The number of potential sites for the first-stage test in Exercise 11.78 is quite large and the readings can be expensive. Accordingly, the test is conducted with a sample of 25 observations. Because...

The number of potential sites for the first-stage test in Exercise 11.78 is quite large and the readings can be expensive. Accordingly, the test is conducted with a sample of 25 observations. Because the secondstage 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. Calculate the probability that the first-stage test will not conclude that the site is feasible when the actual mean wind velocity is 25 mph. (Assume that σ is 8.) Discuss how the process can be improved.

Exercise 11.78

The feasibility of constructing a profitable electricityproducing 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. Discuss the consequences and potential costs of Type I and Type II errors.