Ingots are huge pieces of metal, often weighing in excess of 20,000 pounds, made in a giant mold. 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 only about 75% of the ingots have been free of cracks. The data from 5000 ingots produced after some changes were made to the process are found in the file Ingots in eLC. The variable Crack indicates whether a crack was found (1) or not (0). The variable Impurities shows the amount (in ppm) of impurities found in a sample from each ingot.

Select a random sample of 100 ingots and test the claim that the cracking rate has decreased from 25%. Now select a random sample of 500 ingots and test the claim again. Prepare a short report about your findings including any differences you see between the two samples