Chapter 9.2, Problem 21BB

Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 − α can be found by using the following expression:

$E=z_{\alpha /2}\sqrt{\frac{p_1{q}_1}{n_1}+\frac{p_2{q}_2}{n_2}}$

Replace n₁ and n₂ by n in the formula above (assuming that both samples have the same size) and replace each of p₁, q₁, p₂, and q₂ by 0.5 (because their values [ire not known). Solving for n results in this expression:

$n=\frac{z_{\alpha /2}^2}{2E^2}$

  Use this expression to find the size of each sample if you want to estimate the difference between the proportions of adult men and women who are college graduates. Assume that you want 90% confidence that your error is no more than 0.02.