Three Randomly Selected Households Are Surveyed as a Pilot Project

Essay

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, 8, and 9. Consider the values of 3, 8, and 9 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 8, and 9. The nine different samples are as follows: (3, 3), (3, 8), (3, 9), (8, 3), (8, 8), (8, 9), (9, 3), (9, 8), and (9, 9). (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?