\documentclass[11pt,titlepage]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\allowdisplaybreaks

\jot=.2in \pagestyle{plain} \setlength{\topmargin}{-0.5in}
% \setlength{\footheight}{0 in}
\setlength{\textheight}{9.5in}
\setlength{\oddsidemargin}{-0.2in}
\setlength{\evensidemargin}{-0.1in}
\setlength{\textwidth}{6.7in}
\font\heada=cmbx10 scaled\magstep3
\font\headb=cmsl10 scaled\magstep1
\font\headc=cmr8
\pretolerance=10000
\setlength{\parindent}{2 em}

\begin{document}
\noindent {\heada Project 10 - Categorical Data Analysis}\\

\smallskip

\noindent {\headb Statistics 401: Fall 2007}\\
{\it Due Wednesday, May 2}
\bigskip

% 12.26 on page 538 is good!

\noindent Use R to complete this project. Attach all R commands used
to complete this project in an appendix. Annotate with the problem
number.   Label and reference all figures and tables.

\begin{enumerate}
\item {\em Science} in August 11, 2006 published a paper ``Public
Acceptance of Evolution."  Adults from 34 countries were asked
whether the statement ``Human beings, as we know them, developed
from earlier species of animals" was true or false, or whether the
the respondent was unsure or did not know. Turkey had the lowest
proportion of its population who thought that evolution is true
(about 25\%). The United States had the next lowest proportion who
believe that evolution is true. The results from a SRS of $n=1484$
US adults is given in the following table:

\begin{center}
\begin{tabular}{||c|c|c|c||}
  \hline
  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
  True & Not sure & False & Total
  \\\hline
   593 & 579  & 312 & 1484\\
  \hline
\end{tabular}
\end{center}

The {\em Science} paper reported that twenty years ago in 1985, the
proportion of the US population who believed in evolution was 0.45;
the proportion who were not sure was .07; and the proportion who
overtly rejected evolution was 0.48. Use a Goodness of Fit Test to
determine whether these proportions are different in today's US
population.

\begin{enumerate}
\item Give an unbiased estimate of $\pi_{\rm true}$, the proportion
of the US population in 2006 who believe that evolution is true.

\item Construct a bar chart to display the data. Include the plot in
your report.

\item State the appropriate hypotheses to be tested.
\item Check the assumptions.
\item Display a table of the expected counts.  Label it and refer to it from the text of your report.
\item Display a table of the $\chi^2$ contributions.  Label it and refer to it from the text of your report.

\item Give the test statistic value.
\item Give the distribution of the test statistic assuming ${\rm H}_0$ is true.
\item Give the $p$-value
\item Make a decision at $\alpha=.05$.
\item Draw a conclusion in the context of this problem.
\item Is a follow-up necessary?   Either way, explain why.  If appropriate, do the follow-up.   Explain
what output you are using and specify which proportion(s) appears to
be different than its hypothesized value.

\end{enumerate}


\item In March 25, 2005, {\em Animal Behavior} published Creel and Winnie's
``Responses of elk herd size to fine scale spatial and temporal
variation in the risk of predation by wolves."  This is MSU's own
Scott Creel of Bridger Ridge Run fame.  The paper hit national news
in January - so scientists DO get rich and famous - well OK, maybe
only kind of famous and not so rich - see the USA Today article at
the STAT401 web site.  In the paper, Creel and Winnie are studying
how far from the timber elk herds in the Greater Yellowstone
ecosystem (which includes Gallatin Canyon) aggregate when there are
wolves present. The following table shows the numbers of bulls, cows
and calves at three different ranges of distance (in meters) to the
timber when there are wolves present (from Table 1 in the {\em
Animal Behavior} paper):
\begin{center}
\begin{tabular}{||l|c|c|c|c|c||}
  \hline
  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
   & 0-30 & 31-100  & 101-300 & $>$ 300 & Totals\\\hline
  Bulls & 479 & 493 & 158 & 18 & 1148\\
  Cows & 454 & 517 & 192 & 53 & 1216 \\
  Calves & 86 & 108 & 25 & 9 & 228\\
  \hline
\end{tabular}
\end{center}

