one tailed test, lower tail critical: degree of freedom=22 and t--2.92. WHat is the p-value?

Question

This is statistics and I am not quite sure how to figure this out. I hhave five questions asking the same thing just with different numbers. SO if I can get the steps to answer this one I can do the rest,

Answer 1

From tables a 1-tail test for 22 dof lies between 0.001 (3.505) and 0.005 (2.819).

We can produce an approximate linear relationship between the probability p and the t-value.

(2.819-3.505)/(0.005-0.001)=-171.5; p=-171.5t+c where c is a constant to find.

Plug in (t,p)=(0.001,3.505): 3.505=-0.1715+c, c=3.6765.

When p=2.92, 2.92=-171.5t+3.6765, t=0.7565/171.5=0.0044.

The p-value is therefore 0.0044.