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

Note that the population mean is m 5 1 1 2 1 3 1 4 4 5 2.5

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

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

(a) and

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