\documentstyle[11pt,bj,txfonts]{article}

\frenchspacing

\begin{document}

\begin{center}
\bf 36-303: Sampling, Surveys \& Society\\
HW01: Due Thursday Feb 4, 2008 in class\\
{\em Please turn in HW on paper -- much easier for the TA to grade!}
\end{center}

\noindent\ul{\em Reminders:}
\begin{itemize}
\item Things to turn in:
\begin{itemize}
\item Due Next Tues: Team Assig. I.2 (revised two project proposals,
  using feedback emailed from me)
\item Due Next Thurs: This assignment 
\end{itemize}
\item Things to read:
\begin{itemize}
\item Done already: Groves Ch 1, 2
\item This week: 
\begin{itemize}
\item Groves, Ch 5
\item Groves, Ch 11 (pp 345-358)
\item Groves, Ch 4 (pp 93-102)
\end{itemize}
\item Use as a reference: Lohr, Appendix B
\end{itemize}
\item Clear, careful writing and interpretation of results is an
  important part of both weekly homeworks and the projects.  {\em I
    always expect neatly typed or neatly handwritten work.}
\item Always be judicious about including computer output and graphs:
  show enough that we can clearly see what you are doing, but not so
  much that we will get lost or bored leafing through your work!
\item Mostly homeworks will be submitted on paper in class.

\end{itemize}

\noindent\ul{\em Exercises to Turn In (there are 4 excercises):}
\begin{enumerate}

\item In 2008 Hart Research Associates, a public opinion survey
  organization, conducted a survey of American high school students
  for the Horatio Algier foundation.  The results were reported in a
  document entitled ``The State of Our Nation's Youth.''
\begin{enumerate}
\item Find the report and/or homepage for this survey on the web, and
  fill out, as completely as possible, a table like Tables 1.1--1.6 of
  the Groves text, for this survey.  You may (or may not) need to find
  additional web pages to get the information you need.
\item Please comment on any items in your table that would make it
  difficult to understand or believe the results of the survey
  (e.g. you couldn't get the information, or the information you got
  worries you in some way).  {\em If you are happy with all the information
  in your table, just say that.}
\item The survey gives an overall 95\% margin of error for the results.
  Find it, report it, and show that the method of calculating margin
  of error that we did in class produces approximately the same margin
  of error.
\end{enumerate}

% \item The Health Behavior in School-Age Children Study (HBSC) is an
%   international survey conducted under the auspices of the World
%   Health Organization.
% \begin{enumerate}
% \item Find the home page for this survey project on the web, and fill
%   out, as completely as possible, a table like Tables 1.1--1.6 of the
%   Groves text, for the the ``2001/02 HBSC International Report: Young
%   People's Health in Context''.  You may need to use links from the
%   homepage to get the information you need.
% \item Please comment on any items in your table that would make it
%   difficult to understand or believe the results of the survey
%   (e.g. you couldn't get the information, or the information you got
%   worries you in some way).  {\em If you are happy with all the information
%   in your table, just say that.}
% \end{enumerate}

\item In 2009, Hart Research Associates conducted a survey of US
  Employers for the Association of American Colleges and Universities'
  LEAP\footnote{Liberal Education and America's Promise} program,
  entitled ``Raising the Bar: Employers' Views on College Learning in
  the Wake of the Economic Downturn''.  Re-do question \#1 (all three
  parts!) for this survey.

% \item {\tt HireMeNow.com}, an online temporary and contract employment
%   agency, conducted a survey in 2007 to determine the reaction of
%   employers to online video resumes.  Find information from online
%   press releases and/or news reports about this survey, and re-do
%   question \#1 (both parts!) for it.

% \clearpage

\item Consider a set of $n$ trials involving independent and
identically distributed random variables $X_1, X_2,\ldots, X_n,$ where
the outcome of $1$ corresponds to success and the outcome of $0$
corresponds to failure,
and the probability of success on each trial is $p$.
\begin{enumerate}  
\item Show that $E(X_i)=p$, and $\Var(X_i)=p(1-p)$ for $i=1,2,\ldots,n$.

\item Let $Y= X_1+ X_2 +\ldots + X_n.$ Show that $E(Y)=np$, and
$\Var(Y)=np(1-p)$.

\item Let $\hat{p}=Y/n$.  Show that $E(\hat{p})=p$, and
$\Var(\hat{p})=p(1-p)/n$.
\end{enumerate}

\item We say that two discrete random variables are {\em independent}
  if $P[X=x,Y=y] = P[X=x]\times P[Y=y]$ for all specific values $x$
  and $y$ that $X$ and $Y$ could be.
\begin{enumerate}

\item The table below shows the distribution for two random variables
  $X$ abd $Y$.  For example, \\ $P[X=1, Y=3] = 3/8$.
\begin{center}\spacing{1.5}
\begin{tabular}{ccc}
$x$ & $y$ &  $P[X=x,Y=y]$ \\
\hline
 1 & 4 &  $\frac18$ \\
 1 & 3 &  $\frac38$ \\
 2 & 4 &  $\frac38$ \\
 2 & 3 &  $\frac18$
\end{tabular}
\end{center}
Use the information in the table to show whether $X$ and $Y$ are
independent, or not.

\item For any two discrete random variables $X$ and $Y$ (not
  necessarily the ones in part (a)), show that \underline{\bf If} $X$
  and $Y$ are independent, \underline{\bf then} $P[X=x|Y=y] = P[X=x]$,
  for any specific $x$ and $y$ that $X$ and $Y$ could be.

\end{enumerate}


% Following for a later hw assignment (hw2?)
%
% \item {\tt
%   http://www.cmu.edu/osp/regulatory-compliance/human-subjects.html}
%   lists CMU IRB application forms and various training materials for
%   ethical conduct of human subjects research.  Under ``Training''
%   there is a link to ``NIH Online Training''.
% \begin{enumerate}
% \item Follow the ``NIH Online Training'' link and take the free
%   training there (this will take 2 hours or less).
% \item {\bf Print (or save in a file) your Certificate of Completion}
%   at the end of the course.  Turn in a printed copy of your
%   Certificate of Completion with this homework.\\[1.2em]
%  {\em If you already
%     have an active certificate of completion from a course on ethical
%     treatment of human subjects in research, that you took earlier,
%     you can just attach a copy of that older certificate with your hw,
%     without taking the NIH training course.}
% \end{enumerate}
% (You can use the certificate of completion for several years, in any
 %future human subjects research approval process you may be involved in.)



\end{enumerate}

\end{document}
