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

For this population the mean is m 5 1 1 2 1 3 1 4 4

5 2.5 Suppose that a random sample of size 2 is to be selected 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 2, 4 3, 1 3, 2 3, 4 4, 1 4, 2 4, 3

a. Compute the sample mean for each of the 12 possible samples.

b. Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram.

c. Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. 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.)

d. In what ways are the two sampling distributions of Parts

(b) and

(c) similar? In what ways are they different?