In 2012, a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $ 443,705 with a standard deviation of $ 196,196.

a) What assumptions and conditions must be checked before finding a confidence interval for the mean? How would you check them?

b) Find a 95% confidence interval for the mean value per home.

c) Interpret this interval and explain what 95% confidence means.

d) Suppose nationally, the average foreclosed home sold for $ 350,000. Do you think the average sale price in the sampled community differs significantly from the national average? Explain.