Generating a sampling distribution Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. Th e population consists of the numbers 1, 2, 4, and 9. Th e parameter of interest is the mean of this population. Th e sample is an SRS of size n 5 2 drawn from the population.

(a) Find the mean of the four numbers in the population. Th is is the population mean m.

(b) Th ere are only six possible samples of size 2 that can be chosen. One such sample is {1, 2}. For this sample, x 5 1.5. Th is statistic, x, is an estimate of the population mean m. List the other fi ve possible SRSs of size 2, and compute the value of x for each.

(c) Make a dotplot that shows the distribution of x-values from (b). Th is is the sampling distribution of x.

(d) Find the mean of the six x-values from (b). How does this compare to the population mean m?