Question

The data below represent the number of days absent per year in a population of three employees of a small company:

1 4 7    

1. Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compare the mean of all the samples means and also compute the population mean. Are they equal? What is the property called?
2. Repeat (a) for all the sampling distribution of the mean in (a) for n= 3. Which sampling distribution has less variability? Why?
3. Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distribution have the least variability – those in (a) or (b) ? Why?

Show your work!

Answer 1

Required 27 samples are as follows:

1 1 1
1 1 4
1 1 7
1 4 1
1 7 1
4 1 1
7 1 1
4 4 4
4 4 1
4 4 7
4 1 4
4 7 4
1 4 4
7 4 4
7 7 7
7 7 1
7 7 4
7 1 7
7 4 7
1 7 7
4 7 7
1 4 7
1 7 4
4 7 1
4 1 7
7 1 4
7 4 1