Question

Three randomly selected households are surveyed. The numbers of people in the households are 2, 4​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 2, 4​, and 12. Listed below are the nine different samples. Complete parts​ (a) through​ (c). 22​,22   22​,44   22​,1212   44​,22   44​,44   44​,1212   1212​,22   1212​,44   1212​,1212 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. Sample Median Probability ▼ nothing ▼ 4 6 3 nothing ▼ 8 4 6 nothing ▼ 10 14 7 nothing ▼ 8 16 13 nothing ▼ 12 18 24 nothing ​(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 the mean of the sample medians. B. The population median is equal to double the mean of the sample medians. C. The population median is equal to half of the mean of the sample medians. D. 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). 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 do not make good estimators of population medians. B. The sample medians target the population​ median, so sample medians do not make good estimators of population medians. C. The sample medians do not target the population​ median, so sample medians make good estimators of population medians. D. The sample medians target the population​ median, so sample medians make good estimators of population medians. Click to select your answer(s).

Answer 1

sample
median	probability
2	1/9
3	2/9
4	1/9
7	2/9
8	2/9
12	1/9

D. 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).

A. The sample medians do not target the population​ median, so sample medians do not make good estimators of population medians.