Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 2, 3, and 10 (based on Data Set 22 in Appendix B). Consider the values of 2, 3, and 10 to be a population. Assume that samples of size n = 2 are randomly selected without replacement.

a. Find ? and ?.

b. After finding all samples of size n = 2 that can be obtained without replacement, find the population of all values of by finding the mean of each sample of size n = 2.

c. Find the mean ?_x? and standard deviation ?_x? for the population of sample means found in part (b).

d. Verify that

and N-n nV N-1