Question

Use the sample data below to test the hypotheses

H ₀: p ₁ = p ₂ = p ₃

H _a: Not all population proportions are the same

	Populations
Response	1	2	3
Yes	200	200	92
No	150	200	108

where p _i is the population proportion of yes responses for population i. Using a .05 level of significance. Use Table 12.4.

Compute the value of the   ² test statistic (to 2 decimals).

The p-value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

What is your conclusion?
- Select your answer -Conclude all population proportions are equal.Conclude not all population proportions are equal.Item 3

Answer 1

To Test :-

H0 :- P1 = P2 = P2

H1 :- Not all proportion are equal

		P1	P2	P3	Total
Yes	Observed	200	200	92	492
	Expected	181.26	207.16	103.58	492.00
	O - E	18.74	-7.16	-11.58	0.00
	(O - E)² / E	1.94	0.25	1.29	3.48
No	Observed	150	200	108	458
	Expected	168.74	192.84	96.42	458.00
	O - E	-18.74	7.16	11.58	0.00
	(O - E)² / E	2.08	0.27	1.39	3.74
Total	Observed	350	400	200	950

Test Statistic :-
= Σ (Oi - Ei )2 / Ei
= 7.22

P ( > 7.2153) = 0.0271

P value is between 0.025 and .05

Reject null hypothesis if P value < α = 0.05
P value = 0.0271 < 0.05, hence we reject null hypothesis
Conclusion = Reject null hypothesis

We can conclude not all population proportions are equal.