An e-commerce business wishes to estimate the proportion of its web site users who entered false phone numbers when registering. A sample of 250 users is chosen at random. Of these, 37 are discarded because of database errors. Of the remaining users, 19 had registered with false phone numbers.
(a) Find a 99% confidence interval for the proportion of registered users with false phone numbers and explain what it indicates. Use language that a manager could easily understand.
(b) The manager wants the margin of error to be 2% or less. How large a sample should be taken?
(c) The manager decided that a margin of error of 3% will be sufficient. How large a sample must be taken now?
(d) The business is interested in trying to redesign its web site to cut down on the number of registrations with false phone numbers. How large a sample of registrations would be needed if they wanted to test their success using a = 0.1 and wanted to be able to detect a decrease from 10 to 5% with probability 0.8?