Question

The (simulated) data (mg decrease per decilitre of blood) for the Omega-3 group is stored in Table A1, and the data for the control group is stored in Table A2. You are required to calculate a 95% confidence interval for the average difference in cholesterol reduction and to test the hypothesis that there was no difference between the two diets in average reduction of cholesterol.

1. How many patients were in each diet group?

2. What was the mean (decrease) in cholesterol for the Omega-3 group of patients?

3. What was the standard deviation in that group? LABORATORY ASSIGNMENTS INTRODUCTORY STATISTICS LABORATORY 37

4. What was the mean (decrease) in cholesterol for the control group of patients?

5. What was the standard deviation in the control group?

6. What is the estimated difference of means?

7. Standard error of the difference between means 2 2 2 1 2 1 n s n s = + What is the standard error of the difference of means?

b) Calculate the margin of error of the estimated difference of means. For this large-sample 95% confidence interval we can approximate with a z value which is z0.025 = 1.96. Calculate the confidence interval as difference between means ± margin of error.

8. What is the margin of error of the estimated difference?

9. What is the lower limit for the 95% confidence interval of the difference in cholesterol reduction between Omega-3 and control diets?

10. What is the upper limit?

DATA A1:

86.6
73.9
99.4
67.9
82.3
80.3
82.8
77.9
76.8
85.9
62.5
34
120.9
57
114.9
83.7
103.5
67.4
86.1
87.6
104.2
123
91.7
95.2
95.8
90.7
72.9
72.9
62
98.1
70
77.3
34.8
58
66.7
100.6
98.6
75
52.9
54
42.1
86.7
68.9
68.8
76
87.1
99.2
119.3
88.5
90.9 DATA A2 52.5 38.6 60.7 90.8 57.9 38.6 31.9 35.2 27.7 31.5 39.4 80.4 61.1 88.1 37.5 43.5 35.6 81.6 55.2 66.7 56.3 47.4 105.2 51.7 35.8 58.9 24.5 92.8 55 52.5 110.2 86.5 30.7 50.8 58.2 75.1 73.9 12.5 23.3 96.6 55.6 102.9 103 50.2 88.7 53.7 41.5 24.7 80.3 84.4

Answer 1

1. How many patients were in each diet group? 50

2. What was the mean (decrease) in cholesterol for the Omega-3 group of patients? 81.06

3. What was the standard deviation in that group?   20.26

4. What was the mean (decrease) in cholesterol for the control group of patients?   58.75

5. What was the standard deviation in the control group? 25.04

6. What is the estimated difference of means?   22.32

7. The standard error of the difference between means 2 2 2 1 2 1 ns ns = + What is the standard error of the difference of means? -0.67689

b) Calculate the margin of error of the estimated difference of means. For this large-sample 95% confidence interval we can approximate with a z value which is z0.025 = 1.96. Calculate the confidence interval as a difference between means ± margin of error

8. What is the margin of error of the estimated difference? 4.55

9. What is the lower limit for the 95% confidence interval of the difference in cholesterol reduction between Omega-3 and control diets?  13.27

10. What is the upper limit?   31.36

Please see the attached image for the workings. Thanks. Let me know in case of any doubts.