Chapter 5, Problem 5.64ACB

Study of why EMS workers leave the job. A study of full-time emergency medical service (EMS) workers published in the Journal of Allied Health (Fall 201 1) found that only about 3% leave their job in order to retire. (See Exercise 3.45, p. 158.) Assume that the true proportion of all full-time EMS workers who leave their job in order to retire is p = .03. In a random sample of 1,000 full-time EMS workers, let $\hat{p}$ represent the proportion who leave their job in order to retire.

1. a. Describe the properties of the sampling distribution of $\hat{p}$.
2. b. Compute $P\left(\hat{p}\prec .05\right)$. Interpret this result.
3. c. Compute $P\left(\hat{p}\succ .025\right)$. Interpret this result.