Studies have shown that the risk of developing coronary disease increases with the level of obesity. A study comparing two methods of losing weight: diet alone and exercise alone were conducted on 82 men over 1-year period. Forty-two men dieted and lost an average of 16.0 lb over the year, with a standard deviation of 5.6 lb. Forty-five men who exercised lost an average of 10.6 lb, with a standard deviation of 7.9 lb. Construct a 99% confidence interval for the difference in the mean weight loss by these two methods. State any assumptions you made and interpret the result you obtained.