Question: Confidence Interval for Comparing Diets A randomized trial tested the effectiveness of diets on adults. Among 40 subjects using the Weight Watchers diet, the mean weight loss after one year was \(3.0 \mathrm{lb}\) with a standard deviation of \(4.9 \mathrm{lb}\). Among 40 subjects using the Atkins diet, the mean weight loss after one year was \(2.1 \mathrm{lb}\) with a standard deviation of \(4.8 \mathrm{lb}\). Construct a \(95 \%\) confidence interval estimate of the difference between the population means. Does there appear to be a difference in the effectiveness of the two diets? Does the amount of weight loss appear to justify either diet?

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