Take the offer First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the...

Take the offer First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer. To test the effectiveness of the campaign, First USA recently sent out offers to a random sample of 50,000 cardholders. Of those, 1184 registered.

 a) Give a 95% confidence interval for the true proportion of those cardholders who will register for the offer.

 b) If the acceptance rate is only 2% or less, the campaign won’t be worth the expense. Given the confidence interval you found, what would you say?