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 36 sample problems. The new algorithm completes the sample problems with a mean time of 22.83 hours. The current algorithm completes the sample problems with a mean time of 23.06 hours. The standard deviation is found to be 3.511 hours for the new algorithm, and 3.471 hours for the current algorithm. Conduct a hypothesis test at the 0.1 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: State the null and alternative hypotheses for the test

Step2: Compute the value of the test statistic. Round your answer to two decimal places

Step 3: Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to two decimal places

Step 4: Make the decision for the hypothesis test

Answer 1

Step 1:

H0: μ1 = μ2 vs H1: μ1 < μ2

Step 2: Test Statistics

T-Value = -0.28

Step 3:

DF = 69, P-Value = 0.390

Critical Value with 69 DF

TCritical = -1.29

Here, T-Value < TCritical Therefore, we accept the null hypothesis at a 10% level of Significance.

OR

P-Value > Alpha(0.1) , Therefore, we accept the null hypothesis at a 10% level of Significance.

Conclusion: The claim that the new algorithm has a lower mean completion time than the current algorithm is wrong.

Dear Student,

I am waiting for your feedback. I have given my 100% to solve your queries.If you are satisfied with my given answer. Can you please please like it.

Thank You!!!