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\title{Stat 185 -Exam 1}
\author{}
\date{}

\begin{document}
\maketitle
\pagestyle{empty}
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\begin{flushright}
	Name:\underline{\hspace{2.2in}}
\end{flushright}

\noindent Please write all your solutions (answers with organized supporting work) on separate paper, put your name on this sheet, and staple it all together when you turn it in. \\
I don't plan to grade anything written on the exam sheet itself.

\begin{enumerate}
	\item A survey was conducted to study the smoking habits of NC residents. Below is a data 
        matrix displaying a portion of the data collected in this survey. Note that ``N/A'' refers to a missing component of the data.
        \begin{center}
        \scriptsize{
        \begin{tabular}{rccccccc}
        \hline
        	& sex 	 & age 	& marital 	& grossIncome 					     & smoke & amtWeekends	& amtWeekdays \\ 
        \hline
        1 	& Female & 42 	& Single 	& \$2600 			     & Yes 	 & 12 cig/day   & 12 cig/day \\ 
        2 	& Male	 & 44	& Single 	& \$9500 & No	 & N/A 			& N/A \\ 
        3 	& Male 	 & 53 	& Married   & \$7200 		     & Yes 	 & 6 cig/day 	& 6 cig/day \\ 
        \vdots & \vdots & \vdots & \vdots & \vdots 				             & \vdots & \vdots 	    & \vdots \\ 
        200 & Male  & 40   & Single 	& \$5,200   & Yes 	 & 8 cig/day 	& 8 cig/day \\   
        \hline
        \end{tabular}
        }
        \end{center}
        \begin{enumerate}
        \item What does each row of the data matrix represent?
        \item How many participants were included in the survey?
        \item Indicate whether each variable in the study is numerical or categorical. If numerical, identify as 
        continuous or discrete. If categorical, indicate if the variable is ordinal.
        \item What is the population under study?
        \item What is the sample?
        \end{enumerate}

     \item A 2010 survey asked 827 randomly sampled registered voters in California ``Do you support? Or 
        do you oppose? Drilling for oil and natural gas off the Coast of California? Or do you 
        not know enough to say?" Below is the distribution of responses, separated based on 
        whether or not the respondent graduated from 
        college.  \\[1.3mm]
        \noindent\begin{minipage}[c]{0.6\textwidth}
        \begin{enumerate}
        \item What percent of college graduates and what percent of the non-college graduates 
		in this sample oppose drilling for oil and natural gas off the Coast of California?
        \item Does support vs opposition for drilling appear to be independent of education?
        \end{enumerate}
        \end{minipage}
        \begin{minipage}[c]{0.4\textwidth}
        \begin{center}
        \begin{tabular}{l c c}
                    & \multicolumn{2}{c}{\textit{College Grad}} \\
        \cline{2-3}
                    & Yes       & No    \\
        \cline{1-3}
        Support     & 154       & 132   \\
        Oppose      & 180       & 126   \\
        Do not know & 104       & 131   \\
        \cline{1-3}
         Total      & 438       & 389       
        \end{tabular}
        \end{center}
        \end{minipage}
        
	\item Given the data set $\{3, -2,  5,  8,  3,  8,  4,  0,  1, -1\}$,
	\begin{enumerate}
		\item Compute the corresponding five point summary
		\item Find the inter-quartile range
		\item Draw the corresponding box-plot
	\end{enumerate}
	
	\item Let $X$ be the data set $\{3,4,6,7,10\}$.
	\begin{enumerate}
		\item Write down the formula showing that the mean of $X$ is $6$.
		\item Compute the standard deviation of $X$, again showing your work.
	\end{enumerate}

	\item On average, the 127 college football teams in Division I gained 5322 yards throughout the 2016 season with a standard deviation of 887 yards.
        \begin{enumerate}
          \item Use a normal model to estimate the number of teams that rushed more than 6000 yards.
          \item A histogram for this data is shown in figure \ref{fig:hist}. Based on the histogram, do you see any issues with using a normal model for this estimate?
        \end{enumerate}

	\item Continuing with the previous example on college football teams, suppose that the average Win/Loss percentage for teams was 52\%, with a standard 
	deviation of 20\%. Suppose also that the correlation between total yards gained and Win/Loss percentage is 0.69.
	\begin{enumerate}
		\item What is the regression line estimating Win/Loss percentage in terms of total yards gained?
 		\item What Win/Loss percentage does the regression line predict if the total yards gained is 6000?
	\end{enumerate}
\end{enumerate}


\begin{figure}[htbp]
\begin{center}
\includegraphics*[width=4in]{yards_hist.pdf}
\caption{A histogram of total yards gained by each team for the 2016 season}
\label{fig:hist}
\end{center}
\end{figure}


\end{document}  
