ILLUSTRATION OF THE CENTRAL LIMIT THEOREM

Consider all samples of size 2 from a finite population that consists of the numbers 5, 6, 7, 8, 9, 10.

1. Show that the mean of the finite population is 7.5 and variance is 2.9167. Compute the standard deviation.

2. List all random samples of size 2 taken without replacement from this finite population and calculated the mean of each sample.

3. Construct the probability distribution of the sample means from the samples of size 2 enumerated in question 2.

4. Calculate the mean, variance, and standard deviation of the probability distribution obtained in question 3. Compare these results with the terms indicated by the Central Limit Theorem (in these computations use the finite correction factor for the variance/standard deviation since the population is of size variance).