Question

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

Answer 1

Option B.

Explanation:

As we know that

Margin of error = Z * standard error

Here , the only way to decrease the value of margin of error is to decrease either the value of z or value of standard error as both are directly proportional to margin of error.

Z-value can be decreased by using lower confidence intervals. Standard error can be decreased by increasing sample size (as given in option B)

The answer is option B as it is using sample size of 50 instead of 35 thus decreasing standard error and ultimately decreasing margin of error.