Consider the following to answer the question(s) below:
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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions.
-The Quality Control Department wants to estimate the true percentage of rework for electrical components to within 4%, with 99% confidence. How many components should they sample?
A) 651
B) 1000
C) 344
D) 438
E) 579

Question

Quizplus · Accepted Answer

The formula for calculating the sample size with a specified margin of error and confidence level is:

n = (Z^2 * p * (1 - p)) / E^2

Where:
Z = the Z-score for the specified confidence level (2.58 for 99% confidence)
p = an estimate of the true proportion (use 0.12, the sample proportion of non-electrical components reworked)
E = the desired margin of error (use 0.04)

Plugging in the numbers, we get:

n = (2.58^2 * 0.12 * 0.88) / 0.04^2
n ≈ 438

Therefore, the Quality Control Department should sample 438 electrical components in order to estimate the true proportion of rework for electrical components to within 4%, with 99% confidence. Choice D is correct.

Consider the Following to Answer the Question(s) Below