STAT 3093 - FINAL EXAM - 1997 AUGUST 9
                                                                    
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QUESTION ONE  [24]                                                               
 1) Suppose you are given the chart below as a computer produced stem &          
    leaf diagram of the GPA's of the set of students in some small program.      
    Scale is given by the largest item which is 34.                              
               -0 | 99                                                           
               +0 | 0011111112222222222222233333333333333334444                  
                1 |                                                              
                2 |                                                              
                3 | 4                                                            
     a) Cases where the GPA could not be calculated because                      
        not all grades were in were probably coded as        ______________      
     b) What kind of error probably created the GPA of 34?                       
 .                                                                               
     ______________________________________________________________________      
 .                                                                               
                                                                                 
 2) To quadruple your precision you must mulitply your sample size by -          
                          1.414  2  3  4  6  8  12  14  16  20  25  40  400      
                                                                                 
 3) Rank these as as "BEST" "MIDDLE" and "WORST" according to                    
    suitability for describing with a standard deviation.                        
           * Distances flown by paper airplanes in assignment 7  __________      
           .                                                                     
           * Heights of students now writing this exam.          __________      
           .                                                                     
           * Income of Canadian citizens                         __________      
                                                                                 
 4) A 9000 digit sequence from a base five random number generator               
    is tested with a chi-square test.  The generator is rejected                 
    when a chi-square statistic of 11.1 results.                                 
  Which of these (more than one) are correct?                                    
  a) The probability the generator is DEFECTIVE is 2.5%                          
  b) The probability the generator is GOOD      is 2.5%                          
  c) The probability the generator is DEFECTIVE is 97.5%                         
  d) The probability the generator is DEFECTIVE is 5%                            
  e) The probability the generator is GOOD      is 5%                            
  f) The probability the generator is DEFECTIVE is 95%                           
  g) For a GOOD      generator Pr{chi-square > 11.1} = 0.025.                    
  h) For a DEFECTIVE generator Pr{chi-square > 11.1} = 0.025.                    
  i) For a GOOD      generator Pr{chi-square > 11.1} = 0.975                     
  j) For a GOOD      generator Pr{chi-square > 11.1} = 0.05.                     
  k) For a DEFECTIVE generator Pr{chi-square > 11.1} = 0.05.                     
  l) For a GOOD      generator Pr{chi-square > 11.1} = 0.95.                     
  m) Either the generator is DEFECTIVE or something unlikely has happened.       
  n) Either the generator is GOOD      or something unlikely has happened.       
                                                                                 
 5) X and Y are independent random variables with variances of                   
    74 and 30, respectively. Evaluate the variance of (X-Y+9).  ____________     
                                                                                 
 6) A normal distribution has expectation 1000 and std. dev. 200.                
    How much probability lies between -1150 and 1150?                            
                                                                 ___________
                                                                    
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QUESTION TWO  [20]                                                               
Use the Minitab printout below in answering these questions                      
                                                                                 
Complete this table:                                                             
             X:           5       7       9      11      13                      
             Y:         143     152     176     190     204                      
                                                                                 
             FIT:      ____    ____    ____    ____    ____                      
                                                                                 
             RESIDUAL: ____    ____    ____    ____    ____    (7) -------       
                                                                                 
Identify the standard deviation of residuals on the Minitab                      
printout by circling and labelling it                                            
                                                                                 
Identify the sum of squares of residuals on the Minitab                          
printout by circling and labelling it                                            
                                                                                 
Calculate a 95% confidence interval                                              
for the slope                            _______ to _______                      
                                                                                 
--------------------------------------------------                               
   Selections from (simulated) Minitab output                                    
   Data Display                                                                  
   Row     X      Y                                                              
     1     5    143                                                              
     2     7    152                                                              
     3     9    176                                                              
     4    11    190                                                              
     5    13    204                                                              
                                                                                 
   Regression Analysis                                                           
                                                                                 
   The regression equation is                                                    
   Y = 101 + 8.00 X                                                              
                                                                                 
   Predictor       Coef       Stdev                                              
   Constant     101.000       5.447                                              
   X             8.0000      0.5774                                              
                                                                                 
   s = 3.651                                                                     
                                                                                 
   Analysis of Variance                                                          
   SOURCE       DF          SS          MS                                       
   Regression    1      2560.0      2560.00                                      
   Error         3        40.0        13.33                                      
   Total         4      2600.0             
                                                                    
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QUESTION THREE [28]                                                              
This question concerns the data of this stem & leaf diagram                      
           1 | 1 4      2                                                        
           2 | 2 2      2                                                        
           3 | 1 3 5    3     Largest number is 78                               
           4 | 2        1                                                        
           5 |          0                                                        
           6 | 1 4 5    3                                                        
           7 | 0 2 7 8  4                                                        
Consider this as a random sample from some population.                           
                                                                                 
(a) Calculate the sample mean                                __________          
                                                                                 
(b) The standard deviation of this data is 24.02, from                           
this estimate the standard deviation of the sample mean      __________          
                                                                                 
(c) Calculate a 99% * NOT 95% * confidence interval                              
for the mean                                         _______ to _______          
                                                                                 
Among a class of 670, all calculating such a confidence interval                 
from INDEPENDENT samples, what is the expected number of                         
intervals which do NOT cover the population mean?           __________           
                                                                                 
