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\begin{document}
\begin{center}
{\heada PROJECT 1 SOLUTIONS}\\
{\headb Statistics 401: Fall 2016}\\
\end{center}
This quiz is worth 29 points.


\begin{enumerate}
\item From the article {\em Monitoring the Health of Canine Heroes}:

\begin{enumerate}
\item The scientific method is:
\begin{enumerate}
\item Observe some phenomenon \vspace{-0.1in}

\item State a hypothesis explaining the phenomenon\vspace{-0.1in}

\item Collect data\vspace{-0.1in}

\item Test: Does the data support the hypothesis?\vspace{-0.1in}

\item Conclusion.  If the test fails, go back to step 2.
\end{enumerate}

\item The scientists in the article followed the scientific method
by:

\begin{enumerate}
\item Observe that ``Many human responders who assisted at the World Trade Center have suffered from respiratory (pulmonary)
problems."

\item Professor Otto ``was expecting all sorts of
pulmonary problems"  in  the search and rescue dogs who worked at Ground Zero compared to other search and rescue dogs.

\item Data was collected from 95 search-and-rescue dogs who worked at  the World Trade Center and the Pentagon in 2001
 and also from search-and-rescue 55 dogs who had not worked at Ground Zero: ``Each year, veterinarians took blood samples and chest X-rays and collected information about the dogs’ health and behavior.
Whenever dogs enrolled in the study pass away, researchers performed a full autopsy." 

\item The data from the 9/11 dogs compared to other dogs did not support Professor Otto's hypothesis.

\item The data failed to suggest that dogs that responded to the
9/11 disaster were more likely to be diagnosed with cancer or respiratory problems than search-and-rescue dogs that
weren’t involved.

\end{enumerate}

\item Search-and-rescue dogs at Ground Zero and the Pentagon after 9/11 are the individuals of interest.

\item The explanatory variable is whether, in 2001, the dog worked at
the World Trade Center (Ground Zero), the Pentagon, or neither.  The response variable is whether or not a dog ``suffered from respiratory (pulmonary) problems."

\item Table 1 shows that both of the variables from 1d are categorical.



\begin{center}
Table 1: Variables in the Search and Rescue Dog Study
\begin{tabular}{||l|l|l||}\hline
Variable & Type & Properties\\ \hline
Location in 2001 & Categorical & $3$ levels: Ground Zero, Pentagon, neither\\
Pulmonary problems & Categorical & $2$ levels: Yes, No\\\hline
\end{tabular}
\end{center}

\item The ``300 search-and-recue dogs (that) were deployed to the World Trade Center and the Pentagon" in 2001 is the finite population of interest.

\item Although the article does not explicitly say, the following statement in the article suggests that the researchers employed a {\bf voluntary response sample}: ``For search-and-rescue dog handlers, though, helping the dogs was reason enough to join the 9/11 canine health study."    That is, Professor Otto's team may have contacted ALL of the search-and-rescue dogs in the government's database and asked for volunteers to participte in the study.  In this scenario, {\bf selection bias} will be present if those who volunteered are systematically different from those who did not (e.g., dogs in certain geographic locations or or dogs with extroverted handlers).   On the other hand, Professor Otto's team may have tried to implement a {\bf stratified random sample} (with srata equal to 9/11 work or not) by randomly selecting animals from the {\bf sampling frame} of search-and-rescue dogs in the government's database.  Unfortunately, some handlers likely refused to participate in the study.  In this case, the sample could suffer from {\bf non-response bias} if those who participated in the study are systematically different from those dogs who were selected to be in the study but failed to respond.  Either of the previous sampling plans could also suffer from {\bf measurement bias} if different veterinarians examined the X-rays, performed physicals and did the behavioral assessments.
    
    
    
\item The article reports on an observational study of search-and-rescue dogs because no treatment was applied by the researchers.
\end{enumerate}

\item
\begin{enumerate}
\item (2 pts) Table 2 displays a list of the variables and variable types
from the Jellyfish study.

\begin{center}
Table 2: Variables in Jellyfish Study
\begin{tabular}{||l|l|l||}\hline
Variable & Type & Properties\\ \hline
Case & Categorical & $46$ levels: $1,2,3,\ldots,46$\\
Location & Categorical & $2$ levels: Dangar I., S.~Bay\\
Breadth & Numerical & continuous \\
Length & Numerical & continuous \\ \hline
\end{tabular}
\end{center}

\item (2 pts) The investigator wants to know
whether or not the location of the jellyfish can be determined given
its dimensions.  Thus, the response variable is Location.  The
explanatory variables are Breadth and Length.


\item (2 pts) The R commands to read in the data and then display the data are:

{\tt
\begin{center}
\begin{tabular}{|l|}\hline
D=read.table("jellyfish.txt",header=TRUE)\\
attach(D)\\
D\\ \hline
\end{tabular}
\end{center}
}







\end{enumerate}

\item (6 pts) The mean length of a jellyfish from Dangar Island is
12.34mm and the mean length of a jellyfish from Salamander Bay is
18.98mm. The difference between these is ``large with respect to the
standard deviation" of each (3mm and 1.94mm respectively), so we may
conclude that, on the average, longer jellyfish are from Salamander Bay.
We'll learn later in this course how ``t-procedures" can be used to quantify ``large with respect to the
standard deviation".  See the Appendix for the code and output from
R.




\end{enumerate}


\newpage
\centerline{\bf Appendix A}

\begin{verbatim}
# Problem 2c
> D=read.table("jellyfish.txt",header=TRUE)
> attach(D)
> D
\end{verbatim}
\verbatiminput{project1.jellyfish.txt}


\begin{verbatim}
# Problem 3
> tapply(Length,Location,mean)
      DI       SB
12.34091 18.97917
> tapply(Length,Location,sd)
      DI       SB
3.005496 1.936375
\end{verbatim}

\end{document}
