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 resulting 95% confidence interval based on these
Data is .0758 to .1339. Which of the following is the correct interpretation?
A) The percentage of electronic components that are reworked is between 7.6% and
13)4%.
B) We are 95% confident that between 7.6% and 13.4% of electrical components are
Reworked.
C) The margin of error for the true percentage of electrical components that are
Reworked is between 7.6% and 13.4%.
D) All samples of size 450 will yield a percentage of reworked electrical components
That falls within 7.6% and 13.4%.
E) None of the above.

Question

Quizplus · Accepted Answer

The 95% confidence interval means that if we take 100 different random samples of the same size from the population of electrical components and calculate the confidence interval for each sample, 95 of those intervals will contain the true percentage of reworked components. The correct interpretation is that we are 95% confident that the true percentage of reworked electrical components is between 7.6% and 13.4%. Option A describes the interval without mentioning the confidence level. Option C refers to the margin of error, but it should be stated as the half-width of the confidence interval. Option D is incorrect because it implies that the same range applies to all possible samples of size 450, which is not true.

One Division of a Large Defense Contractor Manufactures Telecommunication Equipment