The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuit boards is tested, resulting in 18 labeled as defective (a) Verify the assumption for statistical inference on the population proportion. (b) Construct a 95% confidence interval for the proportion defective. (c) What sample size would be required to decrease the margin of error in this situation to 0.015? (d) Use the confidence interval you found in part b to test if the proportion defective is not equal to 0.04 using 0.05 level of significance (List hypotheses, confidence interval, decision, and conclusion.)

2. A manufacturing plant has one injection-molding machine (machine A) used to form plastic parts. Management is considering purchasing an additional machine (machine B), but only if the machine performs better (same or fewer defective parts as A). A sample of size 300 is selected from machine A and 15 defective parts are found. A sample of size 300 is selected from machine B and 12 defective parts are found. (a) Verify the assumption for statistical inference on the difference in population proportions. b) Test to see if the proportion in the new machine is less than the current machine at alpha = 0.05. (State hypotheses, test statistic, p-value, decision, and conclusion.) (c) What would a type I error be in the context of this situation? (d) What would a type II error be in the context of this situation?