2. A market research company employs a large number of typists to enter data into a computer. A study is conducted to assess how quickly new typists learn the computer system. A random sample of 25 new typists was obtained and their times (in minutes) to learn the computer system were recorded. Based on these data, the 99% confidence interval for the population nts mean time to learn the computer system was calculated to be (44, 92). (a) What is the probability that the sample mean used to calculate this confidence interval is in the confidence interval of (44, 92)? (b) Is is correct to say that the probability the population mean, u, lies in the interval (44, 92) is 0.99? Explain why or why not. (c) What is the margin of error for this confidence interval? (d) Suppose that you would like to test Ho: 1=40 vs. H1: M#40 using the same data that gave the confidence interval (44, 92), with a=0.01. Would you fail to reject Ho? Explain. (e) Suppose you would like to test Ho: H=45 vs. H1: M#45 using the same data that gave the confidence interval of (44, 92), but with a=0.10. Would you fail to reject Ho? Explain