Chapter 8.1, Problem 9E

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. Three possible statistics for estimating μ are

Statistic 1: the sample mean, $\bar{x}$

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. If 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):

1. a. For each of these 10 samples, calculate the values of Statistics 1, 2, and 3.
2. b. Construct the sampling distribution of each of these statistics.
3. c. Which statistic would you recommend for estimating μ? Explain your reasoning.