A television manufacturer claims that (at least) 90% of its TV sets will not need 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 < 0.9. The appropriate hypotheses are then Ho: p = 0.9 versus H: p < 0.9. (a) In the context of this problem, describe Type I and Type II errors. (Select all that apply.) O A Type II error would be not obtaining convincing evidence that less than 90% of the TV sets need no repair when in fact less than 90% need no rерair. O A Type I error would be obtaining convincing evidence that less than 90% of the TV sets need no repair when in fact (at least) 90% need no герair. O A Type I error would be not obtaining convincing evidence that less than 90% of the TV sets need no repair when in fact less than 90% need no герair. O AType II error would be obtaining convincing evidence that less than 90% of the TV sets need no repair when in fact (at least) 90% need no rерair. Discuss the possible consequences of each. (Select all that apply.) O The consumer agency would not take action against the manufacturer when in fact the manufacturer is making untrue claims about the reliability of the TV sets. O The consumer agency might take action against the manufacturer when in fact the manufacturer is not at fault. O The consumer agency would not take action against the manufacturer when in fact the manufacturer is making true claims about the reliability of the TV sets. O The consumer agency might take action against the manufacturer when in fact the manufacturer is at fault. (b) Would you recommend a test procedure that uses a = 0.10 or one that uses a = 0.01? Explain. O Use a = 0.10, as making a Type II error involves not catching the manufacturer when they are at fault. O Use a = 0.10, as making a Type I error involves not catching the manufacturer when they are at fault. O Use a = 0.01, as making a Type I error involves taking action against the manufacturer when in fact the manufacturer is not at fault. O Use a = 0.01, as making a Type II error involves taking action against the manufacturer when in fact the manufacturer is not at fault.