Question

Are teacher evaluations independent of grades? After the midterm, a random sample of 284 students were 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 passing grade were included in the summary table. Use a 5% level of significance to test the claim that teacher evaluations are independent of midterm grades.

Midterm Grade

Teacher Evaluation	A	B	C	Row total
Positive	35	33	28	96
Neutral	25	46	35	106
Negative	20	22	40	82
Column Total	80	101	103	284

(A) State the null and alternate hypotheses.

(B) Identify the appropriate sampling distribution: Chi-square test of independence, Chi-square goodness of fit, or Chi-square for testing or estimating σ² or σ.

(C) What is the value of the sample test statistic?

(D) Find or estimate the P-value.

(E) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis?

Answer 1

A) Ho:teacher evaluations are independent of midterm grades.

Ha:teacher evaluations are dependent of midterm grades.

B)

Chi-square test of independence

C)

Applying chi square test:

Expected	Ei=row total*column total/grand total	A	B	C	Total
	positive	27.04	34.14	34.82	96
	neutral	29.86	37.70	38.44	106
	negative	23.10	29.16	29.74	82
	total	80	101	103	284
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	positive	2.3417	0.0381	1.3347	3.715
	neutral	0.7908	1.8287	0.3085	2.928
	negative	0.4157	1.7589	3.5401	5.715
	total	3.548	3.626	5.183	12.3571

alue of the sample test statistic =12.357

d)

degree of freedom(df) =(rows-1)*(columns-1)=

4

for 4 degree of freedom and above test statistic , p value =0.0149

e)

as p value is less than 0.05 level , we reject null hypothesis and conclude that  teacher evaluations are dependent of midterm grades.