(d) Approximately how large a sample is needed to achieve                        
a standard deviation of the sample mean equal to one                             
instead of the value you calculated in (b) ?            N = ___________          
                                                                                 
Use either of the tables handed out in class to                                  
determine a confidence interval for the median       _______ to _______          
                                                                                 
Among a class of 670, all calculating such a median interval                     
from INDEPENDENT samples, what is the expected number of                         
intervals which do NOT cover the population median?         __________
                                                                    
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QUESTION FOUR  [15]                                                              
A die being tested for fairness is tossed 300 times                              
with this result.                                                                
  FACE         1      2      3      4      5      6                              
  COUNT       58     61     45     57     40     39                              
  COUNT-50     8     11     -5      7    -10    -11                              
                                                                                 
                                                                                 
a) Calculate the chi-square statistic.                                           
                                                                                 
b) Under the null hypothesis the probability of a value of                       
chi-square as large or larger than (a) above is nearest                          
                                                                                 
    0.005 0.01 0.025 0.05 0.10 0.25 0.50 0.75 0.90 0.95 0.99 0.995               
                                                                                 
c) Suppose the die is really fair.  In 100 such tests (A single test             
   consists of tossing the die 300 times and calculating chi-square.)            
   the expected number of times chi-square exceeds the valud you got             
   above is closest to --                                                        
                                                                                 
     0.5   1   2.5   5    10   25   50   75   90   95   99   99.5                
                                                                                 
                                                                                 
QUESTION FIVE  [ 5]                                                              
In an experiment like the class paper airplane assignment, save                  
that only one kind of airplane is used, each of ten people throw                 
an airplane five times.  The result can be presented as 50 sep-                  
arate distances or as individual means for ANN, BOB, etc.  Both                  
presentations appear below.  Average and standard deviation for                  
each presentation is also shown.                                                 
          Thrower              Data           Mean                               
          ANN            39 36 50 44 49       43.6                               
          BOB            65 71 63 67 70       67.2                               
          CAL            37 36 23 38 38       34.4                               
          DOT            35 48 45 49 41       43.6                               
          EMMA           38 47 46 43 40       42.8                               
          FAY            31 27 37 28 27       30.0                               
          GAIL           42 44 48 48 49       46.2                               
          HAL            60 51 63 55 69       59.6                               
          IRA            41 43 48 40 51       44.6                               
          JEAN           29 43 39 34 37       36.4                               
          Average            44.84           44.84                               
          Standard Dev.      11.69           11.19                               
                                                                                 
 Calculate a 95% confidence interval for the mean distance flown.                
                                                                                 
                               44.84 +/-  ____________________________

STAT 3093 - FINAL EXAM - 1997 AUGUST 9 - SOLUTION SHEET
                                                                            
                                                               version 1         
QUESTION ONE  [24]                                                               
 1) Suppose you are given the chart below as a computer ......                   
          a) ..................................................  -9              
          b)  ............................... MISSING DECIMAL POINT              
                                                                                 
 2) To quadruple your precision mulitply your sample size by     16              
                                                                                 
 3) Rank as as "BEST" "MIDDLE" and "WORST" for using std.                        
    * Distances flown by paper airplanes in assignment 7     MIDDLE              
    * Heights of students now writing this exam.               BEST              
    * Income of Canadian citizens                             WORST              
                                                                                 
 4) A 9000 digit sequence from a base 5 random # generator                       
  g) For a GOOD generator Pr{chi-square > 11.1} = 0.025.                         
  m) Either the generator is DEFECTIVE or something unlikely...                  
  Grading:  NO ANSWER 1 :: (g)&(m) only 4  :: One right no wrong 3:                 
           one right 1 wrong 2   :: two right 1 wrong 3 
                                                                                 
 5) V{X}=74 V{Y}=30     Evaluate the variance of (X-Y+9).       104              
                                                                                 
 6) How much probability lies between -1150 and 1150?        0.7734              
                                                                                 
QUESTION TWO  [20]                                                               
             X:           5       7       9      11      13                      
             Y:         143     152     176     190     204                      
             FIT:       141     157     173     189     205                      
             RESIDUAL:    2      -5       3       1      -1    [7]               
                                                                                 
                    Identify std of resid and SSQ of residuals [6]               
Interval for B                                                                   
           8 +/- 3.182x 0.58  =  8 +/-  1.84 =  6.16 to  9.84  [7]               
           8 +/- 2.000x 0.58  =  8 +/-  1.15 =  6.85 to  9.15                    
                                                                                 
QUESTION THREE [28]                                                              
     Data:  11 14 22 22 31 33 35 42 61 64 65 70 72 77 78                         
     Sample mean                                            46.47                
     Std of the sample mean                24.02/sqrt(15) =  6.20                
     Interval for MEAN     (30.5 62.4 Normal)        28.0 to 64.9                
     Expected misses (mean)                                  6.70                
     Required sample size                                     577                
     Interval for MEDIAN                       22-70   or   22-72                
     Expected misses (median)                  23.56         4.95                
                                                                                 
                                                                                 
QUESTION FOUR  [15]                                                              
  Chi-Square =   9.60    Upper Tail Probability 0.087                            
                                                                                 
QUESTION FIVE  [ 5]                                                              
Without adjustment   Width = 2     * 11.19 / sqrt(10)  =    7.077                
With adjustment      Width = 2.263 * 11.19 / sqrt(10)  =    8.008                
              >>> No credit if square root 50 is used.