A study found that the average stopping distance of a school bus traveling 50 miles per hour was 264 feet (Snapshot, USA TODAY, March12, 1992). A group of automotive engineers decided to conduct a study of its school buses and found that for 20 buses, the average stopping distance of buses traveling 50 miles per hour was 262.3 feet.

The standard deviation of the population was 3 feet. Test the claim that the average stopping distance of the company's buses is actually less than 264 feet.

Find the P-value. On the basis of the P-value, should the null hypothesis be rejected at a = 0.01? Assume that the variable is normally distributed.