Q1) Supporters claim that new windmill can create on average at least 800 kilowatt of power per day. Daily power generation for windmill is supposed to be normally distributed with standard deviation of 120 kilowatts. Random sample of 100 days is taken to test this claim against alternative hypothesis that true mean is less than 800 kilowatts. Claim will not be rejected if sample mean is 776 kilowatts or more and rejected otherwise.

a) Determine the probability that of a Type I error using decision rule if population mean is in fact 800 kilowatts per day?

b) Find out the probability β of Type II error using this decision rule if population mean is in fact 740 kilowatts per day?

c) Assume that same decision rule is used, but with sample of 200 days. (i) Would value of α be smaller than, larger than, or same as found in part (a)? (ii) Compare value of β with that in part (b).

d) Assume that that sample of 100 days was taken, but with decision rule was changed so that the claim would not be rejected if sample mean was at least 765 kilowatts. (i) Compare value of α with that in part (a); (ii) Compare value of β with that in part (b).