Are low-fat diets or low-carb diets more effective for weight loss? A sample of 78 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 15.0 pounds with a sample standard deviation of 7.77 pounds. A second sample of 74 subjects went on a low-fat diet. Their sample mean weight loss was 16.3 with a standard deviation of 6.10. Can you conclude that the mean weight loss differed between the two diets? Use the α = 0.01 level.
Added by Christina S.
Step 1
- Alternative Hypothesis (H1): The mean weight loss for low-carb diets is not equal to the mean weight loss for low-fat diets (μ1 ≠ μ2). ** Show more…
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Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time the sample mean weight loss was 4.7 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.9 kg. Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? Find the P-value and state a conclusion. Round the answer to four decimal places.
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Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.6 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.8 kg. Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is 0.0233. We can conclude that the mean weight loss is greater for those on the low-carbohydrate diet.
A weight-loss diet claims that it causes weight loss by eliminating carbohydrates (breads and starches) from the diet. To test this claim, researchers randomly assign overweight subjects to two groups. Both groups eat the same amount of calories, but one group eats almost no carbs, and the other group includes carbs in their meals. After 2 months, the researchers test the claim that the no-carb diet is better than the usual diet. They record the proportion of each group that lost more than $5 \%$ of their initial weight. They then announce that they failed to reject the null hypothesis. Which of the following are valid interpretations of the researchers' findings? a. There were no significant differences in effectiveness between the no-carb diet and the carb diet. b. The no-carb diet and the carb diet were equally effective. c. The researchers did not see enough evidence to conclude that the no-carb diet was more effective. d. The no-carb diet was less effective than the carb diet.
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