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\begin{center}
\bf 36-303: Sampling, Surveys \& Society\\
HW01: Due Tue Jan 31, 2012 by 3:30 on Blackboard 
\end{center}

\noindent\ul{\em Announcements:}
\begin{itemize}
\item Please turn in all assignments (homework and project assignments!)
using the ``Turnitin'' tool on Blackboard.  {\em It is best to turn in a 
single pdf file for each assignment.}  You may turn in other formats, 
but if we cannot read it or figure it out, we won't grade it.
\end{itemize}

\noindent\ul{\em Reminders:}
\begin{itemize}
\item Things to do:
\begin{description}
\item[Also Due Thu Jan 31:] 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|.
\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
animportant 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 Remember that most homeworks and project assignments should be submitted as a single pdf using the ``Turnitin'' tool on Blackboard.

\end{itemize}

\hfil{\em [Exercises begin on next page]}
\clearpage

\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 In class we looked at a short article on the recent Pew survey of Mormons in America.  The link to the Pew Research Center reporting website for this survey is \\ \mbox{}\hfil {\tt http://www.pewforum.org/mormons-in-america/}. 
\begin{enumerate}
\item Fill out, as completely as possible, a table like Tables 
1.1--1.6 of the Groves text, for the the Pew survey on Mormons in America. 
You may need to use links from the page listed above 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 2011 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.  Be sure to name the report you use for this exercise so we can go read the same pdf report that you are reading.

% 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}



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% Human subjects stuff for hw02...


\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
``EducationRequirements'' 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 apage
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.)

