A study compared weight loss between patients on diet A and patients on diet B. Patients on diet A lost a mean of 7.1 pounds in six months, whereas patients on diet B lost a mean of 7.4 pounds in six months. Suppose that the study was based on a sample of 500 patients on diet A and 400 patients on diet B and the standard deviation of the amount lost was 3.7 pounds for diet A and 2.9 pounds for diet B. 1. At 5% level of significance, test if there is a difference in the mean weight loss between the two diets. 2. Construct a 95% confidence interval estimate of the difference between the population means in the two diets.