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 three in five subprime mortgages are likely to default nationally. A research economist is interested in estimating default rates in Illinois with 99% confidence. Use Table 1.

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. Roundup your final answer to nearest whole number.)

Margin of error

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.07

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.07)² * 0.5 * 0.5

= 338.56 = 339

sample size = 339