The following data represent the number of days absent per year in a population of four employees of a small company: 1 3 6 7 a.

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

 1 3 6 7   

a.    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?

b.    Repeat (a) for all the sampling distribution of the mean in (a) for n= 3. Which sampling distribution has less variability? Why?

c.    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?

Question 2

Time spent using email per session is normally distributed, µ = 10 minutes and σ = 2 minutes. If you select a random sample of 4 sessions, 

a.    What is the probability that the sample mean is less than 8 minutes?

b.    What is the probability that sample mean is between 8 and 9 minutes?

c.    If you select a random sample of 16 sessions, what is the probability that a as sample mean is between 8 and 9 minutes?

d.    Explain the differences in the results of (b) and (c).