[10 points] A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H0: = 950 hours vs. H1: = 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.

a)Calculate , the probability of a Type II error when = 1000 and = 0.10.

b)Calculate the power of the test.