Consider the following population: {2, 3, 3, 4, 4}. The value of m is 3.2, but suppose that this is not known to an investigator, who therefore wants to estimate m from sample data. Three possible statistics for estimating m are Statistic 1: the sample mean, x Statistic 2: the sample median Statistic 3: the average of the largest and the smallest values in the sample A random sample of size 3 will be selected without replacement. Provided that we disregard the order in which the observations are selected, there are 10 possible samples that might result (writing 3 and 3*, 4 and 4* to distinguish the two 3€™s and the two 4€™s in the population):

For each of these 10 samples, compute Statistics 1, 2, and 3. Construct the sampling distribution of each of these statistics. Which statistic would you recommend for estimating m and why?

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2, 3, 3 2, 3, 4 2, 3, 4* 2, 3*,4 2, 3, 4 2, 4,4* 3, 3, 4 3, 3*, 4 3, 4, 4 3, 4, 4*