A note on the determination of sample sizes for hypergeometric distributions

Sample size determination for testing the hypothesis of equality of two proportions against an alternative with specified type I and type II error probabilities is considered for two finite populations. When two finite populations involved are quite different in sizes, the equal size assumption may not be appropriate. In this paper, we impose a balanced sampling condition to determine the necessary samples taken without replacement from the finite populations. It is found that our solution requires smaller samples as compared to those using binomial distributions. Furthermore, our solution is consistent with the sampling with replacement or when population size is large. Finally, three examples are given to show the application of the derived sample size formula.