This is a practice version of
the final exam, to give you 
and idea of what to expect.

----------------------------

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.

-----------------------------

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
   -------------------------------------------
   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.