14. [I5 Points] DETAILS I DEVORESTAT9 9.2.0335. MY NOTES I An article reported on the results of an experiment in which half of the individuals in a group of 66 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 5.5 kg, and the sample SD was 3.3, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.5 and 2.5, 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 signicance level 0.05. IA usr: SA State the relevant hypotheses. (Use #1 for the vegan diet and [42 for the control diet.) 0 H0: #1 [42 = 0 Ha: \"1 - 142 t 0 O HO: \"1 \"2 = 0 Ha: \"1 - \"2 Z 0 O Ho: \"1 - \"2 = 1 H3: \"1 \"2 1 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. 0 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. O Fail to reject Ho' 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 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. 0 Fall to 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