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 2, 3, and 10. Consider the values of 2, 3, and 10 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 10. The nine different samples are as follows: (2, 2), (2, 3), (2, 10), (3, 2), (3, 3), (3, 10), (10, 2), (10, 3), and (10, 10).
(i) Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability
distribution.
(ii) Compare the population standard deviation to the mean of the sample standard deviations.
(iii) Do the sample standard deviations target the value of the population standard deviation? In general, do standard deviations make good estimators of population standard deviation? Why or why not?