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\centerline{MONT 107N -- Understanding Randomness}
\centerline{Information and Sample Questions for Final Exam}
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\noindent
{\it General Information}
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The final exam will be given on Tuesday, May     
11 from 8:30am to 11:30am in our regular classroom, Stein
307.  The exam will be roughly twice as long as the midterm.
If you are well-prepared and work steadily, I expect that you
will complete it within two hours.  However, if you need more
time, you will have until 11:30am to work on the exam.

The final will cover the material from Parts V - VIII (Chapters 16 - 29) 
of Freedman, Pisani, Purves.  This means in particular:
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\item{1.}  Box models for chance processes, the ``Law of Averages,'' EV and SE,
models for totals versus models for counting/classifying.
\item{2.}  The Central Limit Theorem and using the normal curve to determine probabilities
of various outcomes.   
\item{3.}  Sampling and chance errors in sampling.  (Be aware that there is
a ``correction factor'' for sampling without replacement, but that that factor
is very close to 1 when the population is large and the sample size is relatively
small compared to the population size.) 
\item{4.}  Accuracy for percentages, confidence intervals for percentages in the large
sample case -- a different way to use the SE, but a somewhat difficult concept.  Be sure
you understand exactly what the ``$95\%$ confidence'' refers to and the
ramifications of this.     
\item{5.}  Accuracy for averages, confidence intervals for averages in the 
large sample case.  
\item{6.}  Tests of significance -- large sample ($z$-) tests for percents
and averages, differences of percents and differences of averages.  
Small sample ($t$-) tests for averages.   
\item{7.}  $\chi^2$ tests for ``goodness of fit'' and for independence (understand
the difference and when to recognize the one you want).  
\item{8.}  Chance models and genetics -- I might ask you to do something
with data gathered by Mendel as part of his experiments, for instance. 
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I will supply copies of any tables you need to use.   {\it To minimize the need to 
memorize a lot of stuff, you may bring one side of a $3 \times 5$ inch index card 
to the exam with any formulas or other information you want to include and consult 
it at any time.  I will collect these cards with the exam.}  
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\noindent
{\it Review Session}
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If there is interest, I would be happy to run a pre-exam review session for
the class.  Either morning or afternoon of Friday, May 7 after about 2:00pm 
would be possible.  
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{\it Suggestions on How to Study for This Exam}
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Review the problems from the problem sets and the posted solutions if
there were problems you lost points on. Try those again, and if
necessary look at some of the ``regular'' problems in the text 
that have answers to practice.  The main tricky thing about the material
we have looked at this semester is deciding what kind of question you
are trying to answer.  For example, is the question asking about 
the total of a collection of numbers produced by a chance process,
or is it asking about a percentage, or an average, or the difference
of two averages (that is, is it asking for a two-sample test), etc.?  
And what is the sample size? (This is how you distinguish between $z$- and $t$-tests.)
Or is it really a question about goodness of fit or independence, in 
which case you really want a $\chi^2$-test?  If you think that out first, you will see
which formulas are applicable.  

The appropriate SE formula is the most important component for much of this:
\item{$\bullet$}  SE for {\it sum} of $n$ draws with replacement $ = \sqrt{n} \times SD $ of box.
\item{$\bullet$}  SE for {\it average} of $n$ draws with replacement 
$$ = \sqrt{n} \times {{\rm\ SD\ of\ box}\over n} = {{\rm\ SD\ of\ box}\over \sqrt{n}}$$
(this works for all boxes, including the 0/1 boxes used when dealing with
questions about percents).  
\item{$\bullet$}  SE for {\it percent} $ = { {\rm\ SD\ of\ 0/1\ box} \over \sqrt{n} } \times 100\%$
\item{$\bullet$}  For problems about differences of sums, etc.  the total SE is
$SE = \sqrt{SE_1^2 + SE_2^2}$.  
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\noindent
{\it Please take note}
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No use of cell phones, pagers, I-pods, or any other electronic devices
beyond a calculator will be allowed during the exam -- please turn them off
and stow them in your backpack.
\bye
