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 $\bar { x } = 25.8 \mathrm { mph }$, with a standard deviation of $s = 4.2 \mathrm { mph }$. To determine whether the site meets the organization's requirements, consider the test, $H _ { 0 } : \mu = 25$ vs. $H _ { \mathrm { a } } : \mu 25$, where $\mu$ 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) We are $99 \%$ confident that the site does not meet the organization's requirements.
B) We are $99 \%$ confident that the site meets the organization's requirements.
C) At $\alpha = .01$, there is insufficient evidence to conclude the true mean wind speed at the site exceeds $25 \mathrm { mph }$.
D) At $\alpha = .01$, there is sufficient evidence to conclude the true mean wind speed at the site exceeds $25 \mathrm { mph }$.

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 $\bar { x } = 25.8 \mathrm { mph }$, with a standard deviation of $s = 4.2 \mathrm { mph }$. To determine whether the site meets the organization's requirements, consider the test, $H _ { 0 } : \mu = 25$ vs. $H _ { \mathrm { a } } : \mu > 25$, where $\mu$ 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) We are $99 \%$ confident that the site does not meet the organization's requirements.
B) We are $99 \%$ confident that the site meets the organization's requirements.
C) At $\alpha = .01$, there is insufficient evidence to conclude the true mean wind speed at the site exceeds $25 \mathrm { mph }$.
D) At $\alpha = .01$, there is sufficient evidence to conclude the true mean wind speed at the site exceeds $25 \mathrm { mph }$.

Quizplus · Accepted Answer

At $\alpha = .01$, the test statistic of $1.25$ likely does not exceed the critical value for a one-tailed test, indicating insufficient evidence to reject $H_0$.

A National Organization Has Been Working with Utilities Throughout the Nation