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 48 sample problems. The new algorithm completes the sample problems with a mean time of 19.90 hours. The current algorithm completes the sample problems with a mean time of 21.33 hours. The standard deviation is found to be 4.320 hours for the new algorithm, and 5.402 hours for the current algorithm. Conduct a hypothesis test at the 0.01 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.

H₀: ?₁ (blank) ?₂

H_a: ?₁ (blank) ?₂

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.

Reject H₀ if (blank) (blank) (blank) [NOTE: First blank choices: z or | z | Second blank choices: > or < Third blank: Round answer to 3 decimal places]

Step 4 of 4: Multiple Choice

a) Reject Null Hypothesis

b) Fail to Reject Null Hypothesis

Answer 1

Given N:48 for new let be rue mcan com ple tian Fime 1qrithm fer cuTent time Campletion et true be mecn aqarith m to We tes t H, < 2 Ho: 4 U2 H, = 21.33 S 4.3 2 S2 =54 o 2 ntn+n.2 S n-) Ss2 (n-2) S2 2n 2 8 77 1328 + + 137/. S 353 23.9 2 2 o 99o - 21.33 23.922 tca 24 - 1.43 - 1432 tcay J.43 tral

t g4,0.05 then we Decision Rur If Itcaul tn,ta-, Ho Cut 7. may jcct tcal tg.00T .. We may accept fau to ejcct Ho Wle