Students use many kinds of criteria when selecting courses. \"Teacher who is a v
ID: 3432625 • Letter: S
Question
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.)
Explanation / Answer
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