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\savebox{\namebox}{Exam 1 Solutions}
\markboth{March 1, 2012}{\usebox{\namebox}}
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\savebox{\datebox}{\hbox to 0pt{\llap{36-303: Sampling, Surveys
\& Society}{}}}
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\begin{enumerate}

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% \clearpage

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

\begin{enumerate}

\item\pts5 When making a public report on a survey, which of the following
  is \ul{\bf not} required?
\begin{enumerate}

% \item Who sponsored it, who carried it out.

% \item Sample size and precision (SE) of estimates.

\item[\fbox{iii}] The name of the statistical package used to do the analyses.

% \item Target population, sampling frame, sampling method, response
%   rates.

\end{enumerate}


\item\pts5 Which of the following statements is \ul{\bf most correct}:
\begin{enumerate}

% \item If you do not have a random sample, it cannot be a
%   representative sample.

% \item The only valid random sampling for surveys is sampling without
%   replacement.

\item[\fbox{iii}] It is possible to construct a representative sample without
  random sampling, but it is more difficult to argue that it is really
  representative.

% \item If the sample is random, it is representative, regardless of the
%   response rate.

\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 Avoid harming the subjects if possible.
% \item Maximize possible benefits and minimize possible harms, to  subjects.
% \item Do not do the research if the benefit does not outweigh
% the
%   risks.
% \item Decide when to do a study because the benefits outweigh the
% risks to subjects; and when to forego a study because the risks 
%  outweigh the benefits.
\item[\fbox{iii}] Make sure the subjects get the benefit of some
  compensation for their participation.
% \item None of the above (I.e., all are aspects of beneficence).
\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 You can force the standard error of sample estimates to be zero
%   by making the sampling fraction large enough, as long as the
%   response rate is equal to 1.

% \item To decrease variability in sample estimates, increase the
%   sampling fraction.

% \item To decrease possible bias in sample estimates, increase the
%   response rate.

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

\end{enumerate}


\end{enumerate}


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% \clearpage

% Grave p 288, #5, slightly modified

\item\pts{20} ~

\begin{enumerate}\em

\item\pts{5} During the past four weeks, beginning on [date 4 weeks ago] and 
ending today, have you done any exercise, including sports, physically 
active hobbies, and aerobic exercises, but not including any
activities carried out as part of your job or in the course of
ordinary housework?
\begin{description}

\item[\rule{1.2em}{1pt}] This item is OK as-is.
\item[\hbox to 0pt{~X}\rule{1.2em}{1pt}] This item may not be OK.  I
  want to ask the person who is trying these items the following
  question, to get information to improve this item:

\end{description}

{\rm 

Here are some possible probes:
\begin{itemize}
\item Are there any kinds of exercise that you can think of, that are
  not included in the question yet?
\item How are you thinking about exercise involved in getting to and
  from work (e.g. biking)?
\item Do you know what aerobic means?
\item Do you have any trouble remembering your exercise habits for the
  past month?
\end{itemize}
etc.

}


\item\pts{5} How many times a week do you have milk, butter or other 
dairy products?
\begin{description}

\item[\rule{1.2em}{1pt}] This item is OK as-is.
\item[\hbox to 0pt{~X}\hbox to 0pt {~X}\rule{1.2em}{1pt}] This item
  may not be OK.  I want to ask the person who is trying these items
  the following question, to get information to improve this item:

\end{description}

{\rm 

Here are some possible probes:
\begin{itemize}
\item Can you list other dairy products that the question may be
  referring to?
\item Dairy products are often ingredients in other foods.  How would
  you answer the question if you consumed one of these foods, but no
  dairy products directly?
\item Do you think the amount dairy products consumed should affect
  your answer?
\item What period of time did you use to answer the question? This
  past week?  An ``average'' week for you?  How does an ``average''
  week compare to this past week's consumption?
\end{itemize}
etc.

