Assume a population of 47, 53, 56, and 60. Assume that samples of size n=2 are r

Question

Assume a population of 47, 53, 56, and 60. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through (c).

47,47 47,53 47,56 47,60 53,47 53,53 53,56 53,60 56,47 56,53 56,56 56,60 60,47 60,53 60,56 60,60

A. Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order of the sample medians.

Sample Median, Probability (Type integers or simplified fractions. Use ascending order of the sample medians.)

B. Compare the population median 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?

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?

Explanation / Answer

50

B) The population median is 53, but the mean of the sample medians is 54. The values are not equal.

C)The sample medians do not target the population median of 6, so samplemedians do not make good estimators of population medians.

Sample number Median 1 47 2

50

3 51.5 4 53.5 5 50 6 53 7 54.5 8 56.5 9 51.5 10 54.5 11 56 12 58 13 53.5 14 56.5 15 58 16 60

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