According to the U. S. Department of Commerce, the average price for a new home topped $200.000 for the first time in 1999. In November 1999, the average new-home price was $209.700 (Wall Street Journal Interactive Edition, Jan. 7, 2000). The prices of a random sample of 32 new homes sold in November 2000 yielded T = $216,981 and s = $19,805.

a. What are the appropriate null and alternative hypotheses to test whether the mean price of a new home in November 2000 exceeds $209,700?

b. Compute and interpret the p-value of the test. Do the data provide sufficient evidence to conclude that the mean new-home price in November 2000 exceeded the reported mean price of November 1999?