\setcounter{ExampleCounter}{1}

\paragraph{Step 1:} State the hypotheses.
\begin{center}
\begin{tabular}{c | c}
$H_0$ & $H_1$\\
\hline
& \\
$\mu_1 = \mu_2$ & $\mu_1 \neq \mu_2$\\
$\mu_1 \leq \mu_2$ & $\mu_1 > \mu_2$\\
$\mu_1 \geq \mu_2$ & $\mu_1 < \mu_2$
\end{tabular}
\end{center}

\paragraph{Step 2:} Calculate the test statistic.
\[z = \dfrac{(\overline{x_1}-\overline{x_2})-(\mu_1-\mu_2)}{\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}}\]

\paragraph{Step 3:} Calculate the p value.
\begin{center}
\texttt{normalcdf(-1000000,z,0,1)} or similar
\end{center}

\paragraph{Step 4:} Draw a conclusion.
\begin{itemize}
\item If $p < \alpha$, reject $H_0$.
\item If $p > \alpha$, fail to reject $H_0$.
\end{itemize}

\subsection{Using Your Calculator}
Since the population standard deviation is \emph{known}, use the \texttt{2-SampZTest} in the \texttt{TESTS} menu.  You can either enter the raw data or the summary statistics.
\begin{center}
\begin{tabular}{c c}
\includegraphics[height=1.75in]{Calc2ZTestData}
&
\includegraphics[height=1.75in]{Calc2ZTestStats}
\end{tabular}
\end{center}

Again, make sure to keep the two populations separate, enter the appropriate alternate hypothesis, and selecte either \texttt{Calculate} or \texttt{Draw}.
\vfill
\pagebreak

\begin{example}{Comparing Two Engines}
The mean RPMs of two competing engines are to be compared.  Ten engines of each type are randomly assigned to be tested.  Both populations have normal distributions, and the following table summarizes the details.
\begin{center}
\begin{tabular}{c c c}
Engine & Sample Mean RPM & Population Standard Deviation\\
\hline
\\
1 & 1500 & 80\\
2 & 1600 & 90
\end{tabular}
\end{center}
Do the data indicate that Engine 2 has a higher mean RPM than Engine 1?  Test at a 5\% level of significance.
\vspace*{6.5in}
\end{example}
\vfill
\pagebreak