Assume a population of 46, 50, 52, and 57. 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).50,5746,4646,5046,5246,5750,4650,5050,5252,4652,5052,5252,5757,4657,5057,5257,57a. 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 samplemedians.Sample MedianProbabilitySample MedianProbability(Type integers or simplified 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.O A. The population median is equal to half of 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 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 unbiased estimators of population medians? Why or why not?O A. The sample medians target the population median, so sample medians are biased estimators, because the mean of the sample medians equals the population median.B. The sample medians do not target the population median, so sample medians are unbiased estimators, because the mean of the sample medians does not equal the population median.C. The sample medians do not target the population median, so sample medians are biased estimators, because the mean of the sample medians does not equal the population median.D. The sample medians target the population median, so sample medians are unbiased estimators, because the mean of the sample medians equals the population median.

Solution a. Sample medians are obtained below: sample 1 sample 2 Median 46 46 Excel function=MEDIAN(A1:B1):46 52 46 49 46 50 48 52 50 51 46 52 49 52 52 52 46 57 51.5 52 57 54.5 50 46 48 57 46 51.5 50 50 50 57 50 53.5 50 52 51 57 52 54.5 50 57 53.5 57 57 57 Mean = 51.25 Sample Sample median Probability Sample Sample median Probability 46, 46 46 0.0625 50, 52 51 0.125 46, 50 48 0.125 50, 57 53.5 0.125 46, 52 49 216=0.125 52, 52 52 0.0625 46, 57 51.5 0.125 52, 57 54.5 0.125 50, 50 50 0.0625 57, 57 57 0.0625b. Population values are 46, 50, 52, 57. Median of (46, 50, 52, 57) is 51==MEDIAN(D14:D17). Mean of sample medians is 51.25. Hence, the median of population is not equal to the mean of the sample medians. Correct option is D. c. The sample median do not target the population median. So, sample medians are unbiased estimators .