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 kind that two in five subprime mortgages are likely to default nationally.
A research economist is interested in estimating default rates in Illinois with 95% confidence. How large a sample is needed to restrict the margin of error to within 0.06, using the reported national default rate?