Question

Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default. Suppose a recent report finds that two in five subprime mortgages are likely to default nationally. A research economist is interested in estimating default rates in Illinois with 99% confidence. [You may find it useful to reference the z table.] How large a sample is needed to restrict the margin of error to within 0.07, using the reported national default rate? (Round "z" value to 3 decimal places. Do not round intermediate calculations. Round up your final answer to nearest whole number.)

Answer 1

p = 2/5 = 0.4

Z for 99% confidence interval = Z_0.005 = 2.575

Margin of error = Z_0.005 * sqrt(p * (1 - p) / n)

or, 0.07 = 2.575 * sqrt(0.4 * 0.6 / n)

or, n = 324.77

or, n = 325 (ans)