Question

An article reported on the results of an experiment in which half of the individuals in a group of 70 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 5.7 kg, and the sample SD was 3.5, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.7 and 2.7, respectively. Does it appear that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg? Carry out an appropriate test of hypotheses at significance level 0.05 State the relevant hypotheses. (Use μ'or the vegan diet and μ2 for the control diet.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) p-value = State the conclusion in the problem context. Reject Ho. The data suggests that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg 0 Reject H0' The data suggests that the true average weight loss for the vegan diet does not exceed that for the control diet by more than 1 kg. O Fail to reject H0. The data suggests that the true average weight loss for the vegan diet does not exceed that for the control diet by more than 1 kg. O Fail to reject H0. The data suggests that the true ฮverage weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.

Answer 1

The statistical software output for this problem is:

Two sample T summary hypothesis test: 1 Mean of Population 1 μ2 : Mean of Population 2 (with pooled variances) Hypothesis test results: Difference Sample Diff Std. Err.DF T-Stat P-value H1 H2 2 0.74718519 68 1.3383563 0.0926

Hence,

Hypotheses: Option B is correct.

t = 1.34

P-value = 0.093

Conclusion: Option C is correct.