Hypothesis testing arises naturally from the idea of confidence intervals discussed in Section 6.4: instead of constructing the interval and getting the idea about the uncertainty of the parameter, we could check, whether the sample agrees with our expectations or not. For example, we could test, whether the population mean is equal to zero based on our sample. We could either construct a confidence interval for the sample mean and see if zero is included in it (in which case it might indicate that zero is one of the possible values of the population mean), or we could reformulate the problem and compare some calculated value with the theoretical threshold. The latter approach is in the nutshell what hypothesis testing does.
In this Chapter we will discuss the main mechanism of hypothesis testing, then move to the discussion of type 0, I and II errors that might arise in the process. We then will discuss the idea of a Power of a Test and investigate what it is influenced by. After that we will discuss several basic popular parametric and non-parametric tests and how to select the most appropriate one between them.