In a recent poll of 980 homeowners in the United States one

In a recent poll of 980 homeowners in the United States, one in four homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.95, derive an interval estimate for the proportion of all homeowners in the United States that hold a home equity loan. (Round intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answers to 3 decimal places.)

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)=245
Sample Size(n)=980
Sample proportion = x/n =0.25
Confidence Interval = [ 0.25 ±Z a/2 ( Sqrt ( 0.25*0.75) /980)]
= [ 0.25 - 1.96* Sqrt(0) , 0.25 + 1.96* Sqrt(0) ]
= [ 0.223,0.277]