Question

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?

Answer 1

We can not conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components.

Explanation:

The 95% confidence interval tells us that the true mean of the percentage of rework for electrical components is between 0.0758 (7.58%) and 0.1339 (13.39%), with a degree of confidence of 95%.

The value reported of 12% is included in this interval, so it is possible that the true mean for this value is 12%. In other words, we can not reject the hypothesis that the true percentge of rework is 12%.

Then, we can not conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components.

Answer 2

At the 95% confidence level, management should not conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components, since the upper bound of the confidene interval, which is 0.1339, is higher than 0.12.

Explanation:

To reach a conclusion, we have to observe the confidence interval.

Should management conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components?

Is the upper bound of the confidence interval lower than 12% = 0.12?

If yes, it should conclude that this percentage is lower.

Otherwise, it cannot conclude.

Confidence interval:

0.0758 to 0.1339

0.1339 is higher than 0.12.

So.

At the 95% confidence level, management should not conclude that the percentage of rework for electrical components is lower than the rate of 12% for non-electrical components, since the upper bound of the confidene interval, which is 0.1339, is higher than 0.12.