p-value for t-test
If the test statistic $t$ has $t$ distribution with $n$ degrees of freedom, then the $p$-value of the test for testing
a. left-tailed alternative is $p$-value = $P(t_{n}\leq t)$
.
b. right-tailed alternative is $p$-value = $P(t_{n}\geq t)$
.
c. two-tailed alternative is $p$-value = $2P(t_{n}\geq |t|)$
.
Formula
The $p$-value of t-test for left tailed alternative is
$p$-value = $P(t_{n}\leq t)$
The $p$-value of t-test for right tailed alternative is
$p$-value = $P(t_{n}\geq t)$
The $p$-value of t-test for two tailed alternative is
$p$-value = $2P(t_{n}\geq |t|)$
where,
$t$
is the value of test statistic,$n$
is the degrees of freedom.