A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 45 sample problems. The new algorithm completes the sample problems with a mean time of 10.48 hours. The current algorithm completes the sample problems with a mean time of 12.57 hours. assume the population standard deviation for the new algorithm is 5.174 hours while the current algorithms has the population the standard deviation of 3.121. 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 1 be the true mean completion time for the new algorithm and 2 be the true mean completion time for the current algorithm.

1.

state the null and alternative hypotheses for the test.

h0: u1 - u2

ha: u1 - u2

2.

compute the value of the test statistic. (2 decimal places)

3.

find the p-value associated with the test statistic. (4 decimal places)

4.

make the decision for the hypothesis test (reject/fail)

5.

state the conclusion of the hypothesis test (sufficient/not sufficient)