Three randomly selected households are surveyed as a pilot p

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 10. Consider the
values of 4, 6, and 10 to be a population. Assume that samples of size n = 2 are randomly
selected with replacement from the population of 4, 6, and 10. The nine different samples
are as follows:
(4, 4), (4, 6), (4, 10), (6, 4), (6, 6), (6, 10), (10, 4), (10, 6), 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?

Solution