In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'st table, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-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.
Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Letd = 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?
H
0: ?
d
> 0;H
1: ?
d
= 0; right-tailedH
0: ?
d
= 0;H
1: ?
d
≠ 0; two-tailedH
0: ?
d
= 0;H
1: ?
d
< 0;="">H
0: ?
d
= 0;H
1: ?
d
> 0; right-tailed
(b) What sampling distribution will you use? What assumptions are you making?
The Student'st. We assume thatd has an approximately uniform distribution.The standard normal. We assume thatd has an approximately normal distribution. The Student'st. We assume thatd has an approximately normal distribution.The standard normal. We assume thatd 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.
P-value > 0.2500.125 P-value < 0.250 0.050="">P-value < 0.1250.025="">P-value < 0.0500.005="">P-value <>P-value <>
Sketch the sampling distribution and show the area corresponding to the
P-value.
(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 ??
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 not statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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.
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 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.