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 |
E_{i}=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 χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
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
X^{2}= |
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

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 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 is as
follows.
Supplier
Component
A
B
C
Defective
10
30...

Suppose a random sample of parts from three different factories
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Factory C
Total
Defective
18
14
23
55
Not Defective
222
226
217
665
Total
240
240
240
720
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