ABSTRACT
A hypothesis is a statement about an unknown state of nature. We describe the state of nature with the help of a statistical model. In our context a hypothesis is a specification of the supposed model. In other words: First we believe in a model and then we want to find out the truth about some more details within it. A test of a hypothesis is a procedure based on data to find out whether this hypothesis is true or not. We want that a test gives us the unique answer, like “the fixpoint in the space from which we can move the earth.” That, of course, is an absolute unrealistic dream. The data are random, so the test decision is random too. Nevertheless tests are useful. They give us random decisions, which imply the right answer with high probability. But it is very important to learn the theory behind testing procedures, to know the properties of a test in order to be able to interpret the test results right and carefully. In this chapter we take up two classical approaches for testing hypotheses:
providing evidence by the data for or against a hypothesis
testing as a two-action decision problem.
