Question: A member of the state board of education wants to compare the proportions of National Board Certified (NBC) teachers in private high schools and in public high schools in the state. His study plan calls for an equal number of private school teachers and public school teachers to be included in the study. Let p1 and p2 be these proportions. Suppose it is desired to find a 99% confidence interval that estimates p1 - p2 to within 0.05.
a. Supposing that both proportions are known, from a prior study, to be approximately 0.15, compute the minimum common sample size needed.
b. Compute the minimum common sample size needed on the supposition that nothing is known about the values of p1 and p2.