Use Modern Approach:
Stainless steels can be susceptible to stress corrosion cracking under certain conditons. A materials engineer is interested in determining the proportion of steel alloy failures that are due to stress corrison cracking.
A.) In the absence of premilinary data, how large a sample must be taken so as to be sure that a 98% confidence interval will specify the proportion to within ±0.05.
B.) In a sample of 200 failures, 30 of them were caused by stress corisson cracking. Find a 98% confidence interval for the proportion of failures caused by stress corrison cracking.
C.) Based on the data in part (B), estimate the sample size needed so that the 98% confidence interval will specify the proportion within ±0.05