To illustrate a dependent-samples $t$-test, consider a pretest-posttest study evaluating a training program designed to improve calorie estimates. A sample of $10$ participants estimates calories in a cookie both before and after the training. Subtracting the pretest estimates from the posttest estimates yields a set of $10$ difference scores with a mean ($M$) of $8.50$ and a standard deviation ($SD$) of $24.27$. Using the one-sample $t$-test formula on these difference scores against a hypothetical population mean of $0$, the computed $t$ score is $1.11$. For a one-tailed test with $9$ degrees of freedom ($10 - 1$), the critical value is $1.833$. Because the calculated $t$ score ($1.11$) is less extreme than this critical value, the researcher fails to reject the null hypothesis, concluding that the training program does not significantly increase calorie estimates. The corresponding $p$-value is $.148$, which is greater than the standard $.05$ alpha level.