A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a sample standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a sample standard deviation of 14 pounds. Use your statistical knowledge to prove or refute the following claim using hypothesis testing: the liquid diet yields a higher mean weight loss than the powder diet.