Suppose we do the following study. We have 2 web-servers (server A and server B) which are processing user requests. Both run on the same hardware, but one of them (server B) uses a slightly different algorithm for request processing. When a user request comes in we have 50/50 chance of processing it on each server. So the work being done by each server is the same in long term.
We have 1 hour system-log containing information about all the requests in this hour (all the population, not sample): what server processed the request and how long it took to process.
21:00:00 SERVER-A 0.11s 21:00:00 SERVER-A 0.13s 21:00:00 SERVER-B 0.09s 21:00:00 SERVER-A 0.16s 21:00:00 SERVER-B 0.11s 21:00:01 SERVER-A 0.14s
The log is quite large (~250K requests from each server, ~500K in total).
It turns out, that server B is slightly faster (mean response time is smaller). The question is which test should I use to show statistical significance in difference of response times of those two servers?