4.1 Hypothesis testing
4.1.1 Introduction
If preferred, the reader may begin with the example at the end of this section, then return to the general theory at the beginning.
4.1.2 Classical hypothesis testing
Most simple problems in which tests of hypotheses arise are of the following general form. There is one unknown parameter θ which is known to be from a set Θ, and you want to know whether 
or 
where
Usually, you are able to make use of a set of observations 
whose density 
depends on θ. It is convenient to denote the set of all possible observations 
by 
.
In the language of classical statistics, it is usual to refer to
and to
and to say that if you decide to reject H0 when it is true then ...
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