Three randomly selected households are surveyed as a pilot project for a larger

Question

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 8. Consider the values of 2, 3, and 8 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 8. The nine different samples are as follows: (2, 2), (2, 3), (2, 8), (3, 2), (3, 3), (3, 8), (8, 2), (8, 3), and (8, 8). (a) Find the range of the nine samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution. (b) Compare the population range to the mean of the sample ranges. (c) Do the sample ranges target the value of the population range? In general, do ranges make good estimators of population ranges? Why or why not?

Explanation / Answer

a)

b)

Mean of sample range is 3. Whereas population range is 6 (8-2).

c)

The sample ranges do not target the value of the population range. So sample ranges do not make good estimators of population range.

Sample range Probability distribution 0 3/9 1 2/9 6 2/9 5 2/9

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