In my experiment, I have boxes containing insects. A number of insects from each box was used for an experiment, and this was repeated again a few weeks later. I want to check if there is a significant difference in the means of the response. On the one hand, I feel like because the insects I use in each trial are different individuals (from the same box), I should use a 2-sample t-test to check whether the DV is significanlty different between cohort 1 and cohort 2 (the insects used in week 1, and week 3 respectively), but I have had someone suggest to me that a paired t-test is more appropriate because the insects do come from the same box. Any ideas?
A paired $t$-test is not appropriate here because like you said, the same insects may or may not have been measured. Even if the you had happened to choose the exact same insects the second time, you have no way of "pairing" them so a paired $t$ test is not appropriate and a two sample $t$-test makes more sense and thus your intuition is correct.
Aside from your question, this method of measuring seems quite odd to me. Why not measure all the insects? Is it too many? Also important to ask here, is what is my population? The way you have this experiment set up right now, your population is the box and you are sampling randomly from the box. However, if the insects in the box were themselves a randomly obtained sample from the outside world, then population is larger than that. Just something to think about.