The Ertl Company is well-known for its high-quality die-cast metal alloy toy replicas of tractors and other farm equipment. As part of a periodic procurement evaluation, Ertl is considering purchasing parts for a toy tractor line from three different suppliers. The parts received from the suppliers are classified as having a minor defect, having a major defect, or being good. Test results from samples of parts received from each of the three suppliers are shown below. Note that any test with these data is no longer a test of proportions for the three supplier populations because the categorical response variable has three outcomes: minor defect, major defect, and good. Supplier Part Tested A В C Minor Defect 15 13 23 Major Defect 6 Good 139 126 125 Using the preceding data, conduct a hypothesis test to determine whether the distribution of defects is the same for the three suppliers. Use the chi-square test calculations as presented in this section with the exception that a table with r rows and c columns results in a chi-square test statistic with (r – 1)(c – 1) degrees of freedom. Find the value of the test statistic

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The Ertl Company is well-known for its high-quality die-cast metal alloy toy replicas of tractors and other farm equipment. As part of a periodic procurement evaluation, Ertl is considering purchasing parts for a toy tractor line from three different suppliers. The parts received from the suppliers are classified as having a minor defect, having a major defect, or being good. Test results from samples of parts received from each of the three suppliers are shown below. Note that any test with these data is no longer a test of proportions for the three supplier populations because the categorical response variable has three outcomes: minor defect, major defect, and good.

**Table:**
```
Part Tested        Supplier
                A     B     C
Minor Defect   15    13    23
Major Defect    6     9     6
Good          139   126   125
```

Using the preceding data, conduct a hypothesis test to determine whether the distribution of defects is the same for the three suppliers. Use the chi-square test calculations as presented in this section with the exception that a table with *r* rows and *c* columns results in a chi-square test statistic with \((r - 1)(c - 1)\) degrees of freedom.

Find the value of the test statistic
\[ \chi^2 = \boxed{\phantom{00}} \] (to 2 decimals)

Use Table 3 of Appendix B to determine the *p*-value. 

The *p*-value is \[- \text{Select your answer} -\]

Using a 0.05 level of significance, what is your conclusion?

Conclude that we are \[- \text{Select your answer} -\] to reject the hypothesis that the population distribution of defects is the same for all three suppliers.
Transcribed Image Text:The Ertl Company is well-known for its high-quality die-cast metal alloy toy replicas of tractors and other farm equipment. As part of a periodic procurement evaluation, Ertl is considering purchasing parts for a toy tractor line from three different suppliers. The parts received from the suppliers are classified as having a minor defect, having a major defect, or being good. Test results from samples of parts received from each of the three suppliers are shown below. Note that any test with these data is no longer a test of proportions for the three supplier populations because the categorical response variable has three outcomes: minor defect, major defect, and good. **Table:** ``` Part Tested Supplier A B C Minor Defect 15 13 23 Major Defect 6 9 6 Good 139 126 125 ``` Using the preceding data, conduct a hypothesis test to determine whether the distribution of defects is the same for the three suppliers. Use the chi-square test calculations as presented in this section with the exception that a table with *r* rows and *c* columns results in a chi-square test statistic with \((r - 1)(c - 1)\) degrees of freedom. Find the value of the test statistic \[ \chi^2 = \boxed{\phantom{00}} \] (to 2 decimals) Use Table 3 of Appendix B to determine the *p*-value. The *p*-value is \[- \text{Select your answer} -\] Using a 0.05 level of significance, what is your conclusion? Conclude that we are \[- \text{Select your answer} -\] to reject the hypothesis that the population distribution of defects is the same for all three suppliers.
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