Assume a population of 40, 45, 47 and 53

Assume a population of 40, 45, 4?, and 53. 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). 40,40 4045 40,47 4053 4540 45,45 45,47 4553 4140 47.45 4147 4753 5340 53,45 53,47 5353 a. Find the median of each of the sixteen samples, then summan'ze 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. 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. Choose the correct answer below. 0 A. The population median is equal to double the mean of the sample medians. O B. The population median is equal to half of the mean of the sample medians. O C. The population median is equal to the mean of the sample medians. O D. The population median is not equal to the mean of the sample medians [it is also not hail 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? 0 A. 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. O 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. O C. The sample medians target the population median, so sample medians are unbiased estimators, because the mean of the sample medians equals the population median. O D. The sample medians target the population median, so sample medians are biased estimators, because the mean of the sample medians equals the population median