Bethany Alletzhauser
New member
Let a population consist of values 3, 6, 9. Assume that samples of two values are randomly selected WITH replacement.
a. Find the variance of the population (3, 6, 9).
b. List the nine different possible samples of the two values selected with replacement, then find the sample variance s^2 (which includes the division n-1) for each of them. If you repeatedly select two sample values, which is the mean of the sample variances s^2?
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 division by n). If you repeatedly select two samples, which is the mean value of the population variances?
d. Which approach results in values that are better estimates of the standard deviation^2. Part (b) or part (c)? Why? When computing variances of samples, which is the mean value of the population variances?
e. The preceding parts show that s^2 is an unbiased estimator of the standard deviation^2. Is s an unbiased estimator of the standard deviation?
a. Find the variance of the population (3, 6, 9).
b. List the nine different possible samples of the two values selected with replacement, then find the sample variance s^2 (which includes the division n-1) for each of them. If you repeatedly select two sample values, which is the mean of the sample variances s^2?
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 division by n). If you repeatedly select two samples, which is the mean value of the population variances?
d. Which approach results in values that are better estimates of the standard deviation^2. Part (b) or part (c)? Why? When computing variances of samples, which is the mean value of the population variances?
e. The preceding parts show that s^2 is an unbiased estimator of the standard deviation^2. Is s an unbiased estimator of the standard deviation?