Question

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 16 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n = 32 wind speed recordings (taken at random intervals), the wind speed at the site averaged 16.9 mph, with a standard deviation of 3.5 mph. To determine whether the site meets the organization's requirements, consider the test, H0: μ = 16 vs. Ha: μ > 16, where μ is the true mean wind speed at the site and α = 0.01. Suppose the value of the test statistic were computed to be 1.45. State the conclusion.

a.At α = 0.01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.

b.We are 99% confident that the site does not meet the organization's requirements.

c.At α = 0.01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.

d.We are 99% confident that the site meets the organization's requirements.

Answer 1

Given thats smalple size n = 32

Df = n-1 = 31

Let los be alf = 0.01

Df = n-1 = 31

For one tailed test,

Form Excel ,p value = t.dist.rt( 1.45, 31)

P value = 0.079

Since , p value > 0.01 , we fail to reject the null hypothesis.

Answer : option a

.At α = 0.01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.