p value calculator for t test

In this tutorial we discuss about how to find the $p$-value of the t-test. The p-value of the $t$-test depends on the direction of the alternative hypothesis.

p value definition

$p$ value of the test is the probability that the test statistic under null hypothesis will take on values as extreme as or more extreme than the observed value of test statistic.

The smaller $p$ value of the test indicate strong evidence against the null hypothesis $H_0$.

$p$-Value from of t-test

If the test statistic $t$ has $t$ distribution with $n-1$ degrees of freedom, then the $p$-value of the test for testing

a. left-tailed hypothesis is $p$-value = $P(t_{n-1}\leq t)$.

b. right-tailed hypothesis is $p$-value = $P(t_{n-1}\geq t)$.

c. two-tailed hypothesis is $p$-value = $2P(t_{n-1}\geq |t|)$.