Why Divide by n21? Let a population consist of the values 3, 6, 9. Assume that sam- ples of two values are randomly selected with replacement.
a. Find the variance s2 of the population {3, 6, 9}.
b. List the nine different possible samples of two values selected with replacement, then find the sample variance s2 (which includes division by n 2 1) for each of them. If you repeatedly select two sample values, what is the mean value of the sample variance s2?
c. For each of the nine samples, find the variance by treating each sample as if it is a population. (Be sure to use the formula for population variance, which includes di- vision by n.) If you repeatedly select 2 sample values, what is the mean value of the population variances?
d. Which approach results in values that are better estimates of s2: Part (b) or part (c)? Why? When computing variances of samples, should you use division by n or n 2 1?
e. The preceding parts show that s2 is an unbiased estimator of s2. Is s an unbiased estimator of u?