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Example 132: Recent studies have indicated that low carbohydrate diets are at least as effective as low fat diets in reducing weight. Does it matter which low carbohydrate diet is followed? Two samples of overweight, premenopausal women were randomly assigned to either the Atkins diet or the Zone diet for one year. At no point in the yearlong study was total calorie consumption different between the two groups. The results of the study are summarized below. Construct the 98% confidence interval for the true difference between the weight loss amounts achieved on the two low carbohydrate diets.