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\begin{center}
\large\bf
36-303: Sampling, Surveys and Society\\
Exam 1 SOLUTIONS\\
Thu Feb 17, 2011
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\em

\begin{enumerate}

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\item\pts{20} {\em Multiple Choice (4 parts).  For each part, circle the
  roman numeral of the one best answer.}

\begin{enumerate}

\item\pts5 Following are some of the most important decisions that can
  be made as part of designing a survey.  Which one \ul{\bf doesn't
    belong}?  % groves, p 33
\begin{enumerate}
\item[\fbox{v.}] {\em None of the above (I.e., all are important
  decisions in survey design).}
\end{enumerate}

\item\pts5 It is possible to construct a representative sample without
  random sampling, but it is more difficult to argue that it is really
  representative.
\begin{enumerate}
\item[\fbox{i.}] {\em  True}
\end{enumerate}

\item\pts5 {\em Beneficence} is a basic ethical principle for research
  with human subjects.  Which of the following is \ul{\bf not} an aspect
  of beneficence? % groves, p 378
\begin{enumerate}
\item[\fbox{iii.}] {\em Make sure the subjects get the benefit of some compensation
  for their participation.}
\end{enumerate}

\item\pts5 Two important fractions in sample surveys are the {\em sampling
  fraction} $n/N$ and the {\em response rate} $r/n$ (where $N$ is the
  population size, $n$ is the intended sample size, and $r$ is the
  number in the sample that actually responded).  Which of the
  following is \ul{\bf not} true, for a simple random sample without
  replacement from the target population?

\begin{enumerate}

\item[\fbox{iv.}] {\em You can get a more representative sample by
  increasing $n$, regardless of the response rate. }

\end{enumerate}


\end{enumerate}

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\item\pts{18} Time-wasting survey\ldots
\begin{enumerate}
\item\pts{6} What is the {\bf Target Population} for this survey?

\em The target population appears to be \fbox{American workers}. 

{\bf NOTE:} Other target populations can get full credit, but the
target population should \ul{not} be confined to people who access AOL
and/or salary.com websites.

\em


\item\pts{6} 
Do you think the {\bf coverage error} for this sampling method, for
the target population in part (a), is high or low?  Give at least one
reason for your answer.

\em

The coverage error is likely ot be \fbox{large}.  The set of workers
who access AOL and salary.com websites is not the same as the set of
all American workers.  For example perhaps these kinds of respondents
are already more unhappy with their jobs (which is why they are
checking a salary website, e.g.). 

{\bf NOTE:} Any \ul{well-reasoned} answer that is consistent with your
answer in (a) will get credit.

\em

% \hfil{\sl[Continued on next page]}
% \clearpage

\item\pts{6} Give two other potential problems with the sampling
  method chosen for this survey.  Use words from class to name the
  problem, and then use specific ideas from class, and/or evidence
  from the survey methodology paragraph, to explain what you mean.\\

\ul{Problem 1}:

\em

\fbox{Nonrandom sample.}  Therefore, there is no guarantee that any of
the statistical formulae---about sample size, confidence intervals,
etc. that we use in analysis of surveys---are valid.

{\bf NOTE: Other answers can get full credit as long as they are
  well-reasoned.}

\em

\vspace*{0.25in}

\ul{Problem 2}:

\em

\fbox{Self-selection bias.}  Workers only come to the salary.com
website, for example, if they are curious about salaries.  In
addition, they may waste time on the internet more than other workers
(they voluntarily are looking at AOL or salary.com instead of working,
right now!).

