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 19 miles per hour $( \mathrm { mph } )$ for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of $n = 45$ wind speed recordings (taken at random intervals), the wind speed at the site averaged $\bar { x } = 19.9 \mathrm { mph }$, with a standard deviation of $s = 4.5 \mathrm { mph }$. To determine whether the site meets the organization's requirements, consider the test, $H _ { 0 } : \mu = 19$ vs. $H _ { \mathrm { a } } : \mu 19$, 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 $1.34$. State the conclusion.
A) At $\alpha = .01$, there is insufficient evidence to conclude the true mean wind speed at the site exceeds $19 \mathrm { mph }$.
B) At $\alpha = .01$, there is sufficient evidence to conclude the true mean wind speed at the site exceeds $19 \mathrm { mph }$.
C) We are $99 \%$ confident that the site does not meet the organization's requirements.
D) We are $99 \%$ confident that the site meets the organization's requirements.

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 19 miles per hour $( \mathrm { mph } )$ for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of $n = 45$ wind speed recordings (taken at random intervals), the wind speed at the site averaged $\bar { x } = 19.9 \mathrm { mph }$, with a standard deviation of $s = 4.5 \mathrm { mph }$. To determine whether the site meets the organization's requirements, consider the test, $H _ { 0 } : \mu = 19$ vs. $H _ { \mathrm { a } } : \mu > 19$, 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 $1.34$. State the conclusion.
A) At $\alpha = .01$, there is insufficient evidence to conclude the true mean wind speed at the site exceeds $19 \mathrm { mph }$.
B) At $\alpha = .01$, there is sufficient evidence to conclude the true mean wind speed at the site exceeds $19 \mathrm { mph }$.
C) We are $99 \%$ confident that the site does not meet the organization's requirements.
D) We are $99 \%$ confident that the site meets the organization's requirements.

Quizplus · Accepted Answer

The test statistic of 1.34 is less than the critical value for a one-tailed test at $\alpha = .01$, which is approximately 2.33. Therefore, we fail to reject the null hypothesis, indicating insufficient evidence to conclude that the true mean wind speed exceeds 19 mph.

A National Organization Has Been Working with Utilities Throughout the Nation