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 5, 8, and 11. Consider the values of 5, 8, and 11 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 5, 8, and 11. The nine different samples are as follows:
(5, 5), (5, 8), (5, 11), (8, 5), (8, 8), (8, 11), (11, 5), (11, 8), and (11, 11). (i) Find the range of each of the nine samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution.
(ii) Compare the population range to the mean of the sample ranges. (iii) Do the sample ranges target the value of the population range? In general, do ranges make good estimators of population ranges? Why or why not.?