the answer is c, please explain the process In a study of the effect of air poll
ID: 3237147 • Letter: T
Question
the answer is c, please explain the process
In a study of the effect of air pollution on lung function, a sample of 50 children living in a community with a high level of ozone pollution had their lung capacities measured, and 14 of them had capacities that were below normal for their size. A second sample of 80 children was drawn from a community with a low level of ozone pollution, and 12 of them had lung capacities that were below normal for their size. A 95% confidence interval for the difference in these proportions (high ozone low ozone) was constructed. Which of these is the margin of error of the confidence interval? a. 0.078 b. 0.121 c. 0.147 d. 0.179 e. 0.277Explanation / Answer
high level ozone proportion=p1=14/50=0.28 , sample size of high level ozone=n1=50
var(p1)=p1(1-p1)/n1=0.28*(1-0.28)/50=0.004032
low level ozone proportion=p1=12/80=0.15 , sample size of low level ozone=n1=80
var(p2)=p2(1-p2)/n2=0.15*(1-0.15)/80=0.001594
difference of proportion=p1-p2=0.28-0.15=0.13
var(p1-p2)=var(p1)+var(p2)=0.005626
SE(p1-p2)=sqrt(var(p1-p2))=sqrt(0.005626)=0.075
with (1-alpha)*100% confidence, margin of error= z(alpha/2)*SE(p1-p2)
95% confidence margin of error=z(0.05/2)*0.075=1.96*0.075=0.147
right choice is c.0.147
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