SUMMARY

Business research often requires the analysis of two populations. Three types of parameters can be compared: means, proportions, and variances. Except for the F test for population variances, all techniques presented contain both confidence intervals and hypothesis tests. In each case, the two populations are studied through the use of sample data randomly drawn from each population.

The population means are analyzed by comparing two sample means. When sample sizes are large (n ≥ 30) and population variances are known, a z test is used. When sample sizes are small, the population variances are known, and the populations are normally distributed, the z test is used to analyze the population means. If the population variances are unknown, and the populations are normally distributed, the t test of means for independent samples is used. For populations that are related on some measure, such as twins or before-and-after, a t test for dependent measures (matched pairs) is used. The difference in two population proportions can be tested or estimated using a z test.