TINtsS STATISTICS dule 6 Quiz Question 5 (of 6 10.00 points Exercise 8-49 Algo I

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TINtsS STATISTICS dule 6 Quiz Question 5 (of 6 10.00 points Exercise 8-49 Algo In a recent poil of 1,700 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 0.90, derive an interval (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.) Confidence interval to References eBook & Resources Worksheet Difficulty: 3 Hard Exercise 8-49 Algo Learning Objective: 08-06 Calculate a confidence interval for the population 0 2 3 4 5 6

Explanation / Answer

Solution:

A 90% confidence interval estimate for the proportion of all homeowners in the United States that hold a home equity loan is,
Here p =1/4 and n = 1700 and z = 1.65 for 95% CI
From the standard normal table, the z-critical value at 90% confidence is 1.65
90% C.I = p ± Z/2 * sqrt(p(1-p)/n)
= 0.25 ± 1.65 *sqrt(0.25(1-0.25)/1700)
= 0.2327 to 0.2673
A 90% confidence interval estimate for the proportion of all homeowners in the United States that hold a home equity loan is 0.2327 to 0.2673

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