Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

question 178

Essay

Solve the problem.
-Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later.
The numbers of people in the households are 3, 6, and 10. Consider the values of 3, 6, and 10 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 6, and 10.
The nine different samples are as follows:
(3, 3), (3, 6), (3, 10), (6, 3), (6, 6), (6, 10), (10, 3), (10, 6), and (10, 10). (i) Find the variance of each of the nine
samples, then summarize the sampling distribution of the variances in the format of a table representing the
probability distribution. (ii) Compare the population variance to the mean of the sample variances. (iii) Do the
sample variances target the value of the population variance? In general, do variances make good estimators of
population variances? Why or why not?