in April? Use = 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: d = 0; H1: d > 0; right-tailed
H0: d > 0; H1: d = 0; right-tailed
H0: d = 0; H1: d < 0; left-tailed H0: d = 0;
H1: d 0; two-tailed
(b) What sampling distribution will you use? What assumptions are you making?
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.
The standard normal. We assume that d has an approximately uniform distribution.
The Student's t. 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. (Round your answer to four decimal places.)
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 ?
At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.
Fail to reject the null hypothesis, there is insufficient 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.
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 insufficient evidence to claim average peak wind gusts are higher in January.
Explanation / Answer
A)
As given
alpha = 0.01 [ANSWER]
******************************
As we want to prove that peak wind gusts are higher for January, we have a right tailed test,
H0: d = 0; H1: d > 0; right-tailed [ANSWER, A]
******************************
b)
OPTION D: The Student's t. We assume that d has an approximately normal distribution. [ANSWER]
****************************
c)
As we can see, this is a right tailed test.
The differences are
26
25
8
-24
17
Calculating the standard deviation of the differences (third column):
s = 13.49971941
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 6.037258057
Calculating the mean of the differences (third column):
XD = 10.4
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 1.72263632
As df = n - 1 = 4
Then, using p values, as this is right tailed,
p = 0.080027736 [ANSWER]
************************************
d)
As P > 0.01,
OPTION C: At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. [ANSWER]
***********************************
e)
OPTION A: Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.