SPH 7460 Final Exam  December 17, 2011                                    page 1 of 7

Six Problems - 7 pages               Name: _________________________________________
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1.  Let X = person's height and Y = person's serum creatinine level.  Suppose you
    have a sample of N people and that X and Y are measured on each person.

    a) How would you construct a test for the hypothesis that corr(X, Y) = 0?
       That is, write a program that would do this without using a SAS procedure
       like PROC CORR or an analogous R procedure.  You can assume that X and Y
       are approximately normally distributed.
















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    b) Write a program using the bootstrap that will produce a 95% confidence
       interval for the true correlation.  [Continue on next page if needed]


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SPH 7460 Final Exam  December 17, 2011                                    page 2 of 7

                                      Name: _________________________________________
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SPH 7460 Final Exam  December 17, 2011                                    page 3 of 7

                                      Name: _________________________________________
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2.  A triangle T has vertices (0, 0), (3, 2), and (5, 1).

    a) Find a linear transformation F: R^2 --> R^2 such that F(T) is the triangle
       with vertices (0, 0), (1, 0), and (0, 1).




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    b)  Use part a) to find the area of the original triangle T.







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SPH 7460 Final Exam  December 17, 2011                                    page 4 of 7

                                      Name: _________________________________________
=====================================================================================

 3.  An observation X in a dataset is called an OUTLIER if

           X > Q3 + 1.5 * (Q3 - Q1)  or

           X < Q1 - 1.5 * (Q3 - Q1),
 
     where Q3 is the third quartile of dataset (i.e., 3/4 of the
     observations are less than Q3) and Q1 is the first quartile.

     Write a macro which lists all the outliers for a given variable
     in a dataset.  The call to the macro should be of the form

           %outliers (indata, xvar, outdata),

  where indata is the input dataset, xvar is the variable of
  interest, and outdata is the output dataset of outlying values.









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SPH 7460 Final Exam  December 17, 2011                                    page 5 of 7

                                      Name: _________________________________________
=====================================================================================

 4.  Given the following data:

     Obs      X
     ---    -----
      1       13
      2        4
      3        1
      4       11
      5        1
      6       12
      7        3
      8        5
      9       10
     10        2

You need to decide whether these data came from a Poisson distribution or some
other distribution.  How would you do this?  You can use any software you want -
SAS procedures, R, etc..  The important thing is to describe how you would
approach the problem.







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SPH 7460 Final Exam  December 17, 2011                                    page 6 of 7

                                      Name: _________________________________________
=====================================================================================
 
 5.  A program produces maximum likelihood estimates theta_hat and phi_hat for two 
     parameters, theta and phi.

     The program also computes the the standard error of theta_hat, the standard error 
     of phi_hat, and the covariance of theta_hat and phi_hat.  These are:

     std err (theta_hat) = .5
     std err (phi_hat) = .3
     covar (theta_hat, phi_hat) = .2

     Find the estimated standard error of:    


       g(theta_hat, phi_hat) = theta_hat * phi_hat + cos(theta_hat + phi_hat).









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SPH 7460 Final Exam  December 17, 2011                                    page 7 of 7

                                      Name: _________________________________________
=====================================================================================
 
 6.  Let f(x) = exp(x) + exp(-x).  Write a program using Newton's method that
     will find a solution x to the equation

          f(x) = 3,









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