in a recent poll of 1,000 homeowners in the united states, one in eight homeowners reports having a home equity loan that he or she is currently paying off. using a confidence coefficient of 0.99, construct the confidence interval 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.)
Confidence interval to

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09-12-2022
Mathematics

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in a recent poll of 1,000 homeowners in the united states, one in eight homeowners reports having a home equity loan that he or she is currently paying off. using a confidence coefficient of 0.99, construct the confidence interval 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.)
Confidence interval to

Answer :

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HafsaM HafsaM · Answer 1 · 2022-12-16T05:51:31-05:00

For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).

We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.

If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.

Sample proportion p = 125/1000 = 0.125

given that confidence coefficient = 0.99

α = 1 - confidence coefficient = 1 - 0.99

α = 0.01

z₀.₀₁ / 2 = 2.58

Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity

= p ± z₀.₀₁/2 √p(1-p)/n

= 0.125 ± 2.58 √0.125(0.875)/1000

= 0.125 ± 2.58 √0.0001

= 0.125 ± 0.0258

= (0.125 - 0.0258,0.125 + 0.0258)

= (0.0992, 0.1508)

Hence (0.0992, 0.1508) is the confidence interval.

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