Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.7 kilograms with a sample standard deviation of 7.2 kilograms. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kilograms with a standard deviation of 5.9 kilograms.

a. Construct a 98% confidence interval for the difference in mean weight loss between the low-fat and low-carb diets.

b. A dietitian claims that both diets are equally effective. Does the confidence interval contradict this claim?