Question

A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 41sample problems. The new algorithm completes the sample problems with a mean time of 23.42 hours. The current algorithm completes the sample problems with a mean time of 26.39 hours. Assume the population standard deviation for the new algorithm is 3.442 hours, while the current algorithm has a population standard deviation of 5.364 hours. 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 μ1be 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.

Step 5 of 5: State the conclusion of the hypothesis test.

Answer 1

Each algorithm is applied to a group of 41sample problems.

The new algorithm completes the sample problems with a mean time of 23.42 hours.

The current algorithm completes the sample problems with a mean time of 26.39 hours.

Assume the population standard deviation for the new algorithm is 3.442 hours,

while the current algorithm has a population standard deviation of 5.364 hours.

μ1be the true mean completion time for the new algorithm

μ2 be the true mean completion time for the current algorithm.

Step 1 of 5: State the null and alternative hypotheses for the test.

We want to test the claim that the new algorithm( μ1) has a lower mean completion time than the current algorithm(μ2).

Ho:- μ1 - μ2 >=0

vs

Ha:- μ1 - μ2 < 0

Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 4 of 5: Make the decision for the hypothesis test.

Here P-value = 0.0014

We reject Ho when P-VALUE < LEVEL OF SIGNIFICANCE

P-value = 0.0014 < 0.05

We reject Ho

Step 5 of 5: State the conclusion of the hypothesis test.

We may conclude that the data provide sufficient evidence to support the claim that the new algorithm has a lower mean completion time than the current algorithm.