Consider the following population: {2, 3, 3, 4, 4}. The value of μ is 3.2, but suppos...

Consider the following population: {2, 3, 3, 4, 4}. The value of μ is 3.2, but suppose that this is not known to an investigator, who therefore wants to estimate μ from sample data. Three possible statistics for estimating μ are

Statistic 1: the sample mean,

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 μ and why?