depends how you're sampling the population, doesn't it?

if the sample is drawn only from, say, students from the same class at a particular boarding school, how likely are the effects to apply to the entire population of students?

It depends on what the effect is and the hypotheses you are attempting to distinguish between. Sometimes you have to use your brain and think about it; science is not all randomized controlled trials, p values and curve fitting. :)

I know this is not the way it's done on HN, but since this isn't my thread I feel like I can throw in some amicus support for your side here by pointing out that an N of 30 is a sort of foundational number in stats, although it's not a magical number as there are some pretty rigorous maths behind it.

But it's not like social science people decided that an n of 20 or 30 was a good number to use because that's conveniently what they likely had access to (roughly the size of an undergrad classroom) for field data. and they didn't come up with it anyway), this is a number you're going to find in chapter 1, page 3 or 4 of any introductory stats text.