To illustrate a one-sample $t$-test, suppose a researcher investigates whether students accurately estimate a cookie's calories, known to be $250$ (a hypothetical population mean $\mu_0 = 250$). The null hypothesis states the population mean estimate $\mu$ is $250$. From a sample of $n = 10$ students, the mean estimate ($M$) is $212.00$ with a standard deviation ($SD$) of $39.17$. Using the $t$-statistic formula, the score is calculated as $t = \frac{212 - 250}{39.17 / \sqrt{10}} = -3.07$.