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\title{Stat 185 - Review problems for Exam 3}
\author{}
\date{}

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\noindent Our third exam is next Monday, November 20. Here are a few problems to get you thinking.
There's a good chance that \textit{most} or even all of these problems will be represented on the exam.
There might be one or two more, as well.

\begin{enumerate}
	\item Students purchased 6 bags of potato chips marked 28.3 grams. Weighing the contents of each bag, they found the following masses:
	\begin{center}
        \begin{tabular}{c|c|c|c|c|c}
         29.3 & 28.2 & 29.1 & 28.7 & 28.9 & 28.5
        \end{tabular}
        \end{center}
        \begin{enumerate}
        	\item Perform a $t$-test to determine
		\begin{enumerate}
			\item Whether we should accept the 28.3 gram measurement with a $95\%$ level of confidence
			\item A 95\% confidence interval.
		\end{enumerate}
		\item What is the critical value $t^*$ for a 95\% level of confidence?
        \end{enumerate}

	\item Suppose that we'd like to compare the average incomes of chemistry professors vs math professors.
	A random sample of 12 chemistry professors found that their average salary was \$101,479 per year 
	with a standard deviation of \$4126.
	A random sample of 10 math professors found that their average salary was \$92,842 per year 
	with a standard deviation of \$3096.
	\begin{enumerate}
		\item Write down the hypothesis test.
		\item Compute the standard error for the problem.
		\item Compute the test statistic.
		\item Use a $t$-table to find the $t^*$-value for a 95\% level of confidence
		\item What is the conclusion of the test?
		\item Why shouldn't we use a normal table to compute a $p$ value?
	\end{enumerate}

	\item In a sample of 52 Republicans, 40 were for issue 1 and 12 against. In a sample of 79 Democrats, 65 were for issue 1 and 14 against.
	Let's use this data to explore whether there is a genuine difference in the views of Democrats and Republicans on issue 1 to a 95\% level of confidence.
	\begin{enumerate}
		\item Compute the observed proportions $\hat{p}_R$ and $\hat{p}_D$, as well as the difference $$\hat{p} = \hat{p}_D-\hat{p}_R.$$
		\item Compute the standard error.
		\item Compute the test statistic.
		\item Use a normal table to compute the $p$-value.
		\item State the conclusion of the test.
		\item Why was it OK to use a normal table?
	\end{enumerate}
	
	\item A random sample of 18 college texts compared their local bookstore price to their amazon.com price. 
	The data indicate that, on average, the local price minus the amazon price was \$22 with standard deviation of \$4.
	We are curious if the amazon price is generally \textit{less} than the book store price.
	\begin{enumerate}
		\item Write down the hypothesis test.
		\item Compute the standard error for the problem and test statistic.
		\item State what test you plan to use for this problem and why
		\item What is the conclusion of the test and what is your supporting evidence?
	\end{enumerate}

       \item A college statistics professor expects to assign grades in the following proportions
	\begin{center}\begin{tabular}{r|c|c|c|c|c}
		Grade & A & B & C & D & E \\
		\hline
		Expected Percentage & 10\% & 30 \% & 40\% & 20\% & 0\% \\
		Actual count & 3 & 6 & 8 & 1 & 0
	\end{tabular}\end{center}
	Perform a $\chi^2$ test to examine whether these grade counts agree with the expected grade counts.

	\item Data relating favorite outdoor activities is shown in table 1 below. Suppose I run a \texttt{chisq.test} command on this table and generate the following output:
	\begin{verbatim}
		Pearson's Chi-squared test
		X-squared = 10.424, df = 6, p-value = 0.1079
	\end{verbatim}
	\begin{enumerate}
		\item Draw a picture illustrating how \texttt{X-squared} and \texttt{p-value} fit together.
		\item What hypothesis statement is associated with this test?
		\item How should you interpret the $p$-value?
	\end{enumerate}
\end{enumerate}


\begin{table}[h]
\centering
\begin{tabular}{l|cccc}
  & NE & SE & NW & SW \\
 \hline             
Mountain Bike & 24 & 52 & 36 & 37 \\
Road Bike     & 32 & 42 & 38 & 45 \\
Rock Climb    & 19 & 37 & 28 & 55
\end{tabular}
\caption{Favorite outdoor activities by region}
\label{my-label}
\end{table}

\end{document}  
