The objective of a study by Sairam et al. was to identify the role of various di
ID: 2936247 • Letter: T
Question
The objective of a study by Sairam et al. was to identify the role of various disease states and additional risk factors in the development of thrombosis. One focus of the study was to determine if there were differing levels of the anticardiolipin antibody IgG in subjects with and without thrombosis. Construct a 95% Confidence Interval for the difference in the mean IgG level between subjects with and without thrombosis. Interpret your confidence interval.
Group Mean IgG Levels Sample Size Standard Deviation Thrombosis 59.01 54 44.89 No Thrombosis 46.61 54 34.85Explanation / Answer
TRADITIONAL METHOD
given that,
mean(x)=59.01
standard deviation , s.d1=44.89
number(n1)=54
y(mean)=46.61
standard deviation, s.d2 =34.85
number(n2)=54
I.
stanadard error = sqrt(s.d1^2/n1)+(s.d2^2/n2)
where,
sd1, sd2 = standard deviation of both
n1, n2 = sample size
stanadard error = sqrt((2015.112/54)+(1214.523/54))
= 7.734
II.
margin of error = t a/2 * (stanadard error)
where,
t a/2 = t -table value
level of significance, =
from standard normal table, two tailedand
value of |t | with min (n1-1, n2-1) i.e 53 d.f is 2.006
margin of error = 2.006 * 7.734
= 15.514
III.
CI = (x1-x2) ± margin of error
confidence interval = [ (59.01-46.61) ± 15.514 ]
= [-3.114 , 27.914]
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DIRECT METHOD
given that,
mean(x)=59.01
standard deviation , s.d1=44.89
sample size, n1=54
y(mean)=46.61
standard deviation, s.d2 =34.85
sample size,n2 =54
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
where,
x1,x2 = mean of populations
sd1,sd2 = standard deviations
n1,n2 = size of both
a = 1 - (confidence Level/100)
ta/2 = t-table value
CI = confidence interval
CI = [( 59.01-46.61) ± t a/2 * sqrt((2015.112/54)+(1214.523/54)]
= [ (12.4) ± t a/2 * 7.734]
= [-3.114 , 27.914]
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interpretations:
1. we are 95% sure that the interval [-3.114 , 27.914] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
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