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 FINAL EXAM - STATISTICS 3093 - 1996 DECEMBER
 OPEN BOOK -- NOTES & CALCULATORS ALLOWED -- TIME: 3 HOURS

 QUESTION ONE    [24/80]
    0   0 1
    1   4          The largest number of this stem
    2   2 8        and leaf diagram is  6.4
    3   0 2        Calculate from this data the
    4   0 4 7      quantities requested:
    5
    6   4

 FIRST, SECOND & THIRD QUARTILES _______ _______ _______

 MEAN (AVERAGE)                           ______________

 STANDARD DEVIATION                       ______________

 95% CONFIDENCE INTERVALS

     FOR MEDIAN               ____________ TO __________

     FOR MEAN                 ____________ TO __________




 QUESTION TWO     [8/80]

 Each of a class of 16 is given a different block of digits from
 the same random number generator.    All 16 test the generator
 using a chi-square test at alpha=0.10 ((NOT 0.05))  Assume all
 their work is correct.  Even though the generator is OK some
 of the class will probably reject it.   What is ---

 a) The expected number of rejections                     __________

 b) The (small) probability that nobody rejects it        __________

 c) The probability that (exactly) one person rejects it. __________





 QUESTION THREE   [8/80]

 (A) Invent two sets of data:
   i)  One OBVIOUSLY suitable for techniques using a standard deviation
       (such as confidence intervals for the mean).
   ii) One OBVIOUSLY NOT suitable for techniques using a std. dev.

 (B) Invent two scatter plots:
   i)  One OBVIOUSLY suitable for regression (least squares) techniques.
   ii) One OBVIOUSLY NOT suitable for regression techniques.

 


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 QUESTION FOUR   [24/80]
  This table describes a simple linear regression
  (least squares fit). Fill in the missing numbers.

  Hint: Since two points determine a line, you can solve
  for the fitted line after finding any 2 points on it.
  After that, the rest is straightforward.

     X                1      2      3      4      5

     Y               18     18  _____     16     34


     FITTED LINE  _____  _____  _____  _____     27


     RESIDUAL         3  _____     -2     -8      7


  Calculate the quantity which is an analog of the standard
  deviation describing the size of a "typical" residual.
  (Minitab reports this quantity as "s".)




 QUESTION FIVE   [16/80]
 X is distributed as follows: P{X=1}= 0.3 , P{X=2}= 0.5 , P{X=3}= 0.2
 Evaluate (as a number) the expectation and variance of 60/X
      X              1    2    3
     Probability     0.3  0.5  0.2
     60/X           60   30   20




 Y is distributed the same way as X, and X and Y are independent.
 Evaluate (as a number) the expectation and variance of

           (a)        60/X  +  30/Y                        _________

           (b)        60/X  +  30/X                        _________
 ((Look carefully to see which are Y`s and which are X`s.))