[R] Stats Question: Single data item versus Sample from Normal Distribution

[Ross Clement]

Hi. I have a question that I have asked in other stat forums but do not
yet have an answer for. I would like to know if there is some way in R
or otherwise of performing the following hypothesis test.

I have a single data item x. The null hypothesis is that x was selected
from a normal distribution N(mu,sigma). The alternate hypothesis is that
x does not come from this distribution.

However, I do not know the values of mu and sigma. I have a sample of
size N from which I can estimate mu and sigma. So, say that I have
N(m,s,N), and x. I would like to say with some certainty (e.g. 95%) that
I can, or can't reject the hypothesis that x came from N(mu,sigma). I
would also like a power test to say how large N should be given the
degree of accuracy I need when accepting or rejecting individual x
values.

What is the name of the hypothesis test I need for this? Is it built
into R, or are there packages I could use?

Thanks in anticipation,

Ross Clement.