# Simulate sampling from the population described in Exercise

Simulate sampling from the population described in Exercise 6.3 by marking the values of x , one on each of four identical coins (or poker chips, etc.). Place the coins (marked 0, 2, 4, and 6) into a bag, randomly select one, and observe its value. Replace this coin, draw a second coin, and observe its value. Finally, calculate the mean for this sample of n = 2 observations randomly selected from the population (Exercise 6.3, part b). Replace the coins, mix them, and, using the same procedure, select a sample of n = 2 observations from the population. Record the numbers and calculate for this sample. Repeat this sampling process until you acquire 100 values of . Construct a relative frequency distribution for these 100 sample means. Compare this distribution with the exact sampling distribution of found in part e of Exercise 6.3. [Note: The distribution obtained in this exercise is an approximation to the exact sampling distribution. However, if you were to repeat the sampling procedure, drawing two coins not 100 times, but 10,000 times, then the relative frequency distribution for the 10,000 sample means would be almost identical to the sampling distribution of x found in Exercise 6.3, part e.]

Exercise 6.3

The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:

a. List all the different samples of n = 2 measurements that can be selected from this population.

b. Calculate the mean of each different sample listed in part a.

c. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?

d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of found in part b, and find the probability of each. Then give the sampling distribution of the sample mean in tabular form.

e. Construct a probability histogram for the sampling distribution of .