Three Randomly Selected Households Are Surveyed as a Pilot Project $n = 2$

question 94

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 4, 6, and 9. Consider the values of 4, 6, and 9 to be a population. Assume that samples of size $n = 2$ 2 are randomly selected with replacement from the population of 4, 6, and 9. The nine different samples are as follows:
(4, 4), (4, 6), (4, 9), (6, 4), (6, 6), (6, 9), (9, 4), (9, 6), and (9, 9).
(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?