{\bf NOTE: Other answers can get full credit as long as they are
  well-reasoned.}

\em


\end{enumerate}

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\item\pts{18} {\sl[continuation]} Replicate study among 4732 employees
  (faculty and staff) on the Pittsburgh campus of CMU.
\begin{enumerate}

\item\pts{6} Suppose you are able to get a simple random sample of 100
  CMU Pittsburgh employees, and (remarkably) all of them respond to
  your survey.  You find that 40\% of the respondents list web surfing
  as their \#1 distraction.  Construct a confidence interval for $p$,
  the true proportion of Pittsburgh Campus CMU employees for whom web
  surfing is the \#1 distraction.  {\em (Hint: The SD is
    $\sqrt{p(1-p)}$.)} \\

\em

{\bf NOTE:} This should have been for a 95\% CI, and a simple random
sample without replacement.  These corrections were made in class
during the exam.\\

The CI is $(\hat p - ME, \hat p + ME)$, where $\hat p = 0.40$ and 
\begin{eqnarray*}
   ME & = & (1.96)\times FPC \times \frac{SD}{\sqrt{n-1}} \\
   & = & (1.96)\times \sqrt{1 -
     100/4732}\times\frac{\sqrt{.5(1-.5)}}{\sqrt{100-1}}\\
   & = & 0.097
\end{eqnarray*}
where we have taken the ``worst case'' $SD = \sqrt{p(1-p)} =
\sqrt{.5(1-.5)} = .5$.

Therefore the CI is (0.40 - 0.097, 0.40 + 0.097) or \fbox{$(0.303, 0.497)$}.

{\bf NOTE:} Small variations, such as using $2\approx 1.96$, or using
  $p=.40$ insteaad of $p=.5$ in the SD calcuation, are fine.

\em

% \hfil{\sl[continued on next page]}

% \clearpage

\item\pts{6} Suppose you wanted to get a confidence interval in part
  (a) with a margin of error of 0.05 (5\%).  What would the sample
  size need to be, if you were doing simple random sampling {\em with
    replacement}?

\em

{\bf NOTE:} This should have been for a 95\% CI.  This was corrected
in class during the exam.\\

The sample size should be at least
\begin{eqnarray*}
    n_0 & = & \frac{(1.96)^2 (SD)^2}{ME^2} \\
    & = & \frac{(1.96)^2 (\sqrt{.5(1-.5)})^2}{(.05)^2}\\
    & = & 384.16
\end{eqnarray*}
So the sample size should be \fbox{$n=385$} (rounding up to the next
whole person).

\em

\item\pts{6} Suppose you wanted to get a confidence interval in part
  (a) with a margin of error of 0.05 (5\%).  What would the sample
  size need to be, if you were doing simple random sampling {\em
    \ul{without} replacement}?

\em

{\bf NOTE:} This should have been for a 95\% CI.  This was corrected
in class during the exam.\\

The sample size should be at least
\begin{eqnarray*}
\frac{Nn_0}{N+ n_0} & = & \frac{(4732)(384.16)}{4732+384.16} ~ = ~ 355.31
\end{eqnarray*}
so the sample size should be at least \fbox{$n= 356$}, again rounding
up to the nearest whole person.

\em

\end{enumerate}

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% \clearpage

% Groves, p. 401, #2, modified.

\item\pts{20} Informed consent situations...

\em

{\bf NOTE:} For each problem below I give a possible ``good'' answer.
Other ``good'' answers could get full credit, if they are
well-reasoned, well-written, and include all relevant plausible
assumptions, etc.

\em

\begin{enumerate}
\item\pts{5} As a part of a face-to-face survey, the interviewer is
  asked to observe how many books are visible in the respondent's
  living room.
%\ans
\begin{enumerate}\em
\item[]\rule{1em}{1pt} Approve.
\item[]\ul{X~} Disapprove.  {\em Please Change the Following:}\\

Please obtain informed consent before counting the books, and make
sure the respondent knows that the book count will be part of the data
collected.\\

\item[] Reason:\\

Informed consent should be obtained before collecting {\em any} data
from a respondent.\\

{\bf NOTE:} If you assumed informed consent had already been obtained
prior to counting the books, it would be OK to approve this study.

