8.7 Consider the following population: {1, 2, 3, 4}.

Note that the population mean is

1+2+3+4 4 2.5 a. Suppose that a random sample of size 2 is to be se- lected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account): 1,2 1,3 1,4 2,1 2,3 3,1 3,2 3,4 4,1 4,2 2,4 4,3 Compute the sample mean for each of the 12 pos- sible samples. Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.) b. Suppose that a random sample of size 2 is to be se- lected, but this time sampling will be done with re- placement. Using a method similar to that of Part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.) c. In what ways are the two sampling distributions of Parts (a) and (b) similar? In what ways are they different?