P-value for lower/upper tailed t-test I was wondering if the P-value found from a t-table is the same for both lower and upper tailed? For instance let's say I find the P-value in this table: 
to be 0.05, and I am investigating the lower tail not upper, would my p-value still be 0.05 for lower tailed? and the same for upper tailed, would it be the same?
 A: Hint: Since the Student's $t$-distribution is symmetric, this is the same as asking if the $T$ statistic in the upper-tailed test is equal to the absolute value of that of the lower-tailed test.
A: Best to look at this with an example.  Suppose my hypothesis takes on the form $$H_0 : \mu = \mu_0 \quad {\rm vs.} \quad H_a : \mu < \mu_0.$$  Now, if I calculate the test statistic $$T = \frac{\bar x - \mu_0}{s/\sqrt{n}} \sim t_{n-1},$$ and I obtain a value of $T = 1.45$, then immediately I know that the data does not suggest that $\mu < \mu_0$; i.e., there is insufficient evidence to reject the null, because the test statistic is positive:  the sample mean exceeds the hypothesized mean.  On the other hand, if I calculate the test statistic and obtain $T = -2.5$ for $n-1 = 11$ degrees of freedom, then I would look up $2.5$ in the table you have above and find that the resulting $p$-value is approximately $0.015$.  Note that we look up the positive value because the $p$-value for the hypothesis I wrote above is equivalent to a $p$-value for a corresponding hypothesis in the other direction but with the test statistic's sign reversed.
To put it in a nutshell, for a sampling distribution that is symmetric about zero, if you reverse the direction of the test and also reverse the sign of the test statistic, the $p$-value is the same.
