The one-sample $t$-test is a statistical procedure used to compare a single sample mean ($M$) against a specific, hypothetical population mean ($\mu_0$) that serves as an interesting standard of comparison. By defining a null hypothesis ($\mu = \mu_0$) and an alternative hypothesis ($\mu \neq \mu_0$), researchers use this test to determine if the sample data provide enough statistical evidence to conclude that the true population mean differs from the hypothesized value.