Tests about a Population Mean: σ Known
In this section we discuss hypothesis tests about a population mean that are based on the normal distribution. These tests are called z tests, and they require that the true value of the population standard deviation σ is known. Of course, in most real-world situations the true value of σ is not known. However, the concepts and calculations of hypothesis testing are most easily illustrated using the normal distribution. Therefore, in this section we will assume that—through theory or history related to the population under consideration—we know σ. When σ is unknown, we test hypotheses about a population mean by using the t distribution. In Section 9.3 we study t tests, and we will revisit the examples of this section assuming that σ is unknown.
Chapter 9
Testing a “greater than” alternative hypothesis by using a critical value rule
In Section 9.1 we explained how to set up appropriate null and alternative hypotheses. We also discussed how to specify a value for α, the probability of a Type I error (also called the level of significance) of the hypothesis test, and we introduced the idea of a test statistic. We can use these concepts to begin developing a seven step hypothesis testing procedure. We will introduce these steps in the context of the trash bag case and testing a “greater than” alternative hypothesis.