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 95% confidence interval based on this data is 0.0742 to 0.1302. Which of the following is the correct interpretation?
A) The percentage of electronic components that are reworked is between 7.4% and 13.0%.
B) We are 95% confident that between 7.4% and 13.0% of electrical components are reworked.
C) The margin of error for the true percentage of electrical components that are reworked is between 7.4% and 13.0%.
D) All samples of size 450 will yield a percentage of reworked electrical components that falls within 7.4% and 13.0%.
E) The probability of 95% that the true number of electrical parts that have to be reworked is between 7.4% and 13.0% is 0.95.

Question

Quizplus · Accepted Answer

The 95% confidence interval means that if we were to take multiple random samples of the same size and calculate the confidence intervals for each one, we can expect 95% of these intervals to contain the true percentage of reworked electrical components. Therefore, option B correctly interprets the meaning of the confidence interval. Options A, C, and E focus on the specific values in the interval, which are not necessarily exact values for the true percentage of reworked electrical components. Option D is incorrect because not all samples of the same size will yield the same confidence interval.

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