Question

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 90% confidence interval for the mean duration of the foreclosure process in Boston.

Answer 1

Answer:

[293.21;372.28]

Step-by-step explanation:

Hello!

You are asked to construct a 90% Confidence Interval for the mean duration of the foreclosure process in Boston.

The Study variable is X: duration of foreclosure in Boston. X≈N(μ;σ²)

Sample n=8

To study the population sample you can use either a Z or a t-statistic. Since the sample is less than 10, I'll choose a Student t-statistic, because it is more potent with small samples than the Z, but either one is a good choice.

X[bar]= 332.75

S= 59.01

$X[bar] ± t_{n-1; 1-\alpha /2}*\frac{S}{\sqrt{n} }$

$332.75 ± 1.895*\frac{59,01}{\sqrt{8} }$

[293.21;372.28]

With a confidence level of 90% you'd expect the interval [293.21;372.28] to contain the population mean of the duration of the foreclosure process in Boston.

I hope you have a SUPER day!