This chapter has explained how to compare two populations by using confidence intervals and hypothesis tests. First we discussed how to compare two population means by using independent samples. Here the measurements in one sample are not related to the measurements in the other sample. We saw that in the unlikely event that the population variances are known, a z-based inference can be made. When these variances are unknown, t -based inferences are appropriate if the populations are normally distributed or the sample sizes are large. Both equal variances and unequal variances t -based procedures exist. We learned that, because it can be difficult to compare the population variances, many statisticians believe that it is almost always best to use the unequal variances procedure.

Sometimes samples are not independent. We learned that one such case is what is called a paired difference experiment. Here we obtain two different measurements on the same sample units, and we can compare two population means by using a confidence interval or by conducting a hypothesis test that employs the differences between the pairs of measurements. We next explained how to compare two population proportions by using large, independent samples. Finally, we concluded this chapter by discussing how to compare two population variances by using independent samples, and we learned that this comparison is done by using a test based on the F distribution.