The confidence interval is given by
where
is the sample mean and 
is the standard error of the mean. In turn, the standard error of the mean is 
where 
is sample size.
We have
The endpoints of the confidence interval correspond to the finite endpoints of the rejection region. That is,
for which we can solve for
. We get
which is the critical value for a confidence level of
.
where
We have
The endpoints of the confidence interval correspond to the finite endpoints of the rejection region. That is,
for which we can solve for
which is the critical value for a confidence level of