

\subsection{\bf Hypothesis Testing---III}

\begin{slide}
\begin{itemize}
\item We define $r$ as region in $Y$ space where we will deem
hypothesis (1) to be true and (0) to be false.

\item In the remaining region of $Y$ space, $R-r$, ($R$ is total $Y$
range) we will take (0) to be true, (1) to be false.

\item This scheme is characterized by two constants:

\item 1.\ $\alpha = $ level of significance or size of test $=
{\displaystyle\int\limits_r} P^{\ (0)}_Y (y) dy$.  

\begin{description}
\item{$\bullet$} $\alpha$ is chance that (0) will be declared false
when it is in fact true.
\end{description}

\item 2.\ $\beta = {\displaystyle\int\limits_{R-r}} P^{\ (1)}_Y (y) dy$
is the contamination, i.e.,

\begin{description}
\item{$\bullet$} $\beta$ is chance that (0) will be declared true when
it is in fact false.
\end{description}

\item Clearly, it depends on the application for the
balance between efficiency $1-\alpha$ and contamination $\beta$.
\end{itemize}
\end{slide}

