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. Supplier Component A B C Defective 17 22 42 Good 483 478 458 (a) Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. OH PAPPc H: All population proportions are not equal. OH PAPP H: Not all population proportions are equal. OH: All population proportions are not equal. H₂PA PPC OH: Not all population proportions are equal. H₂PA PB PC (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. O Reject H. We conclude that the suppliers do not provide equal proportions of defective components. O Do not reject H₂, We cannot conclude that the suppliers do not provide equal proportions of defective components. O Do not reject H₂, We conclude that the suppliers do not provide equal proportions of defective components. O Reject H. We cannot 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 CV Significant Diff > CV A vs. B A vs. C B vs. C Can any suppliers be eliminated because of poor quality? (Select all that apply.) Supplier A Supplier B Supplier C none
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. Supplier Component A B C Defective 17 22 42 Good 483 478 458 (a) Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. OH PAPPc H: All population proportions are not equal. OH PAPP H: Not all population proportions are equal. OH: All population proportions are not equal. H₂PA PPC OH: Not all population proportions are equal. H₂PA PB PC (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. O Reject H. We conclude that the suppliers do not provide equal proportions of defective components. O Do not reject H₂, We cannot conclude that the suppliers do not provide equal proportions of defective components. O Do not reject H₂, We conclude that the suppliers do not provide equal proportions of defective components. O Reject H. We cannot 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 CV Significant Diff > CV A vs. B A vs. C B vs. C Can any suppliers be eliminated because of poor quality? (Select all that apply.) Supplier A Supplier B Supplier C none
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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.
Supplier
Component
Defective
17 22 42
Good
483 478 458
(a) Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers.
OH PA PB = Pc
0
H: All population proportions are not equal.
OH PA = P₁ = Pc
H: Not all population proportions are equal.
OH: All population proportions are not equal.
H₂PAP=Pc
OH,: Not all population proportions are equal.
H₂: PA=PB = Pc
(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.
O Reject H. We conclude that the suppliers do not provide equal proportions of defective components.
O Do not reject H. We cannot conclude that the suppliers do not provide equal proportions of defective components.
O Do not reject H. We conclude that the suppliers do not provide equal proportions of defective components.
O Reject H. We cannot 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
CV i
Significant
Diff > CV
A vs. B
A vs. C
B vs. C
Can any suppliers be eliminated because of poor quality? (Select all that apply.)
Supplier A
Supplier B
Supplier C
none
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