Photolithography plays a central role in manufacturing integrated circuits made on thin disks of silicon. Prior to a quality-improvement program, too many rework operations were required. In a sample...

Photolithography plays a central role in manufacturing integrated circuits made
on thin disks of silicon. Prior to a quality-improvement program, too many rework operations
were required. In a sample of 200 units, 26 required reworking of the photolithographic step.
Following training in the use of Pareto charts and other approaches to identify significant
problems, improvements were made. A new sample of size 200 had only 12 that needed
rework.

Find a large sample 99% confidence interval for the true difference of the
proportions.