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\title{Stat 185 - Review problems for Exam 1}
\author{}
\date{}

\begin{document}
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\noindent Our first exam is this coming Friday, September 22. 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 A random sample of registered 
	voters from Tampa, FL were asked if they support the DREAM Act, 
	a proposed law which would provide a path to citizenship for people brought illegally to the US as children.
	The survey also collected information on the political ideology of the respondents. The results of the survey by political ideology 
        are shown below as well as in figure \ref{mosaic}.
        \begin{center}
        \begin{tabular}{l l c c c c}
                                &                           & \multicolumn{3}{c}{\textit{Political ideology}} \\
        \cline{3-5}
                                &                           & Conservative  & Moderate  & Liberal   & Total \\
        \cline{2-6}
                                & Support & 			186            & 174       & 114       & 474 \\
                                & Don't support        & 151           & 161       & 52        & 364 \\
                                & Not sure             & 35            & 28         & 9         & 72 \\
        \cline{2-6}
                                & Total                     & 372           & 363       & 175       & 910
        \end{tabular}
        \end{center}
        \begin{enumerate}
        \item What percent of these Tampa, FL voters support the DREAM Act?
        \item What percent of these Tampa, FL voters who identify themselves as 
        conservatives are also in support the DREAM Act?
        \item Do political ideology and views on immigration appear to be independent? 
        Explain your reasoning.
        \end{enumerate}


	\item Given the data set $\{2, 3, 6, 3, 10, 2, 0, 4, 2, 2\}$,
	\begin{enumerate}
		\item Compute the corresponding five point summary
		\item Find the inter-quartile range
		\item Draw the corresponding box-plot
	\end{enumerate}
	
	\item Compute the mean and standard deviation of the set $\{8, 2, 1, 8, 3\}$.

\newpage

	\item According to \url{https://goo.gl/DanB3A}, Utah has the lowest percentage of adults who smoke at $9.1\%$. Turns out this is based on a CDC survey 
	named BRFSS. Let's suppose that there are 120 individuals in that survey.
	\begin{enumerate}
		\item Identify the population.
		\item Identify the sample.
		\item I don't actually believe the $9.1\%$ so I went down to Woody's Tavern and surveyed 11 customers. As it turned out, 5 of them smoked!
		Identify any problems that you see with my ``study''.
	\end{enumerate} 
	
	\item Suppose we are doing a study on the mercury concentration in adults' hair.  We announce the study in Asheville's local newspaper and get 205 people
	willing to participate in our study.  We take a snip of their hair and analyze it for mercury content and ask them to fill out a questionnaire about how many 
	servings of fish they consume on average in a week in order to find out how much eating fish contributes to the amount of mercury in the body.
	\begin{enumerate}
		\item What is the population?
		\item What type of sampling method was used?
		\item What problems do you see with the sampling method?
		\item What is the predictor variable and what is the response variable?
	\end{enumerate}


        \item Suppose that a standardized tests' scores are normally distributed with a mean of 1500 and a standard deviation of 300.
        \begin{enumerate}
          \item According to the normal rules of thumb, what percentage of test takers score 2400 or above?
          \item Use the normal table to compute the proportion of test takers whose scores are between 1400 and 1700.
        \end{enumerate}

	\item Suppose that data sets $X$ is a data set with mean $110$ and standard deviation $15$; $Y$ is a data set with mean $84$ and standard deviation $20$. Furthermore, $X$ and $Y$ have a correlation of $r=0.75$.
	\begin{enumerate}
		\item What is the regression line connecting $Y$ to $X$?
 		\item What value of $Y$ does the regression line predict if $X=85$?
	\end{enumerate}
\end{enumerate}


\begin{figure}[htbp]
\begin{center}
\includegraphics*{dream_act_mosaic.pdf}
\caption{The Mosaic plot for problem 1}
\label{mosaic}
\end{center}
\end{figure}

\end{document}  
