Question: A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect.
(a) Was the company's adjustment successful? Carry out an appropriate test to support your answer.
(b) Describe a Type I error and a Type II error in this setting, and give a possible consequence of each.