Amtrak has pledged that the average delay on journeys between Champaign and Chicago will be no worse than 10 minutes. One unhappy passenger, however, has experienced a mean delay of 15 minutes on a group of five journeys, with a standard deviation of 10.1 minutes. The passenger writes to the customer service manager of Amtrak arguing that his experience proves that the company is not keeping to its pledge. The customer service manager replies, regretting the delays but arguing that such a small sample (5 journeys) cannot prove that the pledge has been broken. 3 a) You are asked to comment on the statistical significance of these data. Using the evidence given and construct a hypothesis test. What is your conclusion? b) The unhappy passenger then gathers together experiences from some of his friends, and finds that from a sample of 50 journeys, the mean delay is 13.4 minutes, and the standard deviation is 9.4 minutes. Once again, you are asked to comment. What is your conclusion this time? c) What other arguments might the customer service manager use to cast doubt on the importance of the unhappy passenger's data?