Two different teaching procedures were used on two different groups of students. Each group contained 100 students of about the same ability. At the end of the term, an evaluating team assigned a letter grade to each student. The results were tabulated as follows.
|
|
Grade
|
|
|
Group
|
A
|
B
|
c
|
D
|
F
|
Total
|
|
I
|
15
|
25
|
32
|
17
|
11
|
100
|
|
II
|
9
|
18
|
29
|
28
|
16
|
100
|
If we consider these data to be independent observations from two respective multinomial distributions with k = 5, test, at the 5 percent significance level, the hypothesis that the two distributions are the same (and hence the two teaching procedures are equally effective).