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 3333 sample problems. The new algorithm completes the sample problems with a mean time of 24.0524.05 hours. The current algorithm completes the sample problems with a mean time of 27.0127.01 hours. Assume the population standard deviation for the new algorithm is 5.3295.329 hours, while the current algorithm has a population standard deviation of 3.0783.078 hours. Conduct a hypothesis test at the 0.10.1 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1μ1 be the true mean completion time for the new algorithm and μ2μ2 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: Compute the p value

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis Ho

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

Answer 1

Here we have : 2. = 33. , = 24.05, S, -50329 n2 = 33, 22 = 27.01, S2 = 3.078 a=0.10 Degreeds freedom (df)= il stay on agrega - 520213 ~ 51 /whole number); step - Hypothesest Hos 1 = M2 Hai MS M2 step-2 Test statistic ftest 24.05 -27.01. #= C 2202 2 + 300782 33 - 1-2.76] step-3 pualue = TRIST (2.76, 51, 1) = (0.0040 step-4 Riedection mile Tsince pualhes oLol, we resect the null hypothesis step-S :Redect Ho deusion) (HO) - conclusion: There is sufficient evidence to support the claim and we conclude mat. new algorithm has lower mean completion time than courrent algoritma