A National Organization Has Been Working with Utilities Throughout the Nation

question 133

Multiple Choice

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 18 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 $n = 136$ wind speed recordings (taken at random intervals) , the wind speed at the site averaged $\bar { x } = 17.4 \mathrm { mph }$ , with a standard deviation of $s = 3.5 \mathrm { mph }$ . To determine whether the site meets the organization's requirements, consider the test, $H _ { 0 } : \mu = 18$ vs. $H _ { \mathrm { a } } : \mu > 18$ , where $\mu$ is the true mean wind speed at the site and $\alpha = .05$ . Fill in the blanks. "A Type I error in the context of this problem is to conclude that the true mean wind speed at the site ________ $18 \mathrm { mph }$ when it actually ______ $18 \mathrm { mph } . "$

• A) equals; equals
• B) equals; exceeds
• C) exceeds; equals
• D) exceeds; exceeds

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Definitions:

Significance Level

The probability of rejecting the null hypothesis when it is actually true, used as a threshold in hypothesis testing.

Model Contribution

Refers to the impact or influence that a statistical model has in explaining the variability of the observed data.

Negative Correlation

Negative correlation indicates that as one variable increases, the other decreases, and vice versa, demonstrating an inverse relationship.

Null Hypotheses

A hypothesis that stipulates there is no statistical significance between the specified sets of data or that any observed differences are due to chance.