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\begin{document}
\begin{center}
{\Huge BMCC MAT150.722 Final Exam}
\end{center}
~\\
You will be given all class to complete this test.
In the event these instructions conflict with what I say in class,
what I say takes precedence.
You are allowed to have one sheet of notes. Each problem is worth 10 points.
Good luck!

\section{Central Limit Theorem}
\textbf{\large
Indicate whether the following pieces of information
are required to apply the central limit theorem.
On your answer sheet write \textbf{T} if can and \textbf{F} otherwise.
} 
\\
\begin{center}
\begin{tabular}[width=6in]{lp{4in}}
(1.1) &
A known population mean $\mu$.
\\~\\
(1.2) &
The sample size must be at least $20$.
\\~\\
(1.3) &
The probability of success $p$ must be constant.
\\~\\
(1.4) &
The original population must be uniformly distributed.
\\~\\
(1.5) &
A known population standard deviation $\sigma$.
\\~\\
(1.6) &
The original population size is at least $100$.
\\~\\
(1.7) &
The original population variance is at most $1$.
\\~\\
(1.8) &
The sample size is at least $30$ or the original population is normally distributed.
\\~\\
(1.9) &
The original population is symmetrically distributed.
\\~\\
(1.10) &
The original population is asymmetrically distributed.
%\\~\\
\end{tabular}
\end{center}

\section{Central Limit Theorem}
\subsection{What value for $\mu_{\obar{x}}$
does the Central Limit Thereom give?}
\begin{enumerate}[(A)]
\item $\mu$ 
\item $\frac{\mu}{\sqrt{n}}$
\item $\sigma$
\item $\frac{\sigma}{\sqrt{n}}$
\item None of these
\end{enumerate}

\subsection{What value for $\sigma_{\obar{x}}$
does the Central Limit Theorem give?}
\begin{enumerate}[(A)]
\item $\mu$ 
\item $\frac{\mu}{\sqrt{n}}$
\item $\sigma$
\item $\frac{\sigma}{\sqrt{n}}$
\item None of these
\end{enumerate}

\subsection{What does the Central Limit Theorem tell you
about the original distribution?}
\begin{enumerate}[(A)]
\item Nothing 
\item It is normally distributed.
\item It is uniformly distributed.
\item It is symmetric.
\item None of these
\end{enumerate}
 
\subsection{What does the Central Limit Theorem tell you
about the distribution of $\obar{x}$?}
\begin{enumerate}[(A)]
\item Nothing 
\item It is normally distributed.
\item It is uniformly distributed.
\item It is symmetric.
\item None of these
\end{enumerate}

\subsection{If $n = 20$ when can you use the Central Limit Theorem?}
\begin{enumerate}[(A)]
\item Never 
\item When the original population is normally distributed.
\item When the original population is uniformly distributed.
\item When the original population is asymmetrically distributed.
\item None of these
\end{enumerate}

\section{Normal Distribution}
\subsection{Calculate the area under the curve of a normal distribution
between the z-scores of $1.64$ and $1.96$}
\begin{enumerate}[(A)]
\item .0255 
\item .055
\item .255
\item .55
\item None of these
\end{enumerate}

\subsection{What $z$-score corresponds to an area of $.8888$?}
\begin{enumerate}[(A)]
\item .8106
\item 1.22
\item 1.645
\item 1.96
\item None of these
\end{enumerate}

\section{Hypothesis Test}
\subsection{What is the relationship of confidence and significance
in a hypothesis test?}
\begin{enumerate}[(A)]
\item Confidence = $1 - $Significance 
\item Confidence = $1 + $Significance 
\item Confidence = $2 \times $Significance
\item Significance = $2 \times $Confidence
\item None of these
\end{enumerate}

\subsection{A critical value is a specific type of}
\begin{enumerate}[(A)]
\item mean
\item $z$-score 
\item distribution
\item significance level
\item None of these
\end{enumerate}

\textbf{Use the following scenario for the next three questions.}

Popeye is buying a large number of cans of spinach from Bluto.
Popeye prefers a particular kind of canned spinach which has 10 ounces of spinach per can.
When Popeye eats spinach, he gains incredible strength,
but for full effect he requires at least 9.5 ounces of spinach.
Further, his mouth is only so large and Popeye is not a wasteful man,
hence his preference for this particular brand.
Popeye's sweetheart is Olive Oyl, something of a coy flapper whose extremely
thin build lends itself well to the fashions of the Roaring Twenties.
\footnote{\url{http://en.wikipedia.org/wiki/Olive_Oyl}}
Bluto is enamored with Olive, and this has caused tension between
Bluto and Popeye in the past.
Therefore Popeye wants to be sure that he's getting
the right amount of spinach in his cans.
As a rough test, Popeye selects 36 cans at random and measures the spinach in each.
He finds the average amount of spinach is 10.21 ounces
and decides to use the sample standard deviation of .6 ounces as
an estimate for the population standard deviation.
He then performs a hypothesis test.

