Ingots are huge pieces of metal, often weighing in excess of 9000 kilograms, made in a giant mould. They must be cast in one large piece for use in fabricating large structural parts for cars and planes. If they crack while being made, the crack may propagate into the zone required for the part, compromising its integrity. Airplane manufacturers insist that metal for their planes be defect-free, so the ingot must be made over if any cracking is detected.

Even though the metal from the cracked ingot is recycled, the scrap cost runs into the tens of thousands of dollars. Metal manufacturers would like to avoid cracking if at all possible. But the casting process is complicated, and not everything can be controlled completely. In one plant, only about 75% of the ingots have been free of cracks. So, in an attempt to reduce the cracking proportion, the plant engineers and chemists made changes to the casting process. The data from 5000 ingots produced since the changes can be found in the file ch12_MCSP_Ingots. The variable Crack indicates whether a crack was found (1) or not (0). Select a random sample of 100 ingots and test the claim that the cracking rate has decreased from 25%. Find a confidence interval for the cracking rate as well. Now select a random sample of 1000 ingots, test the claim, and find the confidence interval again. Compare the two tests and intervals and prepare a short report about your findings, including the differences (if any) you see in the two samples.