This exercise can be done individually or, better yet, as a class project.
a. Use a random-number table or random-number generator to obtain a sample (with replacement) of four digits between 0 and 9. Do so a total of 50 times and compute the mean of each sample.
b. Theoretically, what are the mean and standard deviation of all possible sample means for samples of size 4?
c. Roughly what would you expect the mean and standard deviation of the 50 sample means you obtained in part (a) to be? Explain your answers.
d. Determine the mean and standard deviation of the 50 sample means you obtained in part (a).
e. Compare your answers in parts (c) and (d). Why are they different?