A television manufacturer states that at least 90% of its TV sets will not need service during the first 3 years of operation. A consumer group wants to investigate this statement. A random sample of n = 100 purchasers is selected and each person is asked if the set purchased needed repair during the first 3 years. Let p denote the proportion of all sets made by this manufacturer that will not need service in the first 3 years. The consumer group does not want to claim false advertising unless there is strong evidence that p < 0.9. The appropriate hypotheses are then H0: p = 0.9 versus Ha: p < 0.9.
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 α = 0.01 or one that uses α = 0.10? Explain.