This is a practice version of
the final exam, to give you
and idea of what to expect.
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This is an open book test.
Use any sources you like,
including Excel, Mathematica,
or other calculators.
*Don't* ask other people for help;
I want to see your own work.
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1. Here's a list of some of the statistical
tests that we've covered in class.
For each one, create a sample problem including
data that illustrates how it might be used, and
explain what's going on in your example.
a. Paired Student's-t Test
b. Difference of two Percentages
c. Linear Correlation
2. In a certain survey, fifty people are asked
"do you brush daily?" Forty say that they do.
For a,b suppose that the same survey is
done again.
a. With 95% confidence, how many people do you
expect will say "yes" in the second survey?
b. With 95% confidence, what percentage of
people do you expect will say "yes" in the
second survey?
Now suppose that we do the survey in another
country, and find that thirty people say
that they do.
c. Is this a significant difference?
Explain your method and your decision rule.
Be clear about what you are choosing as
your null hypothesis, and what that implies
about your assumption of the underlying
statistics.
3.
a. Explain what is meant by a "Type-I" and "Type-II"
error.
b. Descibe which of these errors are possible
in problem 2c above, and discuss the probability
of such an error if you can. (If you can't,
make a clear argument why you can't.)
4. The weights of a certain baskteball team are
(220, 240, 230, 225, 250, 190, 195).
Find the mean and standard deviation of
this distribution. Is it approximately normal?
What do the mean and standard deviation tell you?
5. Given this data :
x 1 2 3 4 5 8 10
y 1.1 2.0 1.0 2.5 1.2 4.0 5.0
Is there a correlation between x and y?
How sure are you? Explain.
If x is 6, with 95% confidence what is y?
6. A randomly chosen group of fat people
are divided into several groups.
One group is given a placebo (p).
Each of the others is given drug A, B, or C.
Their weights are measured before and
after two months of exercise and drugs.
Do any of these drugs do any good?
How would you analyze the data?
Is there more than one way to do it?
What assumptions are you making, and
can you test them?
patient drug wt_before wt_after
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1 p 220 210
2 A 190 180
3 B 200 190
4 C 220 200
5 p 225 210
6 A etc.
7 B
8 C
...
(I haven't finished making up reasonable numbers,
but you get the idea.)
7. A coin is flipped 30 times.
What is the probability that it comes up heads 10 times?
Do this two ways: exactly, and using a normal approximation.