Simulate sampling from the population of Exercise 8.7 by using four slips of paper individually marked 1, 2, 3, and 4. Select a sample of size 2 without replacement, and compute derived in Exercise 8.7, Part (a)?
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): Compute the sample mean for each of the 12 possible samples. Use this information to construct the sampling distribution of . (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 . (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?
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