}

% \item\pts{x} Living where you do now and meeting the expenses you 
% consider necessary, what would be the smallest income (before any deductions) 
% you and your family would need to make ends meet each month?
% \begin{description}
% 
% \item[\rule{1.2em}{1pt}] This item is OK as-is.
% \item[\rule{1.2em}{1pt}] This item may not be OK.  I want to ask 
% the person who is trying these items the following question, to 
% get information to improve this item:
% 
% \end{description}
% 
% \vspace*{\fill}


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


\item\pts{5} Some people feel the US federal government should take 
action to reduce the national debt, even if it means unemployment would 
go up a lot.  Others feel the government should take action to reduce
the rate of unemployment even if it means the national debt would go 
up a lot.  Where would you place yourself on the following 7-point scale?
\begin{center}
\begin{tabular}{*{7}{p{0.6in}}}
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\multicolumn{3}{l}{Reduce} & & \multicolumn{3}{r}{Reduce} \\
\multicolumn{3}{l}{Debt} & & \multicolumn{3}{r}{Unemployment} \\
\end{tabular}
\end{center}
\begin{description}

\item[\rule{1.2em}{1pt}] This item is OK as-is.
\item[\hbox to 0pt{~X}\rule{1.2em}{1pt}] This item may not be OK.  I
  want to ask the person who is trying these items the following
  question, to get information to improve this item:

\end{description}

{\rm 

Here are some possible probes:
\begin{itemize}
\item Do you know what the national debt is?
\item{} [If person marks middle category (4):] Did you mark that
  because you're truly neutral, because you don't know, don't want to
  reveal your opinion, or \ldots
\item{} [If person marks any other category:] Did you find it
  difficult to place yourself on this scale?  Are there too many/too
  few categories?
\end{itemize}
etc.

}

\item\pts{5} During the past 12 months, since [date], about how many
days did illness or injury keep you in bed more than half the day? 
Include days while you were an overnight patient in a hospital.
\begin{description}

\item[\rule{1.2em}{1pt}] This item is OK as-is.
\item[\hbox to 0pt{~X}\rule{1.2em}{1pt}] This item may not be OK.  I
  want to ask the person who is trying these items the following
  question, to get information to improve this item:

\end{description}

{\rm 

Here are some possible probes:
\begin{itemize}
\item Is it difficult to remember as far back as a year?  Let's try
  this month by month (or quarter by quarter etc.) and see if that
  changes your answer by much\ldots{} 
\item If you stayed overnight in a hospital for one night, did you
  think of counting that as one day or two?
\end{itemize}
etc.

}


\end{enumerate}


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% \clearpage

% Situational survey question...

\item\pts{20}\label{p:hospitals} 
The American Hospital Association (AHA)\ldots
%
\begin{enumerate}\em

\item\pts{2} What is the {\em target population} for this survey?

{\em Target population is apparently \ul{All community hospitals} (or
  community hospital CEOs, or a similar answer).}


\item\pts{2} What are the {\em units} in the target population?

{\em The units are \ul{hospital CEO's} (or the hospitals themselves,
  or similar\ldots).}

\item\pts{2} What is the {\em sampling frame}?

{\em The sampling frame is \ul{the list of fax and email addresses}
  that they used to distribute the survey.}

\item\pts{2} What {\em sampling method} was used?

{\em 
No ``sampling method'' was used.  Or you could say they tried to
implement a census. 
}

\item\pts{2} What {\em method of data collection} was used to contact
units in the sample and collect data from them?

{\em 
This was a self-administered questionaire (SAQ), emailed or faxed to
the respondents, that the respondents had to return (presumably by the
same methods).  [Any reasonable subset of this answer is OK.]
}

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

\item The press release reports that {\sf ``99.5\% of hospitals
reported experiencing one or more drug shortage in the last six
months and nearly half of the hospitals reported 21 or more drug
shortages.''}
\begin{enumerate}
\item\pts{5} Do you think this is useful information for the AHA?  
Why or why not?

{\em

This is very useful information for the AHA to have.  Here are some
possible reasons:
\begin{itemize}
\item As a headline it is great for promoting the AHA, getting
  contributions, getting hospitals to join th AHA etc.
\item If the survey results are valid (unbiased) and reliable (low
  uncertainty/variability in the results) then it reflects a serious
  problem in hospitals.
\end{itemize}

Another acceptable answer might be: ``This is NOT useful information
for the AHA because it is not a scientifically valid survey.''
Possible reasons could include 
\begin{itemize}
\item No random sampling
\item Only CEO's with an axe to grind would self-select to return the
  survey form
\item No nonresponse followup
\item Not clear their frame actually has good coverage for the target
  population (the hospitals in the frame are probably AHA members, e.g.).
\end{itemize}
etc.

