When homeowners fail to make mortgage payments, the bank forecloses and sells the home, often at a loss. In one large community, realtors randomly sampled 36 bids from potential buyers to determine the average loss in home value. The sample showed that the average loss was $11,560 with a standard deviation of $1500.

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

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

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

d) Suppose that, nationally, the average loss in home values at this time was $10,000. Do you think the loss in the sampled community differs significantly from the national average? Explain.