The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.
A) [126.2730, 539.2270]
B) [259.7393, 405.7607]
C) [279.0056, 386.4944]
D) [291.8600, 373.6400]

Question

Quizplus · Accepted Answer

To construct a 99% confidence interval for the mean duration of the foreclosure process, we first calculate the sample mean and the sample standard deviation. The sample mean ($\bar{x}$) is the sum of all sample values divided by the number of samples (n=8). The sample standard deviation (s) is calculated using the formula for the sample standard deviation of a set of values. Then, we use the formula for the confidence interval: $\bar{x} \pm z*\frac{s}{\sqrt{n}}$, where z is the z-score corresponding to the desired confidence level (for 99%, z ≈ 2.576). Plugging in the values, we get the confidence interval as option B, which indicates the range within which the true mean duration of the foreclosure process in Boston is likely to fall with 99% confidence.

The Mortgage Foreclosure Crisis That Preceded the Great Recession Impacted