Q3. A systems analyst tests a new algorithm designed to work faster than the cur

Question

Q3. A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 59 sample problems. The new algorithm completes the sample problems with a mean time of 22.95 hours. The current algorithm completes the sample problems with a mean time of 24.51 hours. Assume the population standard deviation for the new algorithm is 3.996 hours, while the current algorithm has a population standard deviation of 3.093 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 ?1 be the true mean completion time for the new algorithm and ?2 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: reject or fail to reject null hypothesis

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

a. There is sufficient evidence to support the claim that the mean completion time for the new algorithm is faster than that of the current algorithm.
b. There is not sufficient evidence to support the claim that the mean completion time for the new algorithm is faster than that of the current algorithm

Explanation / Answer

1)
H0 : mu1 = mu2
Ha : mu1 < mu2

2)
z = (x1 + x2) /sqrt(s1^2/n1 +s2^2/n2)
= ( 22.95 - 24.51)/sqrt(3.996^2/59 + 3.093^2/59)
= -2.371

3)

p value = 0.0088

4)

Reject the null hypothesis

5)
There is sufficient evidence to support the claim that the mean completion time for the new algorithm is faster than that of the current algorithm.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.