A television manufacturer claims that (at least) 90% of its TV sets will need no service during the first 3 years of operation. A consumer agency wishes to check this claim, so it obtains a random sample of n = 100 purchasers and asks each whether the set purchased needed repair during the first 3 years after purchase. Let p^ be the sample proportion of responses indicating no repair (so that no repair is identified with a success). Let p denote the actual proportion of successes for all sets made by this manufacturer. The agency does not want to claim false advertising unless sample evidence strongly suggests that p < .9. The appropriate hypotheses are then H0: p = .9 versus Ha: p < .9.
a. In the context of this problem, describe Type I and Type II errors, and discuss the possible consequences of each.
b. Would you recommend a test procedure that uses a = .10 or one that uses a = .01? Explain.