A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of "38" sample problems. The new algorithm completes the sample problems with a mean time of 22.07 hours. The current algorithm completes the sample problems with a mean time of 22.33 hours. The standard deviation is found to be 4.674 hours for the new algorithm, and 5.185 hours for the current algorithm.
Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm.