A First Course in Statistics, 12th Edition

8.2 Determining the Sample Size

The sample sizes n₁ and n₂ required to compare two population proportions can be found in a manner similar to the method described in Section 7.4 for comparing two population means. We will assume equal sized samples (i.e., $n_1=n_2=n$) and then choose n so that $({\widehat{p}}_1- {\widehat{p}}_2)$ will differ from $(p_1- p_2)$ by no more than a sampling error SE with a specified level of confidence. We will illustrate the procedure with an example.

Example 8.3 Finding The Sample Sizes For Estimating $\mathbf{(}{\mathit{p}}_1\mathbf{-}{\mathit{p}}_2\mathbf{)}$: Comparing Defect Rates of Two Machines

Problem

1. A production supervisor suspects that a difference exists between the proportions p₁ and p₂ of defective items produced by two different machines. Experience has shown that the proportion ...