\documentclass[12pt]{article}

\usepackage{bj,txfonts,psfig,multicol}

\def\gap{\vspace*{0.5in}}

\begin{document}

Name:~~\rule{3in}{0.01in}

\begin{center}
\large\bf Review Quiz of Statistics Background Needed for 36-303:
Surveys, Sampling and Society
\end{center}

\begin{quote}
\begin{itemize}
\item You have 30 minutes to do this quiz.  Plan on spending about 5
  minutes per page on the quiz.  It's OK if you don't finish a page,
  just move on to the next one; return to the unfinished ones at the
  end if you have time.
\item Some problems require a little arithmetic, but a calculator will
  not be needed.
%\item If you finish early, please
%look at today's New Articles with care, and make notes on the
%accompanying checklist.
\item Don't forget to put your name at the top of this page.
\end{itemize}
\end{quote}

\begin{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\item Please list any statistics courses you've had (whether or not at
  Carnegie Mellon), starting with the most recent:\\[0.5in]
\rule{6in}{0.01in}\\[0.5in]
\rule{6in}{0.01in}\\[0.5in]
\rule{6in}{0.01in}\\[0.5in]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\item \fig{f:hist} on the next page shows results of a midterm exam in
  an introductory statistics class, for the students who finished the
  test.
\begin{enumerate}

\item What is the name of the graph in \fig{f:hist}?

\gap

\item What shape does the distribution of this variable have,
  approximately?

% \gap

\clearpage

\item Approximately what is the mode on this test?

\gap

\item How many people scored below 65 on this test? {\em  (Assume no one
  scored exactly 65.)}

\gap

\begin{figure}
\begin{center}
\mbox{\psfig{file=histo.eps,width=3in}}
\end{center}
\caption{Distribution of midterm scores in an introductory statistics
  class.}\label{f:hist}
\end{figure}

\end{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\item Here is some summary information on the same test:
\begin{verbatim}
 N   Mean  SE Mean  StDev  Minimum     Q1  Median     Q3  Maximum
93  82.61     1.06  10.21    58.00  77.00   84.00  91.00    99.00
\end{verbatim}


\begin{enumerate}

\item In the summary, what does the first column (``N'' with a ``93''
  under it) mean?

\gap

\item The summary tells us that the median of these test scores is
  84.  How was this number calculated?

\clearpage

% \item The mean of these scores is 82.61.  How was this number
%   calculated?
% 
% \gap
% 
% \gap
%
% \item What does the mean tell us about this set of numbers?
% 
% \gap 
% 
% \gap

\item In the space provided in \fig{f:box}, make a boxplot of the test
  scores, using the information provided in the summary.  {\em (Assume there
  are no outliers.)}

\gap

\item What is an outlier?

\gap

\item How would you check for outliers using information in
  the summary?

\gap 

\gap

\gap
\item Using the information in the summary, calculate an approximate
  95\% confidence interval for the true mean score on this test.


\end{enumerate}

\begin{figure}
\begin{center}
\mbox{\psfig{file=boxplot.eps,width=3in}}
\end{center}
\caption{Boxplot of midterm scores introductory statistics.}\label{f:box} 
\end{figure}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\item \fig{f:scatter} shows the relationship between students' GPA and
  their Final Exam Score in the introductory statistics class.  

\begin{enumerate}

\item What is this graph called?

\gap

\item What numerical information does each dot in \fig{f:scatter} represent?

\gap

\item What kind of relationship is there between the two variables in
  \fig{f:scatter}?

\gap

\item What statistic (single number) would you ask MINITAB or R to
  compute from this data, to quantify the relationship between
  variables like these?

\gap

\end{enumerate}

\begin{figure}
\begin{center}
\mbox{\psfig{file=scatter.eps,width=3in}}
\end{center}
\caption{Relationship between students' GPAs and Final Exam
  Scores.}\label{f:scatter} 
\end{figure}

\comment{
\begin{verbatim}
         GPA  final
Min.    2.60  20.00
1st Qu. 3.08  79.43
Median  3.37 104.20
Mean    3.33 102.40
3rd Qu. 3.56 127.10
Max.    4.00 190.00
SD      0.35  34.38

    corr 
0.7092044 


Call:
lm(formula = final ~ GPA)

Residuals:
     Min       1Q   Median       3Q      Max 
-58.5004 -15.2081  -0.2060  18.2712  74.4810 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -129.483     23.412  -5.531 2.65e-07 ***
GPA           69.526      6.982   9.958  < 2e-16 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 24.36 on 98 degrees of freedom
Multiple R-Squared: 0.503,      Adjusted R-squared: 0.4979 
F-statistic: 99.17 on 1 and 98 DF,  p-value: < 2.2e-16 

\end{verbatim}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\comment{

\clearpage

\item In problem \#3, suppose you wanted to see if men scored
  differently from women on the Final Exam. 

\begin{enumerate}

\item What sort of statistical analysis would you perform?

