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\bf 36-303: Sampling, Surveys \& Society\\
HW01: Due Tue Jan 25, 2010 in class
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\noindent\ul{\em Reminders:}
\begin{itemize}
\item Things to do:
\begin{description}
\item[Also Due Tues jan 25:]  Team Assig. I.1 (two project proposals).
  See handouts ``project-schedule.pdf'' and ``project-ideas.pdf'' on
  the class website, \verb|http://www.stat.cmu.edu/~brian/303|.
\item[Will be assigned in HW02:] {\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 ``Education
  Requirements'' there is a link to ``CITI's website'', the training
  website of the Collaborative Institutional Training Initiative (CITI).
\begin{enumerate}
\item Follow the ``CITI's website'' link. 
\item Select Carnegie Mellon University as your ``participating
  institution'' and create an account.
\item When you have created an account you will be directed to a page
  titled "Select Curriculum" which displays a list of courses on Human
  Subjects Research: Biomedical Research Investigators; Social \&
  Behavioral Investigators, and IRB Members. Choose the {\bf Social \&
    Behavioral Investigators} human subjects research module.
\item The course may take a few hours to complete but can be done over
  a period of time.  When you complete the course, CITI will e-mail
  your completion record to the CMU IRB.
\item From the CITI main menu, you can also print a copy of the
  completion report for this course.  {\em Turn in a printed copy of
    your completion report with this homework.}
\end{enumerate}

{\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 CITI training course.}\\[1em] 
(You can use the certificate of completion for several years, in any
future human subjects research approval process you may be involved
in.)

\end{description}
\item Things to read:
\begin{itemize}
\item Done already: Groves Ch 1
\item This week: Groves, Ch's 2 and 3
\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}

\hfil{\em [Exercises begin on next page]}
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\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 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 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 International Report ``2001/02
  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 For several years, the American Automobile Association (AAA) has
  conducted a survey called the Traffic Safety Culture Index.  The
  2010 report (as well as reports from earlier years) can be found at
  {\tt http://www.aaafoundation.org/reports}.  Re-do question \#1
  (both parts!) for the AAA Traffic Safety Culture Index 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 Groves, Ch 1, p 36, \#6.  I think the most recent report is the
%  ``Grade 12 Reading and Mathematics 2009 National and Pilot State
%  Results''.
%
% NAEP cause of changes from prev years -- save for later.

\item Groves, Ch 2, p. 65, \#1. Be sure to give \ul{\em separate} answers
  in part (d) for {\em sampling error} and for {\em coverage error}. 

\item Groves, Ch 2, p. 67, \#7. % why do we care about nonrespondents?

\end{enumerate}

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Computational problems for later...

\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}

