COMP9334 Revision Questions for Week 5B 1 (Solution)
Question 1
Let us first compare Systems 1 and 2. The mean response time of System 1 minus mean
response time of System 2, over 5 replications, are 0.86, -0.89, 0.26, -2.31, 1.83. The sample
mean and sample standard deviation are, respectively, −0.05 and 1.6025. The 95% confidence
interval is −0.05±t 1.6025 = [−2.0397,1.9397]. Thus we can not determine whether Sys- 4,0.0975 √5
tem 1 is better or worse than System 2. (Note: t4,0.0975 = 2.7764)
Consider the difference: mean response time of System 1 minus mean response time of System 3, we find the 95% confidence interval for this difference is [−1.4356, 2.3716], thus we cannot conclude whether System 1 is better or worst than System 3.
Consider the difference: mean response time of System 2 minus mean response time of System 3, we find the 95% confidence interval for this difference is [0.3266, 0.7094], thus we can conclude System 3 is better than System 2 with 95% confidence.
We can only conclude that System 3 is better than System 2 with 95% confidence. How- ever, we cannot say with 95% confidence which system is the best out of the three.
1