\gap

\item The results of one possible analysis are shown below.  What Null
  Hypothesis is being tested?
{\small
\hspace*{-1em}
\begin{verbatim}
         N   Mean  StDev  SE Mean     Difference = mu (women) - mu (men)
Women   39   99.6   35.5      5.7     Estimate for difference:  -2.40
Men     54  102.0   34.7      4.7     95% CI for difference:  (-17.10, 12.31)
                                      T-Value = -0.32  P-Value = 0.747  DF = 80
\end{verbatim}
}

\gap

\item In this analysis, what part does the ``T-Value'' play?

\gap

\item What part does the ``P-Value'' play?

\gap

\item What conclusions could you draw about the difference between
  mens' and womens' scores?

\gap

\item Using information from the analysis, write down a 95\%
  confidence interval for the women's mean test score.

\gap

\end{enumerate}

}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

\item Summation notation.

\begin{enumerate}

\item Which of the following is the formula for the sample mean?
  (Circle one.)
\begin{enumerate}
\item $\sum_{i=1}^n x_i$
\item $\frac1n\sum_{i=1}^n x_i$
% \item $\sum_{i=1}^n (x_i - \bar x)^2$
\item $\frac1n\sum_{i=1}^n x_i^2 - (\bar x)^2$
\end{enumerate}

\item In the answer you chose, what is the role of the symbol $i$?

\gap

\item In the answer you chose, what is the role of the symbol $x_i$?

\gap

\item Please describe, in words, a step-by-step procedure to carry out
  the computation in this formula:
$$
    \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar x)^2
    \tag{(*)}
$$

\gap

\gap

\gap

\gap

\gap

\gap

\item What quantity does the formula in equation $(*)$ calculate?

\end{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

\item Miscellaneous.

\begin{enumerate}

\item What is the difference between a {\em population} and a {\em
  sample}?

\gap

\gap

\item Suppose I have a box with 3 blue tickets and 2 red
  tickets, and you take a ticket out at random.  What is the
  probability that you will get a red ticket?

\gap

\item Now suppose I have to pay you \$1 if you get a blue ticket and
  \$2 if you get a red one.  Which of the following is a valid formula
  for the {\em expected value} of my payout to you (circle one)?
\begin{enumerate}

\item $(1 + 2)/5$

\item $(3\cdot1 + 2\cdot2)/5$

\item $(1\cdot3 + 2\cdot2)/5$

\item $(3 + 2)/5$

\end{enumerate}

\item Now suppose that we run the experiment in part (b) 100 times, each time
  putting the ticket back in the box, and we tally how many red
  tickets were drawn.  Let the total number of red tickets be $X$.
 What is the name of the distribution of $X$?

\gap

\item The usual parameters for the distribution of $X$ in this case
  are $n$ and $p$.  Give the values of $n$ and $p$.

\gap

\item Which of the following is a valid formula for the expected value
  of $X$?
\begin{enumerate}
\item $E[X] = np(1-p)$
\item $E[X] = \sqrt{p(1-p)/n}$
\item $E[X] = np$
\end{enumerate}

\item What does $E[X]$ tell us about $X$?

\end{enumerate}

\end{enumerate}

\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% VOCAB

histogram
scatter plot

  assoc
  incr/decr
  correl
 
boxplot

  `` assuming there are no outliers make a bpxplot.  
  `` how would you test for outliers?

pop vs sample

given a problem and some output, how does a 2-sample t tet work

conf intervals / interp / make?

chisq test of indep

binomial 

hypergeometric

summation notation

==============

simple probabilty calculations
  - mixture
  - inclusion/exclusion

Expected value calculations

sampling distribution (e.g. normal and gamma for means and variances)

counting, combinatorics



