Directions A study in The Journal of the American Medical Association describes

Question

Directions A study in The Journal of the American Medical Association describes the effects of diets on weight control. In the study, 311 women were randomly divided into four groups. The first group followed the Atkins diet, which is based on very low carbohydrate intake. The second group followed the LEARN (lifestyle, exercise, attitudes, relationships, nutrition) diet, which is based on low fat and high carbohydrate intake. The third group followed the Ornish diet, which is based on very high carbohydrate intake. The fourth group followed the Zone diet, which is based on low carbohydrate intake. Each group received weekly instruction for two months, and there was a follow-up one year from the beginning of the study. The mean weight losses of each group after one year on the diet are shown in the table below. Exercises 1. Opening Paragraph - Begin by writing an opening paragraph where you summarize the statistical concepts you have learned this week and how you plan to integrate those concepts into this task. In Exercises 2–5, perform a two-sample z-test to determine whether the mean weight losses of the two indicated groups are different. For each exercise, write your conclusion as a sentence. Use a level of significance of 0.05. You must show or explain how you arrived at your conclusions. Simply rejecting or failing to reject the null hypothesis is not sufficient. 2. Test the weight losses of people in the Atkins group against those in the LEARN group. 3. Test the weight losses of people in the Ornish group against those in the Zone group. 4. Test the weight losses of people in the LEARN group against those in the Zone group. 5. Test the weight losses of people in the Atkins group against those in the Ornish group. 6. Suppose that in another study, 42 people used an herbal supplement and a high-fiber, low-calorie diet to lose weight. The mean weight loss of this group was 7.05 pounds and the standard deviation was 7.28 pounds. (a) Test the mean weight loss of this group with the Atkins group described previously. Use 0.01. (b) Test the mean weight loss of this group with the Zone group described previously. Use 0.01. 7. In which comparisons in Exercises 2–6 did you find a difference in weight losses? Write a summary of your findings. Please include at least one reference to an outside scholarly source (see Supplemental Syllabus for examples). 8. Metacognition – thinking about thinking and learning. You have analyzed the “how you think” and “how you learn” over the past five weeks. For this week’s metacognitive evaluation, please write a short paragraph (two to five sentences) explaining how your thinking processes have evolved from the first few weeks and how will it will specifically apply to your future career choice. Again, you may need to reference your previous Weekly Case Studies to thoroughly answer this question. Hopefully, this reflective, metacognitive process will remain with you whenever you learn!

Explanation / Answer

Directions A study in The Journal of the American Medical Association describes the effects of diets on weight control.

In the study, 311 women were randomly divided into four groups.

The first group followed the Atkins diet, which is based on very low carbohydrate intake.

The second group followed the LEARN (lifestyle, exercise, attitudes, relationships, nutrition) diet, which is based on low fat and high carbohydrate intake.

The third group followed the Ornish diet, which is based on very high carbohydrate intake.

The fourth group followed the Zone diet, which is based on low carbohydrate intake.

Each group received weekly instruction for two months, and there was a follow-up one year from the beginning of the study. The mean weight losses of each group after one year on the diet are shown in the table below.

n1 = 77

n2 = 79

n3 = 76 and

n4 = 79

x1bar = 10.36

x2bar = 5.73

x3bar = 4.85

x4bar = 3.53

s1= 15.79

s2= 12.50

s3= 13.73

s4= 12.00

1. Opening Paragraph - Begin by writing an opening paragraph where you summarize the statistical concepts you have learned this week and how you plan to integrate those concepts into this task.

In Exercises 2–5, perform a two-sample z-test to determine whether the mean weight losses of the two indicated groups are different.

For each exercise, write your conclusion as a sentence.

Use a level of significance of 0.05.

You must show or explain how you arrived at your conclusions.

We done all these questions by using TI-83 calculator.

steps :

STAT --> TESTS --> 3: 2SampZTest --> ENTER --> Stats --> ENTER --> Input all the values --> select alternative second option --> ENTER --> Calculate --> ENTER

2. Test the weight losses of people in the Atkins group against those in the LEARN group.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of Atkins group.

and mu2 is population mean of LEARN group.

By using TI-83 calculator :

z = 2.0273

P = 0.0426

P < alpha (0.05)

Reject H0 at 5% level of significance.

Conclusion : Population mean of Atkins group is differ than population mean of LEARN group.

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3. Test the weight losses of people in the Ornish group against those in the Zone group.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of Ornish group.

and mu2 is population mean of Zone group.

By using TI-83 calculator :

z = 0.6363

P = 0.5246

P > alpha (0.05)

Accept H0 at 5% level of significance.

Conclusion : Population mean of Ornish group is same as population mean of Zone group.

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4. Test the weight losses of people in the LEARN group against those in the Zone group.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of Learn group.

and mu2 is population mean of Zone group.

By using TI-83 calculator :

z = 1.1285

P = 0.2591

P > alpha (0.05)

Accept H0 at 5% level of significance.

Conclusion : Population mean of Learn group is same as population mean of Zone group.

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5. Test the weight losses of people in the Atkins group against those in the Ornish group.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of Atkins group.

and mu2 is population mean of Ornish group.

By using TI-83 calculator :

z = 2.3042

P = 0.02

P < alpha (0.05)

Reject H0 at 5% level of significance.

Conclusion : Population mean of Atkins group is differ than population mean of Ornish group.

-------------------------------------------------------------------------------------------------------------------------------------------------------------

6. Suppose that in another study, 42 people used an herbal supplement and a high-fiber, low-calorie diet to lose weight. The mean weight loss of this group was 7.05 pounds and the standard deviation was 7.28 pounds.

(a) Test the mean weight loss of this group with the Atkins group described previously. Use 0.01.

n1 = 42

X1bar = 7.05

s1 = 7.28

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of this new group.

and mu2 is population mean of Atkins group.

By using TI-83 calculator :

z = -1.5604

P = 0.1187

P > alpha (0.01)

Accept H0 at 1% level of significance.

Conclusion : Population mean of new group is same as population mean of Atkins group.

---------------------------------------------------------------------------------------------------------------------------------------------------------

(b) Test the mean weight loss of this group with the Zone group described previously. Use 0.01.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean of this new group.

and mu2 is population mean of Zone group.

By using TI-83 calculator :

z = 2.0042

P = 0.045

P < alpha (0.01)

Reject H0 at 1% level of significance.

Conclusion : Population mean of new group is differ than population mean of Zone group.

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