\section{Hypothesis Test}
\subsection{Identify the null hypothesis.}
\begin{enumerate}[(A)]
\item $\mu = 10$
\item $\mu = 10.6$
\item $\mu \neq 10$
\item $\mu > 10$
\item None of these
\end{enumerate}

\pagebreak
\subsection{Identify the alternate hypothesis.}
\begin{enumerate}[(A)]
\item $\mu = 10$
\item $\mu = 10.6$
\item $\mu \neq 10$
\item $\mu > 10$
\item None of these
\end{enumerate}

\section{Hypothesis Test}
\subsection{What is the critical value for a 95\% symmetric hypothesis test?.}
\begin{enumerate}[(A)]
\item .8106
\item 1.22
\item 1.645
\item 1.96
\item None of these
\end{enumerate}

\subsection{What is the critical value for a 99\% symmetric hypothesis test?.}
\begin{enumerate}[(A)]
\item .8106
\item 1.22
\item 1.645
\item 1.96
\item None of these
\end{enumerate}

\section{Hypothesis Test}
\subsection{Calculate the test statistic.}
\begin{enumerate}[(A)]
\item $z =\frac{10.21 - 10}{\frac{.6}{36}} = 12.6$
\item $z =\frac{10.21 - 10}{\frac{.6}{\sqrt{36}}} = 2.1$ 
\item $z =\frac{10.21 - 10}{.6} = .35$
\item $z =\frac{10.21 - 10}{36} = .006$ 
\item None of these
\end{enumerate}

\subsection{Given this information, what do you do with the null hypothesis at 99\% confidence?.}
\begin{enumerate}[(A)]
\item Accept the null hypothesis.
\item Reject the null hypothesis.
\item Fail to reject the null hypothesis.
\item Modify the null hypothesis.
\item None of these
\end{enumerate}

\pagebreak

\section{
If your test statistic falls outside of your rejection reason,
what is the conclusion of your hypothesis test?
}

\section{
Give a definition of the notation $\mu_{\obar{x}}$ in words.
the mean of the sampling distribution of the sample mean
}

\section{
Draw and label symmetric rejection region
you might use for a hypothesis test.
Label the following: critical value, rejection region, mean, test statistic.
}

\pagebreak
~
\pagebreak

\begin{center}
{\Huge Answer Sheet}
~\\~\\
\Large
\begin{tabular}{llllllllll}
1.1 & \blankAnswer &
1.2 & \blankAnswer &
1.3 & \blankAnswer &
1.4 & \blankAnswer &
~1.5 & \blankAnswer \\
1.6 & \blankAnswer &
1.7 & \blankAnswer &
1.8 & \blankAnswer &
1.9 & \blankAnswer &
1.10 & \blankAnswer \\
2.1 & \blankAnswer &
2.2 & \blankAnswer &
2.3 & \blankAnswer &
2.4 & \blankAnswer &
2.5 & \blankAnswer \\
3.1 & \blankAnswer &
3.2 & \blankAnswer & & &
4.1 & \blankAnswer &
4.2 & \blankAnswer \\
5.1 & \blankAnswer &
5.2 & \blankAnswer & & & 
6.1 & \blankAnswer &
6.2 & \blankAnswer \\
7.1 & \blankAnswer &
7.2 & \blankAnswer
%\multicolumn{10}{c}{~}\\
~\\
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8 & \multicolumn{9}{p{5in}}{
{\underline{\hspace{5in}}}
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}\\
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9 & \multicolumn{9}{p{5in}}{
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~\\
10 & \multicolumn{9}{p{5in}}{~}
\end{tabular}
\\
$\mu$\\
\begin{tabular}{c|c}
\hspace{1in}  & \hspace{1in}\\
\hspace{1in}  & \hspace{1in}
\\ \hline
\hspace{1in}  & \hspace{1in}\\
 & 
\end{tabular}
\end{center}

\end{document}
\section{Central Limit Theorem}
\subsection{}
\begin{enumerate}[(A)]
\item  
\item 
\item 
\item 
\item None of these
\end{enumerate}

