Students use many kinds of criteria when selecting courses T

Students use many kinds of criteria when selecting courses. \"Teacher who is a very easy grader\" is often one criterion. Three teachers are scheduled to teach statistics next semester. A sample of previous grade distributions for these three teachers is shown here.

(a) At the 0.01 level of significance, is there sufficient evidence to conclude \"The distribution of grades is not the same for all three professors?\"
(i) Find the test statistic. (Give your answer correct to two decimal places.)

	Professor
Grades	#1	#2	#3
A	11	9	25
B	17	28	26
C	34	31	16
Other	29	42	21

Solution

First find the row totals and columns totals.

professor

grades

1

2

3

Total

a

11

9

25

45

b

17

28

26

71

c

34

31

16

81

other

29

42

21

92

total

91

110

88

289

Then find the expected frequencies for each cell by multiplying the corresponding row total by the column total and dividing by the table total. For example, for b and professor 2, it would be 71*110/289 = 27.02422.

professor

grades

1

2

3

a

14.16955

17.12803

13.70242

b

22.3564

27.02422

21.61938

c

25.50519

30.83045

24.66436

other

28.96886

35.0173

28.01384

Then calculate the chi square test statistic by taking each observed frequency and subtract the expected frequency, square that and divide by the expected frequency, and then sum them up.

Chi square test statistic = (11

	professor
grades	1	2	3	Total
a	11	9	25	45
b	17	28	26	71
c	34	31	16	81
other	29	42	21	92
total	91	110	88	289