Question 665063: New research shows that 40% of randomly selected adult males (n = 250) and 22% of randomly selected adult females (n = 250) have been arrested at least once in their lifetime. Using a 97% confidence level, calculate confidence intervals for both males and females who have been arrested. Then, discuss whether it is possible that the true percentage of males and females who have been arrested might actually overlap.
having a lot of trouble with confidence intervals
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! New research shows that 40% of randomly selected adult males (n = 250) and 22% of randomly selected adult females (n = 250) have been arrested at least once in their lifetime. Using a 97% confidence level, calculate confidence intervals for both males and females who have been arrested. Then, discuss whether it is possible that the true percentage of males and females who have been arrested might actually overlap.
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Males CI:
p-hat = 0.4
ME = z*s
Comment: A 97% CI has 2 equal tails of 1.5%
The z-value with a right tail of 1.5% = -invNorm(0.015) = 2.1701
s = sqrt[p*hat*q-hat/n] = sqrt[0.4*0.6/250]
ME = 2.1701*sqrt[0.4*0.6/250] = 0.0672
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CI Form: p-hat-ME < p < p-hat+ME
97% CI: 0.4-0.0672 < p < 0.4+0.0672
The CI is (0.3328,0.4672)
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Femailes CI:
p-hat = 0.22
ME = 2.1701*sqrt(0.22*0.78/250) = 0.0569
97% CI: 0.22-0.0569 < p < 0.22+0.0569
The CI is (0.1631,0.2769)
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The CIs do not overlap.
Cheers,
Stan H.
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