if n400 and X80 construct a 95 confidence interval estimate

if n=400 and X=80, construct a 95% confidence interval estimate of the population proportion

Solution

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)=80
Sample Size(n)=400
Sample proportion = x/n =0.2
Confidence Interval = [ 0.2 ±Z a/2 ( Sqrt ( 0.2*0.8) /400)]
= [ 0.2 - 1.96* Sqrt(0) , 0.2 + 1.96* Sqrt(0) ]
= [ 0.161,0.239] ~ [ 16.1%, 23.9%]