A professor tests whether the loudness of noise during an exam (low, medium, high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test. (a)...

transtutors.com/questions/-2053149.htm
in
H0 : exams and noise level are independent.
H1 : exams and noise level are Not independent.
(O) Low Medium High Total
Pass exam 20 18 8 46
Fail exam 8 6 10 24
28 24 18 70
Total 56 48 36 140
We calculate expected frequencies by: E = (Row Total) (Column Total)Grand Total
(E) Col-1 Col-2 Col-3
Row-1 46 ∗ 56
140
= 18.40
46 ∗ 48
140
≈ 15.77
46 ∗ 36
140
≈ 11.83
Row-2 24 ∗ 56
140
= 9.60
24 ∗ 48
140
≈ 8.23
24 ∗ 36
140
≈ 6.17
Row-3 70 ∗ 56
140
= 28
70 ∗ 48
140
= 24
70 ∗ 36
140
= 18
To calculate chi-square test statistic we calculate this formula on each...