Question

1. A professor complains that student ratings on the teacher evaluations seems to depend on the grade the student received in their class. In other words, according to this professor, a teacher who gives more good grades gets better ratings, and a teacher who gives more bad grades gets bad ratings. The Student Assembly took a random sample of 300 teacher ratings on which the student’s grade for the course also was indicated. The results are given in the following table.

	Student Final Course Grade
Rating	A	B	C	Fail (D, E or withdrawal)
Excellent	14	17	14	5
Average	25	36	75	14
Poor	21	27	40	12

Test the claim that teacher ratings are independent of student grades. Use an α = 0.05 level of significance.

1. State the null and alternate hypotheses.

2. Calculate the test statistic and p-value. Show work.

3. Make a decision about the null hypothesis. Explain.

4. Summarize the final conclusion in the context of the original claim.

Answer 1

Ho: Teacher natings are independent of studenta grades H, Teacher ratings are dependent of students groede fail Totes observed frequencies (orji course grade Rating A Exellent 14 11:17 Average 15 36 poor 27 To kay 50 129 1. 75 140 loo 21 12 31 11-17 290 Total 140 290 80x100 129x100 loo Expected frequencie caurise grede Rating A Bail Excellent 50x50 12oxso 1129850 31x50 zgo 2go zgo 290 Average sox140 80x140 129x140 31 x 140 zgo ingo 2go Poor ogox100 31 x 100 zgo zgo 290 Total 80 31 Cspan 5 71 Expected frequence ( Eij). Courge groede croo Rating A B Fail Excellent 8.62 13.79 22.24 5.34 average 24,14 38.62 62.28 14.97 poor 17.24 2759 44 48 Toten instone so I 129 290 Totoy so 140 10.89 129 31 ne2go

Test statistic Coij - Ew.)? i=1}=1 =(14-8.62, 2/4 R17 - 13.79) ²/+ (14-22.2432 / + 13.79 22.24 07+* (5-513452 5.34 8-62 + R15-24.14) 21+1C36-38,62) 27 +175 -62-28) 27+ (14-14.9772 14 24.14 38.62 62.28 9441 59372642 +|(21-17.24) 7 (27-27.5935690-494.48)2/4 (12-10.69)? 44.42 10.69 17.24 27.59 = 3.36 + o.75 +3.05 +0.02 + 3,46 to 18 +2.60 too 6+ 0182 +0.01 +0.45 +0.16 -4.92 al.f (r) (6-1) = (3-1) (4-1) =(2)3) Jd. F = 6 nano. of rows c=no, of columns prale = P(X² d. F > 20 ²) =P(x} > K. 92) El p(x2 c14.92) out ont E- 0.979) Ruceler 0,0209. Decision Reject Ho if pwale 222 Here Pralue =0,02 og 2020.05 - Reject Ho conclusion There is sufficient evidence to reject the claim that the teacher ratings are independent of students grades it. teacher ratings are dependent of steedents grades