Question

Are low-fat diets or low-carb diets more effective for weight loss? A sample of 70 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 10.5 pounds with a sample standard deviation of 7.09 pounds. A second sample of 76 subjects went on a low-fat diet. Their sample mean weight loss was 18.0 with a standard deviation of 7.26. Can you conclude that their was no difference in the mean weight loss between the two diets? Use the α = 0.05 level. Be sure to show all 5 steps of your Hypothesis Test! Evaluate using EITHER a Traditional or P-value Hypothesis Test (your choice.)

* If using Traditional - draw the normal curve, labeling the CV, TV, and shading the critical region * If using P-value - explain why you chose your decision.

Next, find the confidence interval using the same alpha.

Last, explain how your confidence interval supports your hypothesis test.

Answer 1

For low-carbohydrate diet:

For low-fat diet:

(1) Null and Alternative Hypotheses

(2) Critical value

At = 0.05, and the critical value for a two-tailed test is z_c = 1.96

(3) Test Statistics

(4) Decision about the null hypothesis

Since it is observed that z = -6.312 < z_c = -1.96, it is then concluded that the null hypothesis is rejected.

P-value approach: The p-value is p = 0, and since p = 0 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that there is difference in the mean weight loss between the two diets​, at the 0.05 significance level.

Confidence interval:

95% confidence interval is

As the Confidence interval does not contain the value 0. We can reject the null hypothesis. And claim that there is difference between the means.