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 22 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 = 33 wind speed recordings (taken at random intervals), the wind speed at the site averaged 22.8 mph, with a standard deviation of 4.3 mph. to determine whether the site meets the organizations requirements, perform the following hypothesis test at the 1% significance level and state your conclusion. ho: μ = 22 ha: μ > 22 at α = 0.01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph. at α = 0.01, there is not sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph. we are 99% confident that the site meets the organizations requirements. we are 99% confident that the site does not meet the organizations requirements.

Explanation:

Step1: Calculate the test - statistic

The formula for the z - test statistic is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\). Here, \(\bar{x} = 22.8\), \(\mu=22\), \(\sigma = 4.3\), and \(n = 33\).

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Step2: Determine the critical value

For a one - tailed test with \(\alpha=0.01\), the critical value \(z_{\alpha}\) is \(z_{0.01}= 2.33\) (from the standard normal distribution table).

Step3: Compare the test - statistic and the critical value

Since \(z = 1.07

Answer:

At \(\alpha = 0.01\), there is not sufficient evidence to conclude the true mean wind speed at the site exceeds \(22\) mph.