10. The distribution of sample means Suppose you are a television network executive interested in how a new pilot show, Stat1stics, will be received by the general US television-viewing population. You hire several market research firms; each recruits a random sample of television viewers and asks them to watch the pilot of Stat1stics. Each firm then gathers 16 respondents and asks each of them, "On a scale of 1 to 10, where 1 means you’ll never watch Stat1stics again, and 10 means you expect to never miss an episode of Stat1stics, how do you rate Stat1stics?" Assume that if you asked every member of the general US television-viewing population about the pilot, the mean response would be 6.5 with a standard deviation of 1.7.