Part 1. The feasibility of constructing a profitable electricity-producing windmill depends on the mean

velocity of the wind. For a certain type of windmill, the mean would have to exceed 20 miles per hour to

warrant its construction. The determination of a site's feasibility is a two-stage process. In the first stage,

readings of the wind velocity are taken and the mean is calculated. The test is designed to answer the

question, Is the site feasible? In other words, is there sufficient evidence to conclude that the mean wind

velocity exceeds 20 mph? If there is enough evidence, further testing is conducted. If there is not enough

evidence, the site is removed from consideration.

a. State the null and alternative hypotheses.

b. What are the consequences and potential costs of Type I and Type II errors?

Part 2. The number of potential sites for the first-stage test is quite large and the readings can be

expensive. Accordingly, the test is conducted with a sample of 25 observations. Because the second-stage

cost is high, the significance level is set at 1%. A financial analysis of the potential profits and costs

reveals that if the mean wind velocity is as high as 25 mph, the windmill would be extremely profitable.

a. Calculate the probability of Type II error that the first-stage test will not conclude that the site is

feasible when the actual mean wind velocity is 25 mph. (Assume that is 8.)

b. Discuss how the process can be improved.