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prohojiy [21]
3 years ago
14

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generat

e electricity. Wind speeds must average more than 20 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 alpha = .01. Suppose the value of the test statistic were computed to be 1.25. State the conclusion.
A) At alpha = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph.
B) At alpha΅= .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.
Mathematics
1 answer:
kap26 [50]3 years ago
7 0

Answer:

B) At alpha = 0.01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph.

Step-by-step explanation:

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 25.

We are using the t-distribution, with test statistic t = 1.25 and 43 - 1 = 42 degrees of freedom. This probability is a right-tailed test.

With the help of a calculator, this p-value is of 0.1091.

Since the p-value of the test is 0.1091 > 0.01, at \alpha = 0.01 there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph, and the correct answer is given by option B.

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