A national organization has been working with utilities throughout the nation to

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 25 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 = 43 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 25.8 mph, with a standard deviation of s = 4.2 mph. To determine whether the site meets the organization's requirements, consider the test, H0: µ = 25 vs. Ha: µ > 25, where µ is the true mean wind speed at the site and = .01. Suppose the value of the test statistic were computed to be 1.25. State the conclusion. A) At = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph. B) At = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph. C) We are 99% confident that the site meets the organization's requirements. D) We are 99% confident that the site does not meet the organization's requirements.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 25
Alternative hypothesis: > 25

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.6405
DF = n - 1

D.F = 42
t = (x - ) / SE

t = 1.25

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.25.

Thus the P-value in this analysis is 0.11.

Interpret results. Since the P-value (0.11) is greater than the significance level (0.01), we have to the null hypothesis.

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

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