Two different teaching procedures were used in two different groups of students. Each group had 100 students of similiar ability. These are the results:

Group A B C D F

I 15 25 32 17 11

II 9 18 29 28 16

Data is independent from two respective multinomial distribution with k = 5. Test at the 5% level the hypothesis that the two teaching methods are equally effective.

So let X be the students in group 1, and Y students in group 2.

So the test statistic would be:

.

Since it's a multinomial distribution, I know that the expectation is np_i, but how would I find p_i?