In 2003, an organuzation surveyed 1,500 adull Americanes and acked about a centa
ID: 3358955 • Letter: I
Question
In 2003, an organuzation surveyed 1,500 adull Americanes and acked about a centain war, TDo you belteve the Unsted States made the right or wrong decsion to use tary arce the right dedision In 2008, Ofe 1 500 ad Aelicans surveyed, 1,000 stahed the United States made population proporions, proos Pao The lower bound of a 90% cortoeroe rten.D Hound to three decmal places as needed) The upper bond or a 90% condence rteras gtard to hee mal places as needed ] 0 orce in the counliry is bebon the lower and pper bournds of the irteresExplanation / Answer
TRADITIONAL METHOD
given that,
sample one, x1 =1000, n1 =1500, p1= x1/n1=0.667
sample two, x2 =570, n2 =1500, p2= x2/n2=0.38
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( (0.667*0.333/1500) +(0.38 * 0.62/1500))
=0.017
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 =1.64
margin of error = 1.64 * 0.017
=0.029
III.
CI = (p1-p2) ± margin of error
confidence interval = [ (0.667-0.38) ±0.029]
= [ 0.258 , 0.315]
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DIRECT METHOD
given that,
sample one, x1 =1000, n1 =1500, p1= x1/n1=0.667
sample two, x2 =570, n2 =1500, p2= x2/n2=0.38
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 = [ (0.667-0.38) ± 1.64 * 0.017]
= [ 0.258 , 0.315 ]
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interpretations:
1) we are 90% sure that the interval [ 0.258 , 0.315] 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
a.
lower bound = 0.258
b.
upper bound = 0.315
c.
B.there is 90% confidence interval that the difference in the proportion of adult americans from 2003 to 2008 who belive that US made the right decision to use military force in the between lower and upper bound intervals
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