Hypothesis testing is a key tool in statistical inference next to point estimation and confidence sets. All three concepts make an inference about a population based on a sample taken from it. Hypothesis testing aims at a decision on whether or not a hypothesis on the nature of the population is supported by the sample.

In the following we shortly run through the steps of a statistical test procedure and introduce the notation used throughout this book. For a detailed mathematical explanation please refer to the book by Lehmann (1997).

We denote a sample of size by , where the are observations of identically independently distributed random variables , . Usually some further assumptions are needed concerning the nature of the mechanism generating the sample. These can be rather general assumptions like a symmetric continuous distribution. Often a parametric distribution is assumed with only parameter ...

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