Three randomly selected households are surveyed. The numbers of people in the ho

Question

Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are the nine different samples (c). 2, 2 2, 4 2, 9 4, 2 4, 4 4, 9 9, 2 9, 4 9, 9 a. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. (Type integers or fractions. Use ascending order of the sample medians.) b. Compare the population median to the mean of the sample medians. Choose the correct answer below. A. The population median is equal to double the mean of the sample medians. B. The population median is equal to half of the mean of the sample medians. C. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). D. The population median is equal to the mean of the sample medians. c. Do the sample medians target the value of the population median? In general, do sample medians make good estimators of population medians? Why or why not? A. The sample medians do not target the population median, so sample medians make good estimators of population medians. B. The sample medians do not target the population median, so sample medians do not make good estimators of population medians. C. The sample medians target the population median, so sample medians make good estimators of population medians. D. The sample medians target the population median, so sample medians do not make good estimators of population medians.

Explanation / Answer

a) Median table:

b) Option D is correct.

c) Option C is correct.

Sample Median Probability 2 1/9 3 2/9 4 1/9 5.5 2/9 6.5 2/9 9 1/9

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