Question

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? Select all that apply. A.The researchers did not see enough evidence to conclude that the​ no-carb diet was more effective. B.There were no significant differences in effectiveness between the​ no-carb diet and the carb diet. C. The​ no-carb diet and the carb diet were equally effective. D.The​ no-carb diet was less effective than the carb diet. E.None of the above interpretations are valid.

Answer 1

Answer: A.The researchers did not see enough evidence to conclude that the​ no-carb diet was more effective

Explanation: The null and alternative hypothesis for the test are,

H0: There is no difference in mean weight between groups of carb diet and no-carb diet,

HA: There is a significant difference in mean weight between groups of carb diet and no-carb diet,

Since the researchers failed to reject the null hypothesis at 5% significance level, there is sufficient evidence that there is a significant difference in mean weight between groups of carb diet and no-carb