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 company. The Quality Control Department plans to check a random sample of the more than 10,000 electrical components manufactured across all divisions.

a) 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 managers sample?

b) They actually select a random sample of 450 electrical components and find that 46 of those had to be reworked. Create the confidence interval.

c) Should the Quality Control Department conclude that the percentage of rework for the electrical components is lower than the rate of 12% for non-electrical components? Explain.