stion: 1 pt 3 of 12 (0 complete) This Quiz: 12 pts possib nra do nized, double-b
ID: 3311651 • Letter: S
Question
stion: 1 pt 3 of 12 (0 complete) This Quiz: 12 pts possib nra do nized, double-blind c clinical trials of a new vaccine, subjects were randomly divided into two groups. Subjects in group 1 recelved the subjects in the control group (group 2) experienced vomiting as a new vaccine while subjects in group 2 received a control vaccine. After the first dose, 107 of 743 subjects in the experimental group (group 1) side effect. Construct a 99% confidence interval for the difference between the two population proportions, p1-p2 Construct a 99% confidence interval estimate. 0: p1-p2Explanation / Answer
TRADITIONAL METHOD
given that,
sample one, x1 =107, n1 =743, p1= x1/n1=0.144
sample two, x2 =67, n2 =638, p2= x2/n2=0.105
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( (0.144*0.856/743) +(0.105 * 0.895/638))
=0.018
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.58
margin of error = 2.58 * 0.018
=0.046
III.
CI = (p1-p2) ± margin of error
confidence interval = [ (0.144-0.105) ±0.046]
= [ -0.007 , 0.085]
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DIRECT METHOD
given that,
sample one, x1 =107, n1 =743, p1= x1/n1=0.144
sample two, x2 =67, n2 =638, p2= x2/n2=0.105
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 = [ (0.144-0.105) ± 2.58 * 0.018]
= [ -0.007 , 0.085 ]
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interpretations:
1) we are 99% sure that the interval [ -0.007 , 0.085] 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, 99% of these intervals will contains the difference between
true population mean P1-P2
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