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 51 sample problems. The new algorithm completes the sample problems with a mean time of 24.83 hours. The current algorithm completes the sample problems with a mean time of 27.75 hours. The standard deviation is found to be 4.193 hours for the new algorithm, and 4.285 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.

State the null and alternative hypotheses for the test

State the value of the test statistic

Determine the decision rule for rejecting the null hypothesis (ie. reject null if z is greater/ less than ....)

Should we accept or reject the null hypothesis?

Answer 1

We reject the null hypothesis because calculated value 3.48 is grater than (>) table value of 1.96 at 5% level of significance level