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 41 sample problems. The new algorithm completes the sample problems with a mean time of 23.42 hours. The current algorithm completes the sample problems with a mean time of 26.39 hours. Assume the population standard deviation for the new algorithm is 3.442 hours, while the current algorithm has a population standard deviation of 5.364 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. State the null and alternative hypotheses for the test. Give the test statistic Give the p- value Can someone also show me how to do this on a ti-84 graphing calculator?

Answer 1

Hypothesis :      Vs   

Here , n > 30 and population standard deviation are known

Therefore , we use Z test

The test statistic under Ho is given by ,

TS = -2.984

p-value = P(Z < -2.984) {as this is left-tailed}

= 0.0014

we reject the null hypothesis as p-value < alpha