A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 42 sample problems. The new algorithm completes the sample problems with a mean time of 12.23 hours. The current algorithm completes the sample problems with a mean time of 13.58 hours. Assume the population standard deviation for the new algorithm is 3.640 hours, while the current algorithm has a population standard deviation of 4.254 hours. Required:
a. Conduct a hypothesis test at the 0.01 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm.