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.

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