\end{enumerate}

\item\pts{5} As part of a telephone survey, the first few moments of
  the interaction between the interviewer and the potential respondent
  are recorded, for use as examples in teaching other interviewers.
%\ans
\begin{enumerate}\em
\item[]\rule{1em}{1pt} Approve.
\item[]\ul{X~} Disapprove.  {\em Please Change the Following:}\\

Recording should not begin until informed consent is obtained (and the
informed consent request should include the information that the rest
of the interview will be recorded).\\

Training tapes would need to be obtained in some other way.\\

\item[] Reason:\\

Informed consent should be obtained before collecting {\em any} data
from a respondent.

\end{enumerate}

% \clearpage

\item\pts{5} Before approaching a parent-child pair for a face-to-face
  interview to study parent-child interations, the interviewer makes
  structured observations of how the parent and child interact in a
  public park.  The observations are used to select parent-child pairs
  for the sample, and become part of the data collected for each
  parent-child pair in the sample.  
%\ans
\begin{enumerate}\em
\item[]\rule{1em}{1pt} Approve.
\item[]\ul{X~} Disapprove.  {\em Please Change the Following:}\\

Parent-child pairs should be selected for the sample, using a method
involving a prior rule that is not based on any information about the
individual respondents.  For example: ``choose every 5$^{th}$
parent-child pair''.\\

\item[] Reason:\\

Again, informed consent should be obtained before collecting {\em any}
data from a respondent.\\

In addition, a weakness of this design is that there can be
interviewer bias in selecting respondents if a prior rule is not
employed (this is not an informed consent problem, but it is a
weakness in the study design).

\end{enumerate}


\item\pts{5} As part of a study of whether voter intentions are
  affected by the sponsor of the survey, some respondents are told
  that the sponsor is an organization different from the one actually
  conducting the survey.
%\ans

\em

{\bf NOTE:} Here are two possible full-credit answers.  (Other
well-reasoned and well-grounded answers would also be acceptable.)

\em

\begin{enumerate}\em
\item[]\rule{1em}{1pt} Approve.
\item[]\ul{X~} Disapprove.  {\em Please Change the Following:}\\

The study cannot be done as proposed.\\

\item[] Reason:\\

Informed consent cannot be obtained if potential respondents are
misinformed.

\end{enumerate}

\vspace*{2em}

\begin{enumerate}\em
\item[]\rule{1em}{1pt} Approve.
\item[]\ul{X~} Disapprove.  {\em Please Change the Following:}\\

You must debrief the respondent after the interview, revealing the
misdirection and the purpose of the study.\\

\item[] Reason:\\

If the goal of the study is to measure whether voter intentions are
affected by the sponsor of the survey, then this misdirection is the
only way to get to the goal.  We can minimize the risks of
misdirection, relative to the benefits, by informing the respondents
after the fact.  [However, note that misdirection studies are
  typically much harder to get approved by IRB's!]

\end{enumerate}


\end{enumerate}

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% \clearpage

% Groves, p. 288, \#2, modified.

\item\pts{24} Revising survey questions\ldots

\def\ans{
\begin{enumerate}
\item\pts3 A Potential Problem:
\vspace{1.25in}
\item\pts3 Suggestion(s) For Rewrite:
\vspace{1.5in}
\end{enumerate}
}

\begin{enumerate}

\item {\em ``What was your income in the past year?\\
  \hspace*{1.8in} Answer here:
  \rule{3in}{1pt}''}   
%\ans
\item\pts3 A Potential Problem:

\em

Any one of the following (or other well-reasoned answers) could
receive credit:
\begin{itemize}
\item The term ``income'' is not well-defined.
\item The term ``in the past year'' is not well-defined.
\end{itemize}

\em

\item\pts3 Suggestion(s) For Rewrite:

\em

Any one of the following (or other well-reasoned answers) could
receive credit:
\begin{itemize}
\item Rewrite to specify more clearly what counts as ``income''
\item Rewrite to clarify which dates should be included in ``in the
  past year''.
\item Rewrite as a series of ``bounded recall'' questions:
\begin{itemize}
\item Are you paid an annaul salary or houry?
\item If hourly, how much did you earn in the past week?  Was that
  typical?  If not, what are your typical weekly earnings?  [then the
    survey worker can multiply by 50 or 52 weeks if desired.]
\item If salary, what is your base annual salary?  Are you also
  elegible for bonuses or other increases?  If so, did you receive any
  since Feb 1, 2010?
\end{itemize}
etc.
\end{itemize}

\em

\end{enumerate}

\item {\em ``Do you favor or oppose universal health care in the
  United States?''}  
%\ans
\begin{enumerate}
\item\pts3 A Potential Problem:

\em

One possible answer: this question is too general. we don't know
exactly what is going through respondent's mind when he/she answers.

