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 76 sample problems. The new algorithm completes the sample problems with a mean time of 21.91 hours. The current algorithm completes the sample problems with a mean time of 23.08 hours. Assume the population standard deviation for the new algorithm is 5.316 hours, while the current algorithm has a population standard deviation of 4.853 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 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 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 hypothesis H0. Round the numerical portion of your answer to three decimal places.

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

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 < μ2

2)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(28.259856/76 + 23.551609/76)
sp = 0.8257

Test statistic,
z = (x1bar - x2bar)/sp
z = (21.91 - 23.08)/0.8257
z = -1.42

3)

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.
Hence reject H0 if z < -1.645

4)

As the value of test statistic, z is outside critical value range, fail to reject the null hypothesis