The employee benefits manager of a small private university would like to estimate the proportion of full-time employees who prefer adopting the first (i.e., plan A) of three available health care plans in the forthcoming annual enrollment period. A reliable frame of the university’s employees and their tentative health care preferences are given in P8_25.XLS.

a. What sample size would be required for the benefits manager to be approximately 95% sure that her estimate of the proportion of full-time university employees who prefer adopting plan A is within 0.15 of the true proportion? Assume that her best estimate of the population proportion parameter p is 1/3.

b. How does the answer to part a change if the benefits manager wants her estimate to be within 0.25 of the actual population proportion? Explain the difference in your answers to parts a and b.