Question

At many colleges and universities calculus III is considered a “weed out” course; a course which a lot of students drop and rethink their major in doing so. I would like us to see if the number of students who withdraw, pass or fail the class is independent of the session it was taken. The following table gives the results from classes from fall 2017-Summer 2019 (plus some randomly selected summers previous to 2017). Test to see if the grading groups are independent of session.

Grades	Fall	Spring	Summer
W	29	29	5
D/F	25	24	8
A/B/C	211	200	89

Answer 1

Ans:

Chi square test for independence:

H0:grading groups are independent of session.

Ha:grading groups are not independent of session.

	Obsered(fo)
Grades	Fall	Spring	Summer	Total
W	29	29	5	63
D/F	25	24	8	57
A/B/C	211	200	89	500
Total	265	253	102	620
	Expected(fe)
Grades	Fall	Spring	Summer	Total
W	26.93	25.71	10.36	63
D/F	24.36	23.26	9.38	57
A/B/C	213.71	204.03	82.26	500
Total	265	253	102	620
	Chi square=(fo-fe)^2/fe
Grades	Fall	Spring	Summer	Total
W	0.160	0.422	2.777	3.358
D/F	0.017	0.024	0.202	0.243
A/B/C	0.034	0.080	0.553	0.667
Total	0.211	0.525	3.531	4.267

Test statistic:

Chi square=4.267

df=(3-1)*(3-1)=4

p-value=CHIDIST(4.267,4)=0.3711

Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that grading groups are not independent of session.