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. ComponentSupplier
ABC
Defective101535
Good490485465
(a)

Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers.

H0: All population proportions are not equal.
Ha: pA = pB = pCH0: Not all population proportions are equal.
Ha: pA = pB = pC H0: pA = pB = pC
Ha: Not all population proportions are equal. H0: pA = pB = pC
Ha: All population proportions are not 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.

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. Reject H0. We cannot 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.)

Comparison
pi − pj
CVij

Significant
Diff > CVij
A vs. B ? Yes No
A vs. C ? Yes No
B vs. C ? Yes No
Can any suppliers be eliminated because of poor quality? (Select all that apply.)

Supplier ASupplier BSupplier Cnone