2. Are low-fat diets or low-carb diets more effective for weight loss? This question was addressed by a scientific study). 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.a. Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet than that of the low-fat diet? Use the correct test statistic and p-value to answer. b. Can you conclude that the mean weight loss on the low-carbohydrate diet is 1kg greater than that of the low-fat diet? Use the correct test statistic and p-value to answer.
Added by Robert C.
Step 1
Given: Sample 1 (low-carb diet): - Sample size (n1) = 77 - Sample mean weight loss (x̄1) = 4.7 kg - Sample standard deviation (s1) = 7.2 kg Sample 2 (low-fat diet): - Sample size (n2) = 79 - Sample mean weight loss (x̄2) = 2.6 kg - Sample standard deviation Show more…
Show all steps
Close
Your feedback will help us improve your experience
Thuc Nguyen and 81 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Low-fat or low-carb? Are low-fat diets or low-carb diets more effective for weight loss? A sample of 58 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 3.2 kilograms with a sample standard deviation of 5.42 kilograms. A second sample of 60 subjects went on a low-fat diet. Their sample mean weight loss was 2.4 kilograms with a standard deviation of 4.48 kilograms. Can you conclude that the mean weight loss differs between the two diets? Let μ1 denote the mean weight lost on the low-carb diet and μ2 denote the mean weight lost on the low-fat diet. Use the =α0.1 level and the TI-84 Plus calculator.
Madhur L.
10. Low-fat or low-carb? 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 kilograms with a sample standard deviation of 7.16 kilograms. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kilograms with a standard deviation of 5.90 kilograms. Can you conclude that the mean weight loss differs between the two diets? Use the α = 0.01 level. a. State the appropriate null and alternate hypotheses. b. Compute the test statistic. c. How many degrees of freedom are there, using the simple method? d. Do you reject H0? State a conclusion. Source: Journal of the American Medical Association 297:969–977
Adi S.
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.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD