T-test interpretation

What is the difference between P(T<=t) two-tail and t Critical two-tail? I am learning how to interpret t tests and don't know which to use in the essay. Thank you.

I'm not sure what you are asking. Many t-tables are constructed with both one-tail and two-tail entries. The t-distribution is symmetric about zero, so \(\displaystyle P(T \ge t) = P(T \le -t)\). Typically the table entries area all positive. For a two-tailed test, the rejection region is \(\displaystyle T \ge t \ OR \ T \le -t\) which has the same probability as \(\displaystyle 2 P(T \ge t)\).

Thank you for the assist. The "P(T<=t) two-tail and t Critical two-tail" appear in the summary for performing a t-Test for paired two sample for means. For example, one of the summaries shows "P(T<=<t) for two tailed test" is 0.035468; directly under this is "t critical two tailed test" is 2.070614. My guess is that I would use the first numerical value; but what is the second value for? If it helps, I use Excel. Many thanks.