Atravel magazine conducts an annual survey where readers rate their favorite cruise ship. ships are rated on a 10 point scale, with higher values indicating better service. a sample of 50 ships that carry fewer than 500 passengers resulted in a average rating of 6.89 with standard deviation 0.52. a sample of 55 ships that carry more than 500 passengers resulted in an average rating of 6.55 with standard deviation 0.83. give a 99.8% confidence interval of the difference between the population mean ratings for smaller ships and the population mean ratings for larger ships. (note, the order of subtraction at the wording carefully.)