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%% Supermarkets, Highways, and Oil Production: Statistics and Social Justice
\title{Residential Proximity to Major Highways}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%      h i g h w a y s
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%  highways contingency table, independence

\section*{Highways Classwork 1:  Contingency tables, Independence} 
Use the Highways article to answer the following questions.
\begin{enumerate}
\item 11,337,933 people make up 3.7\% of the total US population. Using that information, what is the total population of the US?
     \vspace{.5 in}
     

\item Consider the two populations labeled Non-Hispanic White and Non-Hispanic Black. Of these two, which population had more people living within 150 meters of a major highway? Which population had a larger percentage of people living within 150 meters of a major highway? Which of those statistics do you think is more meaningful in this conversation? Why?
     \vspace{.5 in}
     

\item Approximately how many people in the US speak primarily Spanish in their households?
     \vspace{.5 in}
     

\item How do the authors define the "Poor" characteristic? What how many people in the US, in total, are classified as "Poor" under this definition?
     \vspace{.5 in}
     

\item Using the information from the table found in the article, fill in the blanks to complete the following contingency table, {\bf Table 1}.  This compares people's proximity to major highways to the language predominantly spoken in their home.  Each percentage shown is of the row total. 
 \begin{table}[htb]
\begin{tabular}{| l    | r    | r  | r   |}
\hline
 Language & \multicolumn{2}{|c|}{Proximity} & Total \\
   & $<150$ m  &  $>150$ m   &   \\ 
\hline 
English only   &  7,513,304 (3.3\%)  &  220,162,575 (96.7\%)	   &    227,675,879 (100\%) \\
Spanish	& 1,805,261 (5.1\%)   &   &  \\
Other	& 1,059,572 ((4.9\%)   &   &  \\
Total         &     10,378,137    &   &  \\
\hline
\end{tabular}
\end{table}
     

\item Notice that the number you found for "total" in the first column (10,378,137) differs a bit from the "Total" number found in the table in the article (11,337,933). Why do you think this is?
     \vspace{.5 in}
     


\item Repeat each of the counts from Table 1.  Then divide each by the 
{\bf table total} and express as a percent. Record below in  {\bf Table 2}.
 \begin{table}[htb]
\begin{tabular}{| l    | r    | r  | r   |}
\hline
 Language & \multicolumn{2}{|c|}{Proximity} & Total \\
   & $<150$ m  &  $>150$ m   &   \\ 
\hline 
English only   &  7,513,304 (\underline {\hspace {.3 in}} \%)  &  220,162,575 (\underline {\hspace {.3 in}} \%)	   &    227,675,879 (\underline {\hspace {.3 in}} \%) \\
Spanish	& 1,805,261 (\underline {\hspace {.3 in}} \%)   &   &  \\
Other	& 1,059,572 ((\underline {\hspace {.3 in}} \%)   &   &  \\
Total         &     10,378,137  ((\underline {\hspace {.3 in}} \%)      &   &  \\
\hline
\end{tabular}
\end{table}

\newpage
\item What proportion of the US population primarily speaks Spanish in their home?
     \vspace{.5 in}
     


\item What proportion of predominantly Spanish-speakers live close to a major highway?
     \vspace{.5 in}
     


\item Of the people who live close to a major highway, what proportion of them are predominantly Spanish-speakers?
     \vspace{.5 in}
     


\item Two variables are {\bf independent }if the conditional distribution for one variable remains unchanged with respect to the other variable. We will calculate what the distribution {\em would be} if we were to {\bf assume independence}. To do this, first enter the marginal distributions (Total row at the bottom, Total column on the right), and the table total from Table 2.  Then ignore the other values in Table 2; instead, fill in the value for (Row Total) X (Column Total)/(Table Total) . These are {\em expected counts} under the assumption of independence. Round values to 1 decimal place.  Record below in  {\bf Table 3}.
\begin{table}[htb]
\begin{tabular}{| l    | r    | r  | r   |}
\hline
 Language & \multicolumn{2}{|c|}{Proximity} & Total \\
   & $<150$ m  &  $>150$ m   &   \\ 
\hline 
English only   &    &  	   &    227,675,879 \\
Spanish	&    &   &  \\
Other	&    &   &  \\
Total         &     10,378,137    &   &  \\
\hline
\end{tabular}
\end{table}

\item Compare the counts in Table 2 and the expected counts in Table 3.  Are they reasonably close? Do you think there is some evidence that Language and Proximity are independent?  Explain briefly.  

\end{enumerate}




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