\em

\item\pts3 Suggestion(s) For Rewrite:

\em

One possible fix: focus on a specific universal health care option:
``As you know, the {\em Affordable Health Care For America Act} which
was passed by Congress in 2009 and signed into law by President
Obama makes the following provisions
\begin{itemize}
\item prohibiting health insurers from refusing, or charging
  differently for, coverage based on patients' medical histories or
  gender
\item requiring most employers to provide, and most individuals to
  carry, coverage meeting certain minimum standards, or pay a surtax
  for non-compliance
\end{itemize}
Do you generally support or oppose this approach to universal health
care?''

\em

\end{enumerate}

\item {\em ``I am happier than usual these days. (Circle the best
  answer below)\\
\begin{tabular}{rcccl}
                1 & 2 & 3 & 4 & 5  \\
Strongly agree    &   &   &   &    Strongly disagree.''
\end{tabular}
% \begin{description}
% \item[]\rule{1em}{1pt} Strongly agree.
% \item[]\rule{1em}{1pt} Generally agree.
% \item[]\rule{1em}{1pt} Neither agree nor disagree.
% \item[]\rule{1em}{1pt} Generally disagree.
% \item[]\rule{1em}{1pt} Strongly disagree.''
% \end{description}
}%
%\ans
\begin{enumerate}
\item\pts3 A Potential Problem:

\em
Two possible problems (either alone, or some other well-reasoned
answer, could get full credit):
\begin{itemize}
\item We usually don't know what is going through respondents' minds
  with general, as opposed to specific, questions.
\item Middle categories (\#3 above) in Likert items gives respondents a
  chance to ``weasel out'' of answering the question.
\end{itemize}
\em

\item\pts3 Suggestion(s) For Rewrite:

\em
Some possible fixes (either alone, or some other well-reasoned
answer, could get full credit):
\begin{itemize}
\item Precede the general question with some specific ones: ``I am
  generally happier in my work these days''\ldots{} ``I am generally
  happier at home these days''\ldots{} ``I am generally happier with
  my spouse/significant other/family these days''\ldots{} etc.
\item Focus the time period: ``I am generally happier in the past
  month than I have been since the beginning of 2010''\ldots{} etc.
\item Take out the middle category (\#3) so respondents are forced to
  take an agree or disagree choice.
\end{itemize}
\em

\end{enumerate}

\item {\em ``What kind of music do you listen to when you study?\\
\begin{tabular}{p{2in}p{2in}}
\begin{itemize}
\item[]\rule{1em}{1pt} Rap.
\item[]\rule{1em}{1pt} Classical.
\end{itemize}
&
\begin{itemize}
\item[]\rule{1em}{1pt} Classic Rock.
\item[]\rule{1em}{1pt} Industrial Music.
\end{itemize}
\end{tabular}
}%
%\ans
\begin{enumerate}
\item\pts3 A Potential Problem:

\em
Two possible problems (either alone, or some other well-reasoned
answer, could get full credit):
\begin{itemize}
\item Not enough different categories of music.
\item Closed questions may fail to get the ``true'' response if it is
  missing among the many categories listed.
\end{itemize}
\em

\item\pts3 Suggestion(s) For Rewrite:

\em
Two possible fixes (either alone, or some other well-reasoned
answer, could get full credit):
\begin{itemize}
\item Add more categories of music.
\item Add an open-ended ``\rule{1em}{1pt} Other, please write type of
  music here: \rule{5em}{1pt}'' option at the end.
\end{itemize}
\em

\end{enumerate}

\end{enumerate}

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\end{document}

