In a test of weight loss programs, 165 subjects were divided such that 33 subjec

Question

In a test of weight loss programs, 165 subjects were divided such that 33 subjects followed each of 5 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.05 significance level to test the claim that the mean weight loss is the same for the different diets. Should the null hypothesis that all the diets have the same mean weight loss be rejected? A. Yes, because the P-value is greater than the significance level. B. Yes, because the P-value is less than the significance level. C. No, because the P-value is less than the significance level. D. No, because the P-value is greater than the significance level.

Explanation / Answer

We have been provided with the Analysis of variance table for the testing of the hypothesis that all the diets have the same mean weight. Given the values of the F statistic and the p value as well as the critical value we can use either of the two values to conclude about the test. Supposing the level of significance of the test is 5%, we reject the null hypothesis if the p value is smaller than the significance level.

Here as we can see the p value is 0.005725 and the signifiance level is 0.05. Thus we reject the hypothesis that all the diets have the same mean weight.

Thus, option B is correct.

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