Is there an association between distances from the timber and the
type of elk?


\begin{enumerate}
\item Construct a bar chart to display the data. Include the plot in your report.
\item State the appropriate hypotheses to be tested.
\item Check the assumptions.  Assume that Creel and Winnie's data is
from a single SRS of elk.
\item Display a table of the expected counts.  Label it and refer to it from the text of your report.
\item Display a table of the $\chi^2$ contributions.  Label it and refer to it from the text of your report.

\item Give the test statistic value.
\item Give the distribution of the test statistic assuming ${\rm H}_0$ is true.
\item Give the $p$-value
\item Make a decision at $\alpha=.05$.
\item Draw a conclusion in the context of this problem.
\item \label{elkfollowup} Is a follow-up necessary?   Either way, explain why.  If appropriate, do the follow-up using the two highest $\chi^2$ contributions.   Explain
what output you are using and specify which population(s) and which
proportion(s) are different than the others.

\item Give an ecological explanation why the elk appear to behave
as the data suggests in \eqref{elkfollowup}.

\end{enumerate}

\item Read two articles: the April 20, 2007 AP article,
``Poll: Tragedy Hasn't Changed Views On Guns" and {\em Gallup
Poll's} 4/18/07 article ``Americans and Gun Control."  Both are
available at the STAT401 web site.

%Read the April 19, 2007 {\em McClatchy Newspaper} article,
%``Democrats unlikely to revisit gun-control legislation" available
%at the STAT401 web site.
%(http://www.cbsnews.com/stories/2007/04/20/virginiatechshooting/main2712826.shtml),
%(http://www.galluppoll.com/content/Default.aspx?ci=27229&pg=1):

The following table is from the AP-Ipsos poll reported in the AP
article, and the Gallup poll reported in the second article:

\begin{center}
\begin{tabular}{||l|c|c|c|c|c||}
  \hline
  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
   & More Strict & Unchanged & Less Strict & No opinion & Total\\\hline
  October, 2006 (Gallup) & 560 & 330 & 90 & 20 & 1000 \\
  April 2007 (AP-Ipsos) & 468 & 378 & 110 & 40 & 996\\
  \hline
\end{tabular}
\end{center}

Does the evidence suggest that American's opinions towards gun
control has changed since the mass murder at Virginia Tech last
week?


\begin{enumerate}
\item What proportion of respondents in October 2006 favored
stricter gun control?  What proportion of respondents in April 2007
favored stricter gun control?
\item Construct a bar chart to display the data. Include the plot in your report.
\item State the appropriate hypotheses to be tested.
\item Check the assumptions.
\item Display a table of the expected counts.  Label it and refer to it from the text of your report.
\item Display a table of the $\chi^2$ contributions.  Label it and refer to it from the text of your report.

\item Give the test statistic value.
\item Give the distribution of the test statistic assuming ${\rm H}_0$ is true.
\item Give the $p$-value
\item Make a decision at $\alpha=.05$.
\item Draw a conclusion in the context of this problem.
\item \label{gunfollowup} Is a follow-up necessary?   Either way, explain why.  If appropriate, do the follow-up.   Explain
what output you are using and specify which categories exhibit the
association.
\item Comment on any similarities or differences between your results to \eqref{gunfollowup},
and the following statement in the AP article:

\begin{verse}
\noindent Though Monday's horrific killings of 32 students and
teachers — plus the gunman — were fresh in people's minds, there was
scant movement in their attitude toward gun laws. Forty-seven
percent said firearm controls should be tightened, 38 percent said
they should remain unchanged and 11 percent said they should be
loosened -- about the same as in a January survey.
\end{verse}


\end{enumerate}






\end{enumerate}

\end{document}