1.The main trial is conducted and involves a total of 200 patients. Patients are
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Question
1.The main trial is conducted and involves a total of 200 patients. Patients are enrolled and randomized to receive either the experimental medication or the placebo. The data shown below are data collected at the end of the study after 6 weeks on the assigned treatment:
Experimental
(n = 100)
Placebo
(n = 100)
Mean (Standard Deviation) Systolic Blood Pressure
120 (15.4)
137.4 (18.9)
% Hypertensive
14%
22%
% With Side Effects
6%
8%
a.Generate a 95% confidence interval for the difference in mean systolic blood pressures between groups.
b.Generate a 95% confidence interval for the difference in proportions of patients with hypertension between groups.
c.Generate a point estimate for the relative risk of side effects in patients assigned to the experimental group as compared to placebo. Generate a 95% confidence interval for the relative risk.
Experimental
(n = 100)
Placebo
(n = 100)
Mean (Standard Deviation) Systolic Blood Pressure
120 (15.4)
137.4 (18.9)
% Hypertensive
14%
22%
% With Side Effects
6%
8%
Explanation / Answer
1.The main trial is conducted and involves a total of 200 patients. Patients are enrolled and randomized to receive either the experimental medication or the placebo. The data shown below are data collected at the end of the study after 6 weeks on the assigned treatment:
Experimental
(n = 100)
Placebo
(n = 100)
Mean (Standard Deviation) Systolic Blood Pressure
120 (15.4)
137.4 (18.9)
% Hypertensive
14%
22%
% With Side Effects
6%
8%
a.Generate a 95% confidence interval for the difference in mean systolic blood pressures between groups.
95% confidence interval for the difference in mean systolic blood pressures between experimental and placebo groups.
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
100
Sample Mean
120
Sample Standard Deviation
15.4
Population 2 Sample
Sample Size
100
Sample Mean
137.4
Sample Standard Deviation
18.9
Intermediate Calculations
Population 1 Sample Degrees of Freedom
99
Population 2 Sample Degrees of Freedom
99
Total Degrees of Freedom
198
Pooled Variance
297.1850
Standard Error
2.4380
Difference in Sample Means
-17.4000
Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level
95%
Intermediate Calculations
Degrees of Freedom
198
t Value
1.9720
Interval Half Width
4.8077
Confidence Interval
Interval Lower Limit
-22.2077
Interval Upper Limit
-12.5923
95% CI for mean difference = (-22.2077, -12.5923)
b.Generate a 95% confidence interval for the difference in proportions of patients with hypertension between groups.
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
14
Sample Size
100
Group 2
Number of Items of Interest
22
Sample Size
100
Intermediate Calculations
Group 1 Proportion
0.14
Group 2 Proportion
0.22
Difference in Two Proportions
-0.08
Average Proportion
0.1800
Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level
95%
Intermediate Calculations
Z Value
-1.9600
Std. Error of the Diff. between two Proportions
0.0540
Interval Half Width
0.1059
Confidence Interval
Interval Lower Limit
-0.1859
Interval Upper Limit
0.0259
95% proportion difference =(-0.1829, 0.0259)
c.Generate a point estimate for the relative risk of side effects in patients assigned to the experimental group as compared to placebo. Generate a 95% confidence interval for the relative risk.
Experimental
Placebo
side effect
6
8
No side effect
94
92
100
100
Risk in experimental group = 6/100=0.06
Risk in experimental placebo=8/100=0.08
Relative risk =0.06/0.08 =0.75
95% confidence interval for the relative risk = (0.2700, 2.0832)
Experimental
(n = 100)
Placebo
(n = 100)
Mean (Standard Deviation) Systolic Blood Pressure
120 (15.4)
137.4 (18.9)
% Hypertensive
14%
22%
% With Side Effects
6%
8%
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