\setcounter{ExampleCounter}{1}
Since $H_0$ and $H_1$ are contradictory, one (and only one) of them must be true.

\begin{itemize}
\item \text{}
\vspace{0.6in}

\item \text{}
\vspace{0.6in}

\item \text{}
\vspace{0.9in}

\item \text{}
\vspace{0.9in}

\end{itemize}

Medical test analogy: $H_0$ is that you don't have a disease
\begin{itemize}
\item \textbf{Type I Error:} \text{}
\vspace{0.3in}

\item \textbf{Type II Error:} \text{}
\vspace{0.3in}

\end{itemize}

Trial analogy: $H_0$ is that you're innocent (innocent until proven guilty)
\begin{itemize}
\item \textbf{Type I Error:} \text{}
\vspace{0.3in}

\item \textbf{Type II Error:} \text{}
\vspace{0.3in}

\end{itemize}

\paragraph{Summary:} \text{}
\vspace{0.9in}

\begin{example}{Error Types}
Suppose Frank tests his rock-climbing equipment, and $H_0$ is that his equipment is safe.\\

\paragraph{Type I Error:} \text{}
\vspace{0.9in}

\paragraph{Type II Error:} \text{}
\vspace{0.9in}

\end{example}

\begin{example}{Error Types}
The victim of a car accident is brought to the emergency room, and $H_0$ is that she is alive when she comes in.\\

\paragraph{Type I Error:} \text{}
\vspace{0.9in}

\paragraph{Type II Error:} \text{}
\vspace{0.9in}

\end{example}
\vfill
\pagebreak








