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

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 an interval estimate for the proportion of all homeowners in the United States that hold a home equity loan. Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)

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. Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)

Explanation / Answer

Here p=1/4 and n=980 and z=1.96 for 95% CI

Now E=z*sqrt(p(1-p)/n)=0.027

Hence CI=p+/-E=0.25+/-0.027=(0.223,0.277)

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