Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

Essay

Solve the problem.
-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 1, 4, and 8. Consider the values of 1, 4, and 8 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 8.
The nine different samples are as follows: (1, 1), (1, 4), (1, 8), (4, 1), (4, 4), (4, 8), (8, 1), (8, 4), and (8, 8). (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?