A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of70 sample problems. The new algorithm completes the sample problems with a mean time of11.26 hours. The current algorithm completes the sample problems with a mean time of12.81 hours. Assume the population standard deviation for the new algorithm is4.147hours, while the current algorithm has a population standard deviation of5.360hours. Conduct a hypothesis test at the0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let1be the true mean completion time for the new algorithm and2 be the true mean completion time for the current algorithm.

Step 1 of 4:State the null and alternative hypotheses for the test.

Step 2 of 4:Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4:Determine the decision rule for rejecting the null hypothesisH0. Round the numerical portion of your answer to three decimal places.

Step 4 of 4:Make the decision for the hypothesis test.