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.