題組內容

(20%)6. Supporters claim that a new windmill can generate an average of at least 800 kilowatts of power per day. Daily power generation for the windmill is assumed to be normally distributed with a standard deviation of 120 kilowatts. A random sample of 100 days is taken to test this claim against the alternative hypothesis that the true mean is less than 800 kilowatts. The claim will be accepted if the sample mean is 776 kilowatts or more and rejected otherwise.

(a) What is the probability \( \alpha \) of a Type I error using the decision rule if the population mean is in fact 800 kilowatts per day?