A poll randomly sampled the US population on a yesno questio

A poll randomly sampled the US population on a yes/no question.For a sample size of 400,250 responded voted \"yes\" What is the 95% confidence interval for the proportion of Us population voting \"yes\"?

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=250
Sample Size(n)=400
Sample proportion = x/n =0.625
Confidence Interval = [ 0.625 ±Z a/2 ( Sqrt ( 0.625*0.375) /400)]
= [ 0.625 - 1.96* Sqrt(0.0006) , 0.625 + 1.96* Sqrt(0.0006) ]
= [ 0.5776,0.6724]