Is there a relationship between a person's TOEFL score and grade point average (GPA)? Answer to this question based on the following data, which provide both GPA (4-point system) and rank order on the TOEFL from 90 international students.

Data file: chisq4.sav
Variables: TO, GPA

SUBJ    TO     GPA
1       80     3.2
2       34     1.7
3       57     1.9
4       72     1.5
5       62     2.0
6        8     2.3
7       73     2.9
8       51     2.1
9       55     2.6
10      61     1.6
11      33     1.6
12      68     2.9
13      38     3.1
14      26     2.5
15      79     3.5
16      30     4.0
17      18     3.5
18      69     1.5
19      64     2.2
20      43     2.9
21      12     2.5
22      45     4.0
23       1     2.8
24      36     1.8
25       3     3.6
26      24     1.7
27      53     2.5
28      54     2.1
29      52     3.1
30      11     3.7
31      42     3.1
32      65     2.0
33      17     2.4
34      78     2.5
35      10     2.3
36      27     2.8
37      29     1.4
38      22     2.2
39      21     2.3
40      63     2.7
41      31     2.2
42      19     3.9
43      15     4.0
44      49     1.6
45      47     2.5
46      58     1.9
47      77     1.3
48      74     3.2
49      48     3.2
50       5     3.5
51      14     2.9
52      35     3.1
53      13     2.5
54      39     2.8
55      32     1.9
56      23     4.0
57      41     3.7
58      44     2.7
59      71     1.7
60      46     3.8
61      50     3.4
62      70     3.1
63      56     3.5
64       7     3.2
65       2     3.5
66      28     3.2
67      66     3.8
68      76     2.7
69      67     1.5
70      16     2.5
71      37     2.4
72       4     4.0
73      75     3.5
74      60     2.7
75      40     3.6
76       6     2.9
77      59     3.4
78       9     3.3
79      20     2.6
80      25     2.5

Answer the following questions:

1. What kinds of data do the variables in question represent?
    
    
2. If relevant, which is the dependent and which is the independent variable?
    
3.  
   Of the statistics we have studied, which can be employed with these data as they stand? Why?
    
    
    
4. If necessary, which transformation would result in the least amount of loss in precision in the data?
    
    
    
5. If necessary, transform the data and choose your statistic. Explain what transformation and statistic you plan to use.
    
    
    
6. Perform the statistic. Write the resulting figure (F) and the degrees of freedom.
    
    
    
7. Is the result significant at .05?
    
    
8. Check the assumptions underlying whatever statistic you chose to use. Are the assumptions met?