Question

Use the sample data below to test the hypotheses: H0: p1=p2=p3

H1: Not all population proportions are equal

The calculated test statistic is

		6.082
		9.249
		8.851
		10.950

At 2.5% level of significance, the conclusion is

		fail to reject H0
		No test
		No decision
		Reject H0

Answer 1

Observed Values: C1 R1 46 R2 44 Column Total 90 C2 16 44 60 C3 68 82 150 Row Total 130 170 300 Expected Values = [(Row total x Column total)/Grand total] C1 C2 C3 R1 39 26 65 R2 51 34 85

0 46 44 16 44 68 82 E 39 51 26 34 65 85 Total (0-E²/E 1.2564 0.9608 3.8462 2.9412 0.1385 0.1059 9.249 ==2(0-E)? 9.249 E Number of rows =r= 2 Number of columns =C = 3 D.F =(r-1)x(C-1) = 2 Significance level= a = 0.025

P-value = 0.0098 [using Excel function CHIDIST(9.249,2)] Decision rule : Reject HO if P-value <a Here P-value = 0.0098 < 0.025 = a. Conclusion : By decision rule, we reject HO