A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a100-pointscale, with higher values indicating better service. A sample of36shipsthat carry fewer than500 passengersresulted in an average rating of85.47, and a sample of44 shipsthat carry 500 or more passengers provided an average rating of81.90. Assume that the population standard deviation is 4.55 for ships that carry fewer than500 passengersand 3.97 for ships that carry 500 or more passengers.

a) What is the point estimate of the difference between the population mean rating for ships that carry fewer than500 passengersand the population mean rating for ships that carry 500 or more passengers? (Use smaller cruise shipslarger cruise ships.)

b) At 95% confidence, what is the margin of error? (Round your answer to two decimal places.)

c) What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships? (Use smaller cruise shipslarger cruise ships.Round your answers to two decimal places.)