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

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 10. Consider the values of 2, 4, and 10 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 10.
The nine different samples are as follows: (2, 2), (2, 4), (2, 10), (4, 2), (4, 4), (4, 10), (10, 2), (10, 4), and (10, 10). (i)
Find the mean of each of the nine samples, then summarize the sampling distribution of the means in the format
of a table representing the probability distribution. (ii) Compare the population mean to the mean of the sample
means. (iii) Do the sample means target the value of the population mean? In general, do means make good
estimators of population means? Why or why not?