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\textbf{College of the Holy Cross, Spring Semester, 2018} \\
\textbf{MONT 101N -- Analyzing Environmental Data, Final Exam} \\
\textbf{Tuesday, May 15}
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\vskip 40pt
\noindent\textbf{Your Name}: \Blank
\vskip 70pt

\paragraph{Instructions:} Please show all work necessary to justify your answers, and
write your answers in the spaces provided. Use the back of the
preceding page if you need more space for scratch work.  There are
100 possible points distributed as below.

\vskip 2.0truein

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\begin{tabular}{|l||r|}

\hline

Problem & Points/Poss    \strut \\

\hline\hline

I  & \hfil/\  20\hfil \strut \\

\hline

II  & \hfil/\  10\hfil \strut \\

\hline

III  & \hfil/\  20\hfil \strut \\

\hline

IV  & \hfil/\  25\hfil \strut \\

\hline

V  & \hfil/\  25\hfil \strut \\


\hline\hline

Total   & \hfil/100\hfil \strut \\

\hline

\end{tabular}

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\emph{Have an enjoyable and productive summer!}

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\vfill\eject
\noindent
I. {\it Briefly} identify \emph{any 4} of the following.
If you submit answers for more than 4, the best 4 will be counted.  

\begin{enumerate}
\item[(A)] (5) The Central Limit Theorem
\vglue 2.0truein
\item[(B)] (5) A $95\%$ confidence interval for a population mean
\vglue 2.0truein
\item[(C)] (5) A $t$-distribution
\vglue 2.0truein
\item[(D)] (5) Standard normal distribution
\vglue 2.0truein
\item[(E)] (5) The box-and-whisker plot of a data set.  
\vglue 1.5truein
\item[(F)] (5) The $p$-value of a test of hypotheses
\vglue 1.5truein
\end{enumerate}
\vskip 10pt
II.  Short answer
\begin{enumerate}
\item[(A)] (5)  If you want to get polling results with comparable accuracy, do you need a bigger
sample size if the polling is done in Texas than you do if the polling is done
in Delaware?  Explain by using formula for the standard error for a percentage.
\vglue 1.5truein
\item[(B)] (5)  True/False and explain:  If the $p$-value of a hypothesis test works
out to $p = .034$ then we can say that the null hypothesis was \emph{definitely false}.  
\vglue 2.0truein
\end{enumerate}
\vfill\eject
\noindent
III.  Let $X$ represent a normal random variable with $\mu = 4.3$ and $\sigma = 1.4$.  
\begin{enumerate}
\item[(A)] (10) Find $P(3.2 < X < 5.0)$
\vskip 3.0truein 
\item[(B)] (10) Suppose that values of $X$ are sampled $n = 10$ times independently.
Give the \emph{formula for computing} the probability that exactly $5$ out of the $10$ values satisfy 
$3.2 < X < 5.0$.  (The number the correct formula gives is roughly $.2434$ 
if you want to check your answer by computing the value.)
\end{enumerate}
\vfill\eject
\noindent
IV.  A Gallup poll released on April 3, 2017 surveyed a random sample of 706 adults nationwide.
It reported ``that $59\%$ of those sampled say the environment should be prioritized over energy 
production.''  
\begin{enumerate}
\item[(A)] (20) Find the 95\% confidence interval for the actual percentage of Americans
who feel this way.  (Use the conservative method for estimating the standard error.)
\vskip 3.0truein
\item[(B)] (5) Based on your answer to part (A), is $55\%$ a ``believable'' value for the
percentage of all Americans who feel that way?
\end{enumerate} 
\vfill\eject
\noindent
V. (25) A study was conducted by the Florida Game and Fish Commission to assess the amounts
of chemical residues found in the brain tissue of brown pelicans.  In a test for the 
pesticide DDT, random samples of $N_1 = 10$ juveniles (young birds foraging independently)
and $N_2 = 13$ nestlings (birds still being fed by their parents) produced the following
data (DDT measurements in parts per million).  Test the alternative hypothesis that mean amounts
of DDT found in juveniles and nestlings differ versus the null hypothesis that they do not
differ.  Use $\alpha = 0.05$.  
\[
\begin{array}{cc}\hline
\text{Juveniles} &  \text{Nestlings}\\ \hline
       N_1 = 10  &  N_2 = 13\\
       \overline{Y}_1 = .041 & \overline{Y}_2 = .026\\
             S_1 = .017 & S_2 = .006\\
\end{array}
\]
(Notes: This data has important implications regarding the accumulation
of chemical residues over time. You may assume that the population SD's are equal to the sample
SD's in deciding how to set up the test.)

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