Question

Among 180 students of mathematical statistics, 82 did not attend the lecture. The results of the quiz showed that among students who appeared at the lecture 70 students received a positive grade (all students who obtained a positive grade were 95). Examine the appropriate test whether the hypothesis that "passing the quiz is independent of whether the student attends classes" is correct. Assume a significance level of 0.05.

Answer 1

Null hypothesis:Ho:   passing the quiz and whether student attends classes are independent.

alternate hypothesis:Ha: passing the quiz and whether student attends classes are dependent.

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.05 level , critical value       χ2=		3.841	from excel: chiinv(0.05,1)
Decision rule : reject Ho if value of test statistic X2>3.841

Applying chi square test of independence:

Observed		attend	not attend	Total
	pass	70	25	95
	not pass	28	57	85
	total	98	82	180
Expected	Ei=row total*column total/grand total	attend	not attend	Total
	pass	51.72	43.28	95
	not pass	46.28	38.72	85
	total	98	82	180
chi square    χ2	=(Oi-Ei)2/Ei	attend	not attend	Total
	pass	6.459	7.719	14.1784
	not pass	7.219	8.628	15.8465
	total	13.6780	16.3469	30.0249
test statistic X2=		30.025

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that "passing the quiz is not independent of whether the student attends classes" is correct.