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Inverse cumulative probability

Hello all,

   (First of all, I'd like to thank all who replied to my previous
question. I have never encountered such a helpful community before.
Thanks for making a R so welcoming.)

   To calculate a quantile for normal distributions, one simply uses
qnorm(1-a). But if I would want to do the same for a t-test function,
how would I go about doing that? Is there a simple way to do it? (Yes, I
could look in a table, but it's the procedure I'm looking for, not the
values :-)

   I'm studying interference theory, and we got a few exercises to solve
in MiniTab. That was pretty simple, but now I want to solve them in R
instead (this is not a part of the course, so you won't be helping me
with my home work).