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\title{Stat 185 - In class problems \\
\large Monday, November 6}
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\begin{enumerate}		
	\item Suppose that we'd like to compare the average salaries of web developers vs database managers.
	A random sample of 45 web developers found that their average salary was \$78,434 per year 
	with a standard deviation of \$3126.
	A random sample of 52 database managers found that their average salary was \$82,942 per year 
	with a standard deviation of \$4096.
	\begin{enumerate}
		\item Write down the hypothesis test.
		\item Compute the standard error for the problem.
		\item Compute the test statistic.
		\item Use the our normal table to find the $p$-value. \\
		And, why is it OK to use a normal table?
		\item What is the conclusion of the test?
	\end{enumerate}

	\item In this problem, we're going to play with the data here: \url{https://goo.gl/1ky5Qs}. If you go to that URL, 
	you should see some data that you can copy and paste into an R command like  so:\\
	\texttt{df = read.csv(text = "{\color{blue}past-your-data-here}")} \\
	\begin{enumerate}
		\item Based on recent class presentations, can you guess what the data represents?
		\item Figure \ref{fig:boxplots} two side-by-side box and whisker plots - one for our data and one that's an imposter.
		Can you tell which is which?
		\item Find a $95\%$ confidence interval for \texttt{df\$younger\_times}.
		\item Find a $95\%$ confidence interval for the difference between \texttt{df\$younger\_times} and \texttt{df\$older\_times}.
	\end{enumerate}
\end{enumerate}

\begin{figure}[htbp]
\begin{center}
\includegraphics*[width=6in]{boxplots.pdf}
\caption{Box and whisker plots for two data frames}
\label{fig:boxplots}
\end{center}
\end{figure}


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