Question

The following table was derived from a study of HIV patients, and the data reflect the number of subjects classified by their primary HIV risk factor and gender. Test if there is a relationship between HIV risk factor and gender using a 5% level of significance:

	Gender		Total
HIV Risk Factor	Male	Female
IV drug user	24	40	64
Homosexual	32	18	50
Other	15	25	40
	71	83	154

What type of chi-square test will you use (goodness of fit or test of independence)?

What are your hypotheses?
H₀:

H_A:

Fill in the following table to calculate your test statistic:

		IV Drug Use:	Homosexual:	Other:	Total
Male	O =	24	32	15	71
	E =
	(O – E) =
	(O – E)2 / E =
Female	O =	40	18	25	83
	E =
	(O – E) =
	(O – E)2 / E =

df =___________________

Critical value: ______________________

Conclusion: We _____________________ (reject / fail to reject) the Null Hypothesis

Interpretation:

Answer 1

Here we use Chi Square test for Independence because we have attributed data and also we have to find if there is a relationship between HIV risk factor and gender.

Null Hypothesis H0:  there is no relationship between HIV risk factor and gender

Alternative Hypothesis H1:  there is a relationship between HIV risk factor and gender

Level of significance

The Calculation table is given below:

		IV Drug Use:	Homosexual:	Other:	Total
Male	O =	24	32	15	71
	E =				71
	(O – E) =	-5.51	8.95	-3.44
	(O – E)2 / E =	1.0288	3.4752	0.6417	5.1457
Female	O =	40	18	25	83
	E =				83
	(O – E) =	5.51	-8.95	3.44
	(O – E)2 / E =	0.8803	2.9723	0.5487	4.4013

df = (r-1)*(c-1) = (3-1)*(2-1) = 2

The test statistic is

The critical value is : 5.991

Since Chi square calculated is greater than Chi square tabulated , i.e. ( 9.547 > 5.991) We Reject H0

Conclusion : We Reject the Null Hypothesis

Interpretation : The HIV Risk Factor is related to the gender.