The First Internet Bank wants to encourage its customers to do all their banking online. It offers higher interest to depositors and lower interest rates on loans to their internet customers. The Banks goal is to reduce the number of tellers and teller hours as a way of cutting costs and maximizing profits. The Bank still needs to have adequate staffing for its non-internet customers, so it needs to know what proportion of its customers are exclusively online customers.
A random sample of 200 of the Banks customers was surveyed and 65 customers were found to exclusively use online banking.
Construct a 99% confidence interval for the proportion of all bank customers that use online banking.To obtain a margin of error of 2% for the confidence interval in part a., what sample size would be required?
For this part only, assume that the Bank had not yet taken a survey. The Bank wants to know what sample size it should take to be within 2% of the true proportion, with 99% confidence