A nutritionist is interested in the effects of three different diets on weight loss. She randomly assigns 15 participants to each of the three diets and measures their weight loss over a 4-week period. The resulting weight loss data (in pounds) are shown below: Diet 1 Diet 2 Diet 3 7.2 5.5 8.1 6.3 4.9 7.8 5.8 6.2 8.3 7.1 5.1 8.5 6.5 6.3 8.2 5.9 5.7 8.4 7.0 6.1 8.1 6.4 5.4 8.6 5.5 4.8 8.0 6.2 6.0 8.2 5.6 5.6 8.5 7.5 5.9 8.3 6.8 6.4 8.1 5.7 5.2 8.4 7.2 6.0 8.0 Assuming equal variances and a significance level of 0.05, is there a significant difference in weight loss between the three diets?
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When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dan singer, et al., Journal of the American Medical Association, Vol. 293, No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0. Based on these results, does the diet appear to be effective? Does the diet appear to have practical significance?
Hypothesis Testing
Testing a Claim About a Mean
When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 Ib and the standard deviation was 4.9 lb (based on dara from "Comparison of the Atkins, Ornish, Weight Warchers, and Zone Diers for Weight Loss and Heart Disease Reduction," by Dansinger et al. Journal of the American Medical Association, Vol. $293,$ No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0. Based on these results, does the diet appear to be effective? Does the diet appear to have practical significance?
Sheryl E.
A physician who specializes in weight control has three different diets he recommends. As an experiment, he randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pound, were noted. Plan X Plan Y Plan Z At the 0.05 significance level, can he conclude that there is a difference in the mean amount of weight loss among the three diets?
Adi S.
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