Question

a professor is teaching three sections of the same course and wants to determmine if the proprtion of students who passed is statistically different across the classes. the report below shows how many students in each section passed and how many were enrolled

Section 1 - 82 passed 107 enrolled

Section 2 - 74 passed 108 enrolled

Section 3 - 89 passed 115 enrolled

conduct the chi-square test and report the final test statistic

Answer 1

null hypothesis: Ho:  Proportion of students who passed is same across the classes

Alternate hypothesis:Ha:Proportion of students who passed is statistically different across the classes

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

2

for 2 df and 0.05 level of significance critical region       χ2=

5.991

applying chi square test:

Expected	Ei=row total*column total/grand total	section 1	section 2	section 3	Total
	Passed	79.44	80.18	85.38	245
	failed	27.56	27.82	29.62	85
	total	107	108	115	330
chi square    χ2	=(Oi-Ei)2/Ei	section 1	section 2	section 3	Total
	Passed	0.0825	0.4766	0.1536	0.713
	failed	0.2379	1.3737	0.4427	2.054
	total	0.320	1.850	0.596	2.767

test statistic X² =2.767

as test statistic is not in rejection region we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that Proportion of students who passed is statistically different across the classes