If n400 and x25 construct a 99 confidence interval estimate

If n=400 and x=25, construct a 99% confidence interval estimate for the population proportion

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
(x)=25
Sample Size(n)=400
Sample proportion = x/n =0.063
Confidence Interval = [ 0.063 ±Z a/2 ( Sqrt ( 0.063*0.937) /400)]
= [ 0.063 - 2.576* Sqrt(0) , 0.063 + 2.58* Sqrt(0) ]
= [ 0.032,0.094]