To demonstrate a one-sample $t$-test, imagine a health psychologist investigating whether university students accurately estimate the $250$ calories in a chocolate chip cookie. The null hypothesis ($\mu = 250$) assumes accurate estimation. The researcher asks a sample of $10$ students, resulting in a sample mean ($M$) of $212.00$ calories and a standard deviation ($SD$) of $39.17$. Plugging these statistics into the one-sample $t$-test formula yields a $t$ score of $-3.07$. For a two-tailed test with $9$ degrees of freedom, the critical value is $\pm 2.262$. Because the calculated $t$ score is more extreme than this critical value, the researcher rejects the null hypothesis and concludes that students significantly underestimate the cookie's calories. If the researcher had a strong theoretical reason to expect an underestimation, a one-tailed test with a less severe critical value of $-1.833$ could have been used, making it easier to reject the null hypothesis if the results trended in the expected direction.