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

question 36

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 2, 4, and 8. Consider the values of 2, 4, and 8 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 8.
The nine different samples are as follows: (2, 2), (2, 4), (2, 8), (4, 2), (4, 4), (4, 8), (8, 2), (8, 4), and (8, 8). (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?