A simple random sample of 450 residents in the state of New

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within 1 mile of a hazardous waste site. If a 95% confidence interval were calculated for a scenario where p = 0.3 and another scenario where p = 0.7, how would the two confidence intervals compare?

Solution

Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No.Of Observed (n1)=450
P1= X1/n1=0.3
Proportion 2
No.Of Observed (n2)=450
P2= X2/n2=0.7
C.I = (0.3-0.7) ±Z a/2 * Sqrt( (0.3*0.7/450) + (0.7*0.3/450) )
=(0.3-0.7) ± 1.96* Sqrt(0.001)
=-0.4-0.06,-0.4+0.06
=[-0.46,-0.34]