4. A manufacturer of medical devices has two plants and is concerned that more defective items are produced in Plant II than in Plant I. In a random sample of 250 items from Plant I, 28 were defective. In a random sample of 220 items from Plant II, 38 were defective. Let: 1 = Proportion of defective items produced from Plant I p2 = Proportion of defective items produced from Plant II p = Pooled proportion of defective items produced a) Calculate the following point estimates i. p1, the point estimate for P1 ii. p2, the point estimate for P2 iii. p, the point estimate for p iv. (p1 - p2), the point estimate for the difference in proportions. b) Calculate the following standard errors i. s.e.(p,), the standard error for p1 li. s.e.( p2), the standard error for pz ili. s.e.( p1 - p2), the standard error for the difference in proportions. c) Is there any significant evidence to support the claim that plant II produces more defective items? Use a 0.10 level of significance by making use of the i. critical value approach and the ii. p-value approach. d) For the hypotheses Ho: P1 = P2 H1:P1 # P2 Give the i. rejection rule at a 0.01 level of significance ii. p-value ili. standard error of (p, - p2) under Ho: P1 = p2, i.e. when assuming the two population proportions are the same. e) Calculate the following confidence intervals for the difference in proportions i. 95% confidence interval for ( P1 - Pz) ii. 90% confidence interval for ( P, - P2)