Apowder 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 average weight loss than the powder diet. the powder diet group had an average weight loss of 42 pounds with a standard deviation of 12 pounds. the liquid diet group had an average weight loss of 44 pounds with a standard deviation of 14 pounds. conduct a hypothesis test at the 5% level. state the distribution to use for the test.