Problem
An online company runs diet bets where customers can pay an amount of money into a pool in order to achieve a diet goal in a certain time-frame. Those who achieve the goal share the pool of money, minus the company's fee. The company records the weights of a random sample of 12 clients who are participating in a particular diet bet. If the sample has a mean weight of 190.0 lb and a standard deviation of 15.0 lb, calculate the margin of error and construct the 98% confidence interval for the true mean weight of the diet bet participants.