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# Confidence Intervals of the Difference Between Population Means

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In these two exercises, assume that the two samples are independent random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal, unless stipulates otherwise.

The 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 lb with a standard deviation of 4.9 lb. Among 40 subjects using the Atkins diet, the mean weight loss after one year was 2.1 lb with a standard deviation of 4.8 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?

The Confidence Interval for Magnet Treatment of Pain
Construct a 90% confidence interval estimate of the difference between the mean reduction in pain for those treated with magnets and the mean reduction in pain for those given a sham treatment. Based on the result, does it appear that the magnets are effective in reducing pain?
Reduction in pain level after magnet treatment: n = 20, = 0.49, s = 0.96
Reduction in pain level after sham treatment: n = 20, = 0.44, s = 1.4