In an independent-samples $t$-test, the null hypothesis assumes that the means of the two distinct populations are perfectly equal ($\mu_1 = \mu_2$). Conversely, the alternative hypothesis asserts that these two population means are not the same ($\mu_1 \neq \mu_2$). Similar to other hypothesis tests, researchers may utilize a one-tailed test if they have a strong theoretical justification to predict that the difference between the groups will occur in a specific direction.