A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random samp

Question

7 days ago

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A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random samp

le of 35 homeowners. They find a 95% confidence interval for the true mean current debt to be ($56,000, $120,000). Which of the following would correctly produce a confidence interval with a smaller margin of error than this 95% confidence interval?
Using the balances of older homeowners because they will have paid off more of their mortgage
Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error
Using the balances of only fifteen homeowners rather than 35, because there is likely to be less variation in fifteen balances than 35
Using 99% confidence, because then its more likely that the true mean is contained in the confidence interval

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-04-07T21:53:10+03:00

Answer:

Option B.

Step-by-step explanation:

As known,

Margin of error = Z * standard error

The margin of error can only be reduced by lowering either the Z value or the standard error, as both are directly proportional to the margin of error.

The Z-value can be diminished by utilizing lower confidence intervals. Standard error can be minimized by augmenting the sample size (as indicated in option B)

The correct choice is option B because it involves a sample size of 50 instead of 35, which subsequently lowers the standard error and consequently the margin of error.