I think Ikind ofget the z/t discrepancy based on the fact that there is only one z (normal) distribution but many t-distributions (depending on n). Since n is fixed for a given t-distribution, that's why there's now a constraint, because you don't just need a certain sample mean, but you needa certain n of scores to equala certain sample mean.

But is there a more detailed explanation someone can give me that fleshes this idea out a lot more? Do you simply have to have studied "mathematical statistics" (as opposed to the "practical stats" many students are taught) to really appreciate degrees of freedom at a deeper level than what I've said above?