3. “Low-carb” diets have become quite popular recently. In a recent study report

Question

3. “Low-carb” diets have become quite popular recently. In a recent study reported in the New England Journal of Medicine, researchers randomly assigned 63 obese men and women to either a low-carbohydrate diet or a conventional diet. Each subject’s weight loss, as a percentage of body weight, was recorded after 3 months, after 6 months, and after 12 months. a. Is this an observational study or an experiment? Explain briefly. b. Identify the explanatory variable and the response variable. c. Some people exercise more than others, and exercise can affect weight loss. Explain why this exercise level is nevertheless not a confounding variable in this study. d. The researchers wanted to test the claim that people tend to lose more weight on low-carb diets than on conventional diets. Write the null and alternative hypotheses (in symbols only) for testing this claim. e. The p-values were .182 for the 3-month weight losses, .106 for the 6-month weight losses, and .070 for the 12-month weight losses. Summarize the conclusions you would draw.

Explanation / Answer

(a) As we are observing the same number of men and women over a 12 moonth window then it's a observational study.

(b) Explanatory variable is diet and response variable is weight loss

(c) As we have taken all the obese men and women so doing physical exercise does not affect in losing body weight. That's why exercise level is not confounded over there.

(d) let M1i and M2i be the average weight loss over i different month intervals. i=1,2,3 and over two different diets.

then our null hypothesis is

H0 : M1i=M2i  for all I=1,2,3 vs H1 : M1i ne M2i

(d) As for all the tests p-value is greater than 0.05, then we can conclude that We will accept our null hypothesis. But the p-value decreases if the month interval increases. So We can conclude that the effect of two different diet actually have more significant effect on 12 month interval than on 6 month than or 3 month. So at 12 month interval we can marginally conclude it has some effect over the weight loss but at 5% level the significance is low.

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