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Assume a population of 42 49 52 and 58 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 42 42 42 49 52 49 52 42 42 52 52 52 42 58 52 58 49 42 58 42 49 52 58 52 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 Sample Median Probability V A V V 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 49 49 58 49 OA The population median is equal to the mean of the sample medians OB 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 OC The population median is equal to half of the mean of the sample medians O D The population median is equal to 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 The complo medians do not forget the population median so sample medians are unbiased estimators because the mean of the sample medians does not 49 58 58 58 2

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