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\bf 36-303: Sampling, Surveys \& Society\\
HW04: Due Tue Feb 21, 2012 on Blackboard
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\noindent\ul{\em Reminders:}
\begin{itemize}
\item {\bf FIRST MIDTERM HAS BEEN MOVED TO MAR 1} (one week later than
  originally planned).  If you have a conflict with the new date 
  please email me {\em soon} to make other arrangements.
\item Things coming up:
\begin{description}
\item[Due Thu Feb 23:] Team Working Agreement.
\begin{itemize}
\item Read and do the exercises in the twa.pdf file available at
  \verb|http://www.stat.cmu.edu/~brian/303|. 
\item Turn in a completed team working agreement
  \begin{itemize}
  \item On paper and signed by everyone on your team.  Every team
    member should also have a signed copy.
  \item Submit a copy on Blackboard to me.
  \end{itemize}
   \end{itemize}
\item[Due Thu Mar 01:] Team Assig. II.4
  \begin{itemize}
    \item Turn in revised versions of A, B, C, D, E, F, and G for the single
      project you will do this semester.  Details in
      ``project-schedule.pdf'' handout (available at the class
      website,\\ \verb|http://www.stat.cmu.edu/~brian/303|).
   \end{itemize}
    \item[Due Thu Mar 08:] IRB (some teams only)
   \begin{itemize}
   \item If your team have chosen a project with human subjects (people are the 
       units of your population) then your team must complete an IRB application 
       (see link at \verb|http://www.stat.cmu.edu/~brian/303|).  You must
       turn this in to me on blackboard (not the IRB), by {\bf Thu Mar 8}.
   \item If your survey does not involve human respondents, you do not need 
       to complete an IRB form.
\end{itemize}
\end{description}
\item Things to read:
\begin{itemize}
\item You should be reading Lohr, Appendix B (handout, also available
  at class website).
\item For lectures Feb 21 \& 23: Groves, Ch's 7 \& 8.
\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 Blackboard.

\end{itemize}

\noindent\ul{\em Exercises to Turn In (there are 2 groups of exercises):}
\begin{enumerate}

\item[] (See next page)

% \item Groves, Ch 2, pp. 64--65. \#1. % \#5. 
% (already asked in hw02)



% \ item Groves, Ch 5, p. 179, \#1.  Please list two specific advantages,
%   and two specific disadvantages, for {\em each} method discussed.
% (already asked in hw02)
  
\clearpage

\comment{ % already asked in hw02

\item Suppose you want to do a survey of undergraduates on the
  Pittsburgh campus of Carnegie Mellon.  You are considering three
  possible modes of data collection:
  % somewhat likke Groves Ch 5, p 181, \#17
\begin{description}
\item[Email] Email 100 students in C-Book and invite them to take your
  surveymonkey.com survey.
\item[Facebook] Offer the survey to 100 CMU undergrads on Facebook.
\item[Fence] Stop 100 people who look like undergrads, between
  Daugherty and the Fence on campus during the noon hour; ask them the
  questions orally if they agree to be interviewed.
\end{description}
\begin{enumerate}
\item Rank the three modes from greatest to least, in likely coverage error
\item Rank the three modes from greatest to least, in likely nonresponse error
\item Rank the three modes from greatest to least, in likely measurement error
\end{enumerate}
If you think your rankings need {\em short} explanations, feel free to provide them.

}

\item For the following, do not provide responses based on politics,
  social desirability, etc.  Instead, provide analytic responses based
  on the principles outlined in Groves, Ch 7, and/or in class.
\begin{enumerate}
\item Groves, Ch 7, p. 255 \#1.

\item Groves, Ch 7, pp. 255--256, \#5.

\item Groves, Ch 7, p. 256, \#6.

\item Groves, Ch 7, pp 256--257, \#8.  
\end{enumerate}

\item Recall the ``Randomized response'' model, from lecture, for the
  question:
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\fbox{\parbox{4in}{
Flip a coin, but don’t tell me whether it’s heads or tails.
\begin{itemize}
\item If heads, answer truthfully: have you ever cheated in a CMU class?
\item If tails, answer truthfully: is the last digit of your SSN odd?
\end{itemize}
}
}
\end{center}
Recall from lecture that 
\[
   \pi = \frac{\lambda - (1/2)\cdot(1-p)}{p}
\]
where $p=P[Heads]$; $\pi=P[Cheat]$; and $\lambda=P[Yes]$.  Consider a
SRS of $n$ students \ul{\em with replacement}\footnote{Surveys are
  seldom conducted this way, but it is easier for the math.}.  Let
$\hat\lambda$ be the fraction of ``Yes'' answers in the survey, and
let $\hat\pi = (\hat\lambda - \frac12(1-p))/p$.
\begin{enumerate}
\item Show that $E[\hat \pi]=\pi$.
\item Express $Var(\hat\pi)$ in terms of $Var(\hat\lambda)$ and show
  that, as $p$ gets closer and closer to 1, $Var(\hat\pi)$ gets closer
  and closer to $Var(\hat\lambda)$.
\item Suppose you use a fair coin, so that $p=\frac12$, and you think
  the true rate of cheating on campus is around 0.10.  How large a
  sample would you need, so that a 95\% confidence interval for $\pi$
  would be only 0.02 wide?
\end{enumerate}



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