Statistics 3093: Solutions of August 1996 Final

VERSION 11


                                                                      
                                                                           
QUESTION ONE                                                               
Data    .......................   1  1 15 22 24 29 33 41 42 64 68          
Quartiles                              Q1       Q2       Q3                
Mean (Average)     ...........................................  30.91      
Standard Deviation ............................................ 22.07      
                                                                           
QUESTION TWO                                                               
Classify these plots as suitable or unsuitable for regression              
      A: U (outlier)  |   B: S                     |   C: S      
      D: S            |   E: U (varying bandwidth  |   F: U (curved)     
                                                                           
QUESTION THREE                                                             
                             EXPECTATION:    49.95 + 30.24  =   80.19      
                             VARIANCE         2.43 +  9.22  =   11.65      
                             STANDARD DEV                        3.41      
                                                                           
QUESTION FOUR                                                              
 (a) Moss grows indifferently as to side of the tree, and the 60
     trees used are statistically independent in this respect.
                 North   South   East+West   TOTAL
 (b)     OBS      17       19       24         60                          
         EXP      15       15       30         60                          
         DIFF      2        4       -6          0
                 0.27     1.07     1.20       2.53                         
 (c) The table value used is                  5.99 (3-1=2 d.f.)                        
 (d) The null hypothesis is NOT rejected (at the 5% level).
 (e) This data does not provide evidence that moss distinguishes 
     between the North * South * East/West aspects of trees. 
     Comment: This is not the same as saying that that the moss does 
     not distinguish.  The difference may be too small to show up in 
     a sample of this size; to illustrate, this hypothetical larger 
     sample does show evidence that moss distinguishes aspect:
                 North   South   East+West   TOTAL
         OBS      170      190      20         600                         
                                                                           

William Knight / Math Dept / University of New Brunswick -- knight@unb.ca