I have done a study of information request response times in order to find out whether response time differs because of characteristics of the person doing the request.
The studied unit is an organisation, and there are roughly N=500 organisations that can be tested. Since the requests are "open information" (i.e can be freely discussed between collegues and friends) I did not want to sample the whole population, for risk of information contagion between organisations (that they would find it fishy that identical requests came to several offices). In the end, we sent requests to 240 organisations (48 per cent of the population). The groups are balanced ($n_1$=120 and $n_2$=120) and "detectable effect size" came out as something like 32 per cent in G*Power (alpha=0.1, power=0.8, two-tailed $t$-test for difference in means). I would like to get MDE a more acceptable 20 percent (equivalent to start of day / end of day), but that would require a sample size larger than the population I want to generalise to, which is clearly nonsense.
Do sample sizes (in relation to the population) have no relation to the power of a test? In the tools and texts I have seen, the samples seem to come from an almost inexhaustible population (sample size max around 5 per cent of population).