1. The following data were collected in a clinical trial to compare a new drug t
ID: 3132867 • Letter: 1
Question
1. The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol.
New Drug
(n=75)
Placebo
(n=75)
Total Sample
(n=150)
Mean (SD) Total Serum Cholesterol
185.0 (24.5)
204.3 (21.8)
194.7 (23.2)
% Patients with Total Cholesterol < 200
78.0%
65.0%
71.5%
In Problem 2 of this project, you generated a 95 percent confidence interval for the difference in mean total cholesterol levels between treatments. Now, using this same data:
a)Generate a 95 percent confidence interval for the proportion of all patients with total cholesterol < 200.
b)How many patients would be required to ensure that a 95 percent confidence interval has a margin of error not exceeding 5 percent?
New Drug
(n=75)
Placebo
(n=75)
Total Sample
(n=150)
Mean (SD) Total Serum Cholesterol
185.0 (24.5)
204.3 (21.8)
194.7 (23.2)
% Patients with Total Cholesterol < 200
78.0%
65.0%
71.5%
Explanation / Answer
a) Solution:
Confidence Interval Estimate for the Proportion
Data
Sample Size
150
Number of Successes
150*0.715 or 71.5% = 107.25 or 107 approximately
Confidence Level
95%
Intermediate Calculations
Sample Proportion
0.713333333
Z Value
-1.9600
Standard Error of the Proportion
0.0369
Interval Half Width
0.0724
Confidence Interval
Interval Lower Limit
0.6410
Interval Upper Limit
0.7857
b) Solution:
Sample Size Determination
Data
Estimate of True Proportion
0.715
Sampling Error
0.05
Confidence Level
95%
Intermediate Calculations
Z Value
-1.9600
Calculated Sample Size
313.1173
Result
Sample Size Needed
314
Confidence Interval Estimate for the Proportion
Data
Sample Size
150
Number of Successes
150*0.715 or 71.5% = 107.25 or 107 approximately
Confidence Level
95%
Intermediate Calculations
Sample Proportion
0.713333333
Z Value
-1.9600
Standard Error of the Proportion
0.0369
Interval Half Width
0.0724
Confidence Interval
Interval Lower Limit
0.6410
Interval Upper Limit
0.7857
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