Question

Are teacher evaluations independent of grades? After midterms, a random sample of 284 students was asked to evaluate teacher performance. The students were also asked to supply their midterm grade in the course being evaluated. In this study, only students with a grade of A, B, or C were included in the summary table. Use a 5% level of significance to test the claim that teacher evaluations are independent of midterm grades.

Mid Term Grades

Evaluation	A	B	C	Row Total
Positive	53	33	18	104
Neutral	25	46	29	100
Negative	14	22	44	80
column Total	92	101	91	284

Answer 1

H0: Null Hypothesis: The teacher evaluations are independent of midterm grades

HA: Alternative Hypothesis: The teacher evaluations are not independent of midterm grades

Expected Frequencies are calculated as follows:

Evaluation	A	B	C	Row Total
Positive	92X104/284=33.69	36.99	33.32	104
Neutral	32.39	35.56	32.04	100
Negative	25.92	28.45	25.63	80
Column Total	92	101	91	284

Test statistic is calculated asfollows:

O	E	(O - E)2/E
53	33.69	11.07
33	36.99	0.43
18	33.32	7.05
25	32.39	1.69
46	35.56	3.06
14	25.92	5.48
22	28.45	1.46
44	25.63	13.16
Total = =		43.68

So,

Test statistic = = 43.68

ndf = (r - 1) X(c- 1)

     (3 - 1) X (3 -1) = 4

By Technology, P - Value < 0.00001

Since P -value is less than = 0.05, the difference is significant. Reject Null Hypothesis.

Conclusion:
The data do not support the claim that The teacher evaluations are independent of midterm grades