A clinical trial is conducted comparing a new pain reliever for arthritis to a p
ID: 3326434 • Letter: A
Question
A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo and the outcome is pain relief within 30 minutes. The data are shown below.
Pain Relief
No Pain Relief
New Medication
44
76
Placebo
21
99
What is the 90% confidence interval for the difference in the proportions of patients receiving pain relief within 30 minutes between the two treatment groups (new medication minus placebo)?
Answer:
1. insufficient information provided
2.. 0.082 - 0.301
3. 0.099 - 0.284
Pain Relief
No Pain Relief
New Medication
44
76
Placebo
21
99
Explanation / Answer
TRADITIONAL METHOD
given that,
sample one, x1 =44, n1 =120, p1= x1/n1=0.3667
sample two, x2 =21, n2 =120, p2= x2/n2=0.175
I.
standard error = sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where
p1, p2 = proportion of both sample observation
n1, n2 = sample size
standard error = sqrt( (0.3667*0.6333/120) +(0.175 * 0.825/120))
=0.056
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
margin of error = 1.645 * 0.056
=0.0922
III.
CI = (p1-p2) ± margin of error
confidence interval = [ (0.3667-0.175) ±0.0922]
= [ 0.099 , 0.284]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
sample one, x1 =44, n1 =120, p1= x1/n1=0.3667
sample two, x2 =21, n2 =120, p2= x2/n2=0.175
CI = (p1-p2) ± sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where,
p1, p2 = proportion of both sample observation
n1,n2 = size of both group
a = 1 - (confidence Level/100)
Za/2 = Z-table value
CI = confidence interval
CI = [ (0.3667-0.175) ± 1.645 * 0.056]
= [ 0.099 , 0.284]
-----------------------------------------------------------------------------------------------
interpretations:
1) we are 90% sure that the interval [ 0.0995 , 0.2838] contains the difference between
true population proportion P1-P2
2) if a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the difference between
true population mean P1-P2
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