Describe the sampling distribution for the statistic of interest in each of the following stories, including numerical values for the mean and standard deviation of the sampling distribution.
a. A fisherman takes tourists out fishing and has noticed that over the long run, the weights of a certain type of fish that is typically caught is approximately normal with a mean of 10 pounds and a standard deviation of 2 pounds. During a good day, the boatload of eight people catches the limit of 2 fish each, or a total of 16 fish. The statistic of interest is the mean weight of the 16 fish caught on a good day.
b. A fisherman hangs out at the local bar in the evening and hears tourists talking about the weights of the fish they caught that day. He notices that the weights mentioned seem to have a mean of about 20 pounds and a standard deviation of about 4 pounds. He records what he hears as the weights for the next 50 "fish stories" at the bar. The statistic of interest is the mean weight for the 50 stories. Assume that they represent a random sample of all such stories.