One division of a large defense contractor manufactures telecommunication equipment for the military. This division reports that

Question

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One division of a large defense contractor manufactures telecommunication equipment for the military. This division reports that

12% of non-electrical components are reworked. Management wants to determine if this percentage is the same as the percentage rework for the company’s electrical components. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. The 95% confidence interval based on this data is .0758 to .1339. Should management conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components?

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-02-22T15:05:19+03:00

Answer:

It is not possible to claim that the rework percentage for electrical components is less than the 12% for non-electrical components.

Step-by-step explanation:

The 95% confidence interval indicates that the true mean for the rework percentage of electrical components is between 0.0758 (7.58%) and 0.1339 (13.39%), maintaining a 95% confidence level.

The reported figure of 12% falls within this range, suggesting the actual mean could indeed be 12%. This means we cannot dismiss the possibility that the rework percentage is 12%.

<pConsequently, we cannot infer that the proportion of rework for electrical components is below the 12% recorded for non-electrical components.

Leona [12.6K] · Answer 2 · 2026-02-22T15:06:45+03:00

Answer:

Under a 95% confidence level, management should refrain from concluding that the rework percentage for electrical components is below the 12% observed for non-electrical components. This is because the upper limit of the confidence interval, which stands at 0.1339, exceeds 0.12.

Step-by-step explanation:

To arrive at a conclusion, it is necessary to analyze the confidence interval.

Should management assert that the rework percentage for electrical components is less than the 12% for non-electrical components?

Is the upper limit of the confidence interval below 12% = 0.12?

If this is true, they could claim that the percentage is lower.

If not, they cannot make that claim.

Confidence interval:

0.0758 to 0.1339

Notably, 0.1339 is greater than 0.12.

Therefore,

At the 95% confidence interval, management should not assert that the rework percentage for electrical components is below 12%, as the upper limit of the confidence interval, 0.1339, surpasses 0.12.