Question

9.9. Is gender independent of education level? A random sample of people were surveyed and

each person was asked to report the highest education level they obtained. Perform a hypothesis

test. Include all 5 steps.

	High School	Bachelors	Masters
Female	30	60	54
Male	25	40	44

Answer 1

Null hypothesis: Ho: gender is independent of education level

Alternate hypothesis: HA: gender is dependent of education level

degree of freedom(df) =(rows-1)*(columns-1)=		2
for 2 df and 0.05 level of signifcance critical region       χ2=			5.991
Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	High school	Bachelors	Masters	Total
	female	31.30	56.92	55.78	144
	male	23.70	43.08	42.22	109
	total	55	100	98	253
chi square    χ2	=(Oi-Ei)2/Ei	High school	Bachelors	Masters	Total
	female	0.0543	0.1670	0.0567	0.2781
	male	0.0718	0.2206	0.0749	0.3673
	total	0.1261	0.3876	0.1316	0.6454
test statistic X2 =		0.645

Decision:as test statistic is not in critical region, we fail to reject null hypothesis

Conclusion: we can not conclude that gender is not independent of education level