Question

Use the sample data below to test the hypothese. H0: p1=p2=p3. Ha: Not all population proportions are the same.

Population 1: yes 150 no 100. Population 2: yes 150 no 150. Population 3 yes 97 no 103.

Where Pi is the population proportion of yes responses for population i. Using a .05 level of significance the p-value=____?

Answer 1

here applying chi square test of Homogeneity:

Observed	Oi	A	B	C	Total
	Yes	150	150	97	397
	No	100	150	103	353
	total	250	300	200	750
Expected	Ei=row total*column total/grand total	A	B	C	Total
	Yes	132.33	158.80	105.87	397
	No	117.67	141.20	94.13	353
	total	250	300	200	750
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	Yes	2.3585	0.4877	0.7426	3.589
	No	2.6525	0.5484	0.8352	4.036
	total	5.011	1.036	1.578	7.625

for above test statistic 7.625 ; p value =0.0221