20. The national mean sales price for new one-family homes is $181,900 (The New York Times Almanac 2000). A sample of 40 one-family home sales in the South showed a sample mean of $166,400. Use a population standard deviation of $33,500.

a. Formulate the null and alternative hypotheses that can be used to determine whether the sample data support the conclusion that the population mean sales price for new one-family homes in the South is less than the national mean of $181,900.

b. What is the value of the test statistic?

c. What is the p-value?

d. At α  .01, what is your conclusion?