You want to see if a redesign of the cover of a mail-order catalog will increase sales. A very large number of customers will receive the original catalog and a random sample of customers will receive the one with the new cover. For planning purposes, you are willing to assume that the mean will be approximately normal with = 50 dollars and that the mean for the original catalog will be = 25 dollars. You decide to use a sample size of n=900. You wish to test:

H_o : =25

H_o : > 25

You decide to reject H_o if x > 26 and to accept H_o otherwise.

1.) Find the probability of a Type I error, that is, the probability that your test rejects H_o when in fact = 25 dollars. Explain what a Type I error is in this situation.

2.) Find the probability of a Type II error when = 28 dollars. This is the probability that your test accepts H_o when in fact = 28.

3.)Explain two ways that you could increase the power of the test used in this problem.