A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 47sample problems. The new algorithm completes the sample problems with a mean time of 14.75 hours. The current algorithm completes the sample problems with a mean time of 16.77 hours. Assume the population standard deviation for the new algorithm is 3.956 hours, while the current algorithm has a population standard deviation of 5.135 hours. 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. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm. Step 1 of 5: State the null and alternative hypotheses for the test.
Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 5: Find the p-value associated with the test statistic. Round your answer to four decimal places.
Step 4 of 5: Make the decision for the hypothesis test. (reject or fail to reject)
Step 5 of 5: State the conclusion of the hypothesis test. (There is sufficient evidence to support the claim or there is not)