Question

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 the interval estimate for the proportion of all homeowners in the United States that hold a home equity loan. (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

Answer 1

sample proportion, = 0.25
sample size, n = 980
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.25 * (1 - 0.25)/980) = 0.0138

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0138
ME = 0.027

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.25 - 1.96 * 0.0138 , 0.25 + 1.96 * 0.0138)
CI = (0.223 , 0.277)