Chapter 5, Problem 5.53LM

Consider a sample statistic A. As with all sample statistics, A is computed by utilizing a specified function (formula) of the sample measurements. (For example, if A were the sample mean, the specified formula would sum the measurements and divide by the number of measurements.)

1. a. Describe what we mean by the phrase “the sampling distribution of the sample statistic A.”
2. b. Suppose A is to be used to estimate a population parameter θ. What is meant by the assertion that A is an unbiased estimator of θ? E (A) = θ
3. c. Consider another sample statistic, B. Assume that B is also an unbiased estimator of the population parameter α . How can we use the sampling distributions of A and B to decide which is the better estimator of θ?
4. d. If the sample sizes on which A and B are based are large, can we apply the Central Limit Theorem and assert that the sampling distributions of A and B are approximately normal? Why or why not?