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 49 sample problems. The new algorithm completes the sample problems with a mean time of 11.41 hours. The current algorithm completes the sample problems with a mean time of 13.41 hours. The standard deviation is found to be 4.040 hours for the new algorithm, and 4.742 hours for the current algorithm. 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 μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm. Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Answer 1

Answer STEP 3 of 4

It is clear that the sample size is greater than 30, so this is a case of z distribution.

sample size given is 49 for both samples.

We have to use a significance level of 0.05

we have to test the claim that the new algorithm has a lower mean completion time than the current algorithm

According to claim, we have to test the alternate hypothesis or

so, this is a left tailed hypothesis

Now, using the z distribution critical value table for left tailed hypothesis

(for lower tailed or left tailed)

So, rejection rule will be that "if z statistics value is less than -1.645, then reject the null hypothesis"

because z value less -1.645, will give us significant result and we can reject the null hypothesis in that region