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, 6, and 7. Consider the values of 3, 6, and 7 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 6, and 7. The nine different samples are as follows:
(3, 3), (3, 6), (3, 7), (6, 3), (6, 6), (6, 7), (7, 3), (7, 6), and (7, 7).
(i) Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of size n = 2 are randomly selected.
(ii) Does the mean of the sample proportions target the value of the population proportion?
(iii) Does the sample proportion make a good estimator of the population proportion?