A mail-order company claims that at least 60% of all orders are mailed within 48 hours. From time to time the quality control department at the company checks if this promise is fulfilled. Recently the quality control department at this company took a sample of 400 orders and found that 208 of them were mailed within 48 hours of the placement of the orders.
a. Testing at a 1% significance level, can you conclude that the company’s claim is true?
b. What will your decision be in part a if the probability of making a Type I error is zero? Explain.
c. Make the test of part a using the p-value approach and α = .01.