Question

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. Discuss the consequences and potential costs of Type I and Type II errors.

Answer 1

Null Hypothesis H0: The site is feasible and the mean wind velocity exceeds 20 mph.

Alternative hypothesis Ha: The site is not feasible and the mean wind velocity is less than 20 mph

Type I error is rejection of true null hypothesis. Thus, Type I error, that we conclude that the site is not feasible, but in reality, the site is feasible.

The consequence is that the profitable electricity producing windmill will not be constructed. There would not be any financial cost, but the company may miss a feasible site which can be of great financial and business importance.

Type II error is fail to rejection of false null hypothesis. Thus, Type II error, that we could not find any evidence to claim that the site is not feasible, but in reality, the site is not feasible.

The consequence is that the further testing is conducted to determine the feasibility. There would huge financial loss for the company if the company again fails to find any evidence in the second round in favor of mean wind speed less than 20 miles per hour. The company then starts the construction of electricity producing windmill on non-feasible site.