Chapter 7, Problem 4PS

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

a. Assuming that you sample without replacement, select all possible sample of $n=2$ and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean. Are they equal? What is this property called?

b. Repeat $\left(\text{a}\right)$ for all possible sample of $n=3.$

c. Compare the shape of the sampling distribution of the mean in $\left(\text{a}\right)\text{and}\left(\text{b}\right).$ Which sampling distribution has less variability? why?

d. Assuming that you sample with replacement, repeat $\left(\text{a}\right)\text{through}\left(\text{c}\right)$ and compare the results. Which sampling distributions have least variability-those in (a) or (b)? why?