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\bf 36-303: Sampling, Surveys \& Society\\
HW02: Due Tue Feb 1, 2011 in class
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\noindent\ul{\em Reminders:}
\begin{itemize}
\item Things to do:
\begin{description}
\item[Also Due Tues Feb 1:] Team Assig. I.2: Elaborate your I.1
  proposals by adding sections for D, E, F and G on the
  ``project-schedule.pdf'' handout (available at 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, 2, 3
\item This week: Groves, Ch 5, Ch 11 (sections 1--6), Ch 4 (sections
  1--3)
\item Begin reading: Lohr, Appendix B (handout).
\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 Please answer the following questions:
\begin{enumerate}

\item Groves, Ch 5, p. 179, \#1.  Please list two specific advantages,
  and two specific disadvantages, for {\em each} method discussed.

% \item Which of the following modes of data collection is most likely
%   to produce question-order effects:
%   % like Groves Ch 5 p 179 \#4, but added web and reverse-coded
% \begin{itemize}
% \item Face-to-face
% \item telephone
% \item Mail-out/mail-back
% \item Web-based survey (like surveymonkey.com)
% \end{itemize}
% Why?

\item Groves, Ch 5, p. 179, \#5.

\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}
\end{enumerate}


\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 ``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.)

\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}

\end{enumerate}

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