}


\item\pts{5} Do you think this is a scientifically valid inference
about the target population?  Explain carefully why or why not, 
using \ul{\em at least two} concepts from the lecture notes or textbook.

{\em

Here are some reasons (need two):
\begin{itemize}
\item No random sampling
\item Self-selection bias in returning the surveys
\item No nonresponse followup
\item Not clear their frame actually has good coverage for the target
  population (the hospitals in the frame are probably AHA members, e.g.).
\end{itemize}
etc.

}


\end{enumerate}

\end{enumerate}


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% \clearpage
\
% continuation of the hospital survey

\item\pts{25} \ldots assume that the AHA survey is a {\em simple random 
sample (SRS) without replacement}\ldots

\begin{enumerate}\em

\item\pts{10} 17\% of hospitals in the sample reported that patient 
treatment was delayed because of a drug shortage.  Calculate a 95\% 
confidence interval for the same percentage in the population, based 
on the 820 responses in the sample.

{\em

We want the confidence interval to be 
\[
       (0.17 - 2\sqrt{1 - n/N}\cdot SD/\sqrt{n},~
       0.17 + 2\sqrt{1 - n/N}\cdot SD/\sqrt{n})
\]
where
\begin{itemize}
\item $\sqrt{1-n/N} = \sqrt{1-820/5100} = 0.92$
\item $SD \approx \sqrt{0.17(1-0.17)} = 0.38$
\item $\sqrt{n} = \sqrt{820} = 28.64$
\end{itemize}
So the interval is
\[
     (0.17 - 2(0.92)(0.38)/28.64,~
     0.17 + 2(0.92)(0.38)/28.64) = 
     (0.15,~ 0.19)
\]
[if you used 1.96 instead of 2, the interval would be the same].
}


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

\item\pts{5} What is the margin of error (ME) in part (a)?

{\em 
The ME is $2(0.92)(0.38)/28.64 = 0.02$ (or just the half-width of the
interval in part (a).
}

\item\pts{10} Suppose we only want a ME of 0.01.  What should the 
sample size be?

{\em 

Using the estimate 0.17 from above, the SRS with replacement sample
size would be
\[
    n \geq n_0 = \frac{(2)^2(0.17\cdot(1-0.17))}{(0.01)^2} = 5644 % 2822
\]
and then the sample size for SRS without replacement would be 
\[
    n \geq \frac{(5100)(5644)}{5100+5644} = 2679.11~(or~2680)
\]

{\em Note: } If we do not believe 0.17 is a good estimate then we
might use the worst-case value 0.5 instead.  This leads to 
\[
    n \geq n_0 = \frac{(2)^2(0.5\cdot(1-0.5))}{(0.01)^2} = 10000 % 5000
\]
and 
\[
    n \geq \frac{(5100)(5000)}{5100+5000} = 3377.48~(or~3378)
\]

}

{\bf Note:} the ridiculously large sample sizes here are due to a typo
of mine: I asked for a ME of 0.01 when I wanted to ask for 0.05!

% \item\pts{x} 

\end{enumerate}

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% \clearpage

% Groves, p. 402, #8, modified.

\item\pts{15}\label{p:informed} \ldots
informed-consent form\ldots
\begin{enumerate}\em

\item\pts{12} Identify (using the paragraph numbers in the figure) any 
four of the six essential elements
for an informed consent form (by filling out the table below):\\[0.5em]
{\em 
\begin{tabular}{|p{3in}|l|}
\hline
                      & {\bf Number of Paragraph} \\
{\bf Name of Element} & {\bf Where it Appears}     \\
\hline 
&            \\
Purpose of the survey &  (1)            \\ \hline
Risks/Benefits for    &            \\
the Participant       &     (3)       \\ \hline 
&            \\
Confidentiality       &        (4)    \\ \hline
Voluntary; participant &            \\
is allowed to ``opt-out''&     (5)       \\ \hline
\end{tabular}
~\\
}
\item\pts{3} Identify an element of informed consent forms that
is missing from the figure.

{\em

There is no information about how to contact anyone if the
participants have questions or concerns about the research.

{\bf Note: }the six components of informed consent are:
\begin{itemize}
\item Purpose
\item Risks/Benefits
\item Confidentiality
\item Compensation for harm
\item Contact info for any questions
\item Participation is voluntary
\end{itemize}
}

\end{enumerate}


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\end{enumerate}

\end{document}

