Question

Benson Manufacturing is considering ordering electronic components from three different suppliers. The suppliers may differ in terms of quality in that the proportion or percentage of defective components may differ among the suppliers. To evaluate the proportion of defective components for the suppliers, Benson has requested a sample shipment of 500 components from each supplier. The number of defective components and the number of good components found in each shipment are as follows. Component Supplier A B C Defective 15 20 40 Good 485 480 460 (a) Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. H0: Not all population proportions are equal. Ha: pA = pB = pC H0: All population proportions are not equal. Ha: pA = pB = pC H0: pA = pB = pC Ha: All population proportions are not equal. H0: pA = pB = pC Ha: Not all population proportions are equal. (b) Using a 0.05 level of significance, conduct the hypothesis test. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. We cannot conclude that the suppliers do not provide equal proportions of defective components. Do not reject H0. We cannot conclude that the suppliers do not provide equal proportions of defective components. Reject H0. We conclude that the suppliers do not provide equal proportions of defective components. Do not reject H0. We conclude that the suppliers do not provide equal proportions of defective components. (c) Conduct a multiple comparison test to determine if there is an overall best supplier or if one supplier can be eliminated because of poor quality. Use a 0.05 level of significance. (Round your answers for the critical values to four decimal places.) Can any suppliers be eliminated because of poor quality? (Select all that apply.) Supplier A Supplier B Supplier C none

Answer 1

a)

H0: pA = pB = pC Ha: Not all population proportions are equal.

b)

Applying chi square test of homogeneity

Expected	Ei=row total*column total/grand total	A	B	C	Total
	defective	25.0	25.0	25.0	75
	good	475.0	475.0	475.0	1425
	total	500	500	500	1500
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	defective	4.000	1.000	9.000	14.0000
	good	0.211	0.053	0.474	0.7368
	total	4.2105	1.0526	9.4737	14.7368
test statistic X2=		14.737

p value =

0.0006

from excel: chidist(14.737,2)

Reject H0. We conclude that the suppliers do not provide equal proportions of defective components.

c)

Supplier C