A First Course in Statistics, 12th Edition

6.8 A Nonparametric Test about a Population Median (Optional)

In Sections 6.4–6.5, we utilized the z- and t-statistics for testing hypotheses about a population mean. The z-statistic is appropriate for large random samples selected from “general” populations—that is, samples with few limitations on the probability distribution of the underlying population. The t-statistic was developed for small-sample tests in which the sample is selected at random from a normal distribution. The question is, How can we conduct a test of hypothesis when we have a small sample from a nonnormal distribution? The answer is: use a distribution-free procedure that requires fewer or less stringent assumptions about the underlying population—called a nonparametric ...