Question

The National Aeronautics and Space Administration (NASA) has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average at least 15 miles per hour (mph) for a site to be acceptable. Thirty-six wind speed recordings were taken at random intervals on a site under consideration for a wind machine; the wind speeds averaged 14.2 mph with a standard deviation of 3 mph.

a.) Do the data indicate that the site fails to meet NASA requirements for acceptability as a site for the location of an electric power generating wind machine? Use alpha= .10.

b.) In the context of this problem discuss the meaning of Type I and Type II errors. If you were a NASA official, would you recommend the selection of an extremely small (.01) value for , a moderate value (.05), or a reasonably large value (.10) when testing for the acceptability of a site on the basis of its average wind speed? Explain.

Answer 1

a) We will conduct one sampl t test as the population standard deviation is not mentioned.

We will comduct a left tailed test as it has been claimed that the population mean is at least 15

the data do indicate that the site fails to meet NASA requirements for acceptability as a site for the location of an electric power generating wind machine as the null hypothesis ( claim made) is rejected .

b) a type I error is the rejection of a true null hypothesis.In context it means that we have concluded that the site fails to meet NASA requirements for acceptability as a site for the location of an electric power generating wind machine, when it should not be.

while a type II error is failing to reject a false null hypothesis. In context it means that we have concluded that the site meets the NASA requirements for acceptability as a site for the location of an electric power generating wind machine, when it did not meet the requirements.

The significance level, also denoted as , is the probability of rejecting the null hypothesis when it is true.

Reducing the alpha level reduces the chance of a false positive (called a Type I error) but it also makes it harder to detect differences with a t-test. Any significant results you might obtain would therefore be more trustworthy but there would probably be less of them.

Hence we should use a reasonably large value when testing for the acceptability of a site on the basis of its average wind speed.

If you want to reduce Type I risk use moderate value 0.05