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 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 medians of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution (II) Compare the population median to the mean of the sample medians (III)Do the sample medians target the value of the population median? in general, do medians make a good estimators of population medians? why or why not?

Explanation / Answer

(a) The medians of each of the nine samples, the sampling distribution of the medians in the format of a table representing the probability distribution

The sampling distribution of the medians in the format of a table representing the probability distribution

From the above table, Identify the LCF which is just greater than (N+1)/2 = (9+1)/2 = 5 the corresponding x value is Median. That is, Median = 4.5

(B) Population Median is 4 which is middle value of 1,4 and 8.

(C) NO, the sample Median (4.5) is not represent to population medina (4). So median is not good estimator to the population median. Sample mean is good estimator to the population median.

1st sample 2nd sample Median 1 1 1 1 4 2.5 1 8 4.5 4 1 2.5 4 4 4 4 8 6 8 1 4.5 8 4 6 8 8 8

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