A First Course in Statistics, 12th Edition

7.4 Determining the Sample Size

You can find the appropriate sample size to estimate the difference between a pair of parameters with a specified sampling error (SE) and degree of reliability by using the method described in Section 5.5. That is, to estimate the difference between a pair of parameters correct to within SE units with confidence level $(1-\alpha ),$ let $z_{\alpha /2}$ standard deviations of the sampling distribution of the estimator equal SE. Then solve for the sample size. To do this, you have to solve the problem for a specific ratio between $n_1$ and  $n_2.$ Most often, you will want to have equal sample sizes—that is, $n_1=n_2=n.$ We will illustrate the procedure with two examples.

Example 7.6 Finding the Sample Sizes for Estimating $({\mu }_1-{\mu }_2)$ —Comparing ...