Ingots are large pieces of metal. As liquid metal cools, cracks can develop on the surface of the ingot, which can propagate into the interior of the ingot and compromise its integrity. Airplane manufacturers insist that metal for planes be defect free, so the ingot must be made over if any cracking is detected. In one plant that specializes in ingots designed for the airplane industry, 20% of the ingots have had some kind of surface crack. Plant engineers and chemists recently made some changes in the casting process by which the ingots are formed. They are interested in determining if this change has any effect on the crack rate. Of a random sample of 95 castings, 10 have cracks. a. [8] Conduct a thorough test of the appropriate hypotheses. Follow through on each of the 7 steps, as detailed in the text and in class. Use a significance level of 0.10. b. [3] Suppose the engineers desire a 90% confidence interval for the true proportion of cracked ingots for this recently changed casting process. What sample size is required in order to obtain such an interval having width at most 0.08