28.1 Introduction

In Chap. 27, hypothesis tests for one mean were studied. In later chapters, hypothesis tests are discussed in other contexts, too.

The general approach to hypothesis testing is the same for any hypothesis test, and so some general ideas are discussed in this chapter. All hypothesis tests answer questions about unknown population quantities (such as the population mean \(\mu\)), based on sample statistics (such as the sample mean \(\bar{x}\)).

The sections that follow discuss:

The assumptions and forming hypotheses (Sect. 28.2).
The sampling distribution, and the expectations (Sect. 28.3).
The observations and the test statistic (Sect. 28.4).
Weighing the evidence for consistency: \(P\)-values (Sect. 28.6).
Wording conclusions (Sect. 28.7).

When raw data are provided, begin by producing graphical and numerical summaries of the data. The statistical validity conditions, which vary for different hypothesis tests, should always be checked to see if the test is statistically valid.