T-test critical value

It depends on whether you're doing one tail or two tails test. The critical value are usually found by looking up table because there is no closed form formula for computing the critical value.
In fact, the critical value is computed using the incomplete beta function. Numerical methods can be used to evaluate the definite integral numerically.
Microsoft excel provided the implementation for this. To compute the critical value, you can just use this formula.
=TINV(A1/100/(3-C1),B1)
Put this in cell A2. Put the significance value in A1, the degree of freedom in B1, and the one/two tail test (represented as 1 or 2) in C1, then you get the correct value for the critical value for the associated t-test.
Using excel, the critical values obtained are:
[5%, dof=150, one-tail] 2.264125047
[5%, dof=150, two-tails] 1.975905298
[5%, dof=200, one-tail] 2.25840314
[5%, dof=200, two-tails] 1.971896178

2008-08-26 00:05:33 補充：
Thanks for the correction from (victorng_email). I have a typo in the excel function.
It actually outputs the two tail test critical value.

2008-08-26 00:06:11 補充：
The real solution should be

5%, dof=150, one-tails = 1.65507550067786
5%, dof=150, two-tails = 1.97590529767365
5%, dof=200, one-tails = 1.65250810140191
5%, dof=200, two-tails = 1.97189617759775

Given by the formula:
=TINV(A2/100*(3-C2),B2)

I have a little bit of reservation on Andrew's answer.

The critical value of a one-tailed test should not be greater than a two-tailed test [due to greater area on right hand side]

Here's figures obtained from R:
df=150: 1.655076 ; df=200: 1.652508