12. Diet Methods: Here we study the effectiveness of two dieting methods. Method 1 is a diet high in protein, fiber, and fat but low in carbohydrates. Method 2 is a diet low in fat but high in fiber and carbohydrates. There were 60 participants for each method. After one year, Method 1 participants had a mean weight loss of 8.2 pounds with a standard deviation of 1.7 pounds. After one year, Method 2 participants had a mean weight loss of 7.5 pounds with a standard deviation of 1.2 pounds. (a) Construct the 95% confidence interval for the mean weight loss after one year of all people who would complete the Method 1 diet. (b) Construct the 95% confidence interval for the mean weight loss after one year of all people who would complete the Method 2 diet. (c) Based on your answers above, does one method appear to be better than the other