Question

Question 5: (20 points) 30 of 40 girls and 40 of 50 male students were successful in a class. A) Is success dependent on gender? Test with 5% error? B) Is there any difference between success rates with 1% error? What is the difference between the tests in A and B options?

Answer 1

	OBSERVED TABLE
		Success	No Success	TOTAL
	Girl	30	10	40
	Male	40	10	50
	TOTAL	70	20	90
	E1=	RT*CT/GT =	40*70/90
			31.11111111
	O=	OBSERVED FRQ
	E =	EXPECTED FREQ
	EXPECTED TABLE
		Success	No Success	TOTAL
	Girl	31.11111111	8.888888889	40
	Male	38.88888889	11.11111111	50
	TOTAL	70	20	90
	H0:	Success is independent of gender
	H1:	Success is dependent of gender
	level =	0.05
		CALCULATION TABLE
		O	E	O-E	(O-E)2/E
	Girl  S	30	31.11111111	-1.11111	0.03968254
	Male  S	40	38.88888889	1.111111	0.03174603
	Girl  N S	10	8.888888889	1.111111	0.13888889
	Male  N S	10	11.11111111	-1.11111	0.11111111
	SUM =	90	90	3.55E-15	0.32142857
A)	Chi sq test statistics=	0.3214285
	DF =(2-1)(2-1) =1
	p value= 0.5708
	Conclusion:	p value(0.5708) >  0.05
		Fail to Reject Ho
	so we conclude that	Success is independent of gender  at 5%
B)	When  level =1%
	we have
	Conclusion:	p value(0.5708) >  0.01
		Fail to Reject Ho
	so we conclude that	Success is independent of gender  at 1%
	Result of both option is same