To illustrate an independent-samples $t$-test, consider a study comparing the calorie estimates of two distinct groups: frequent junk food eaters ($n = 8$) and rare junk food eaters ($n = 7$). The researcher calculates the sample means and standard deviations for both groups. For the frequent eaters, the mean ($M$) is $168.12$ with a standard deviation ($SD$) of $42.66$. For the rare eaters, $M = 220.71$ and $SD = 41.23$. Using the independent-samples $t$-test formula, the computed $t$ score is $2.42$. The degrees of freedom ($df$) for this combined sample of $15$ participants are $13$ ($15 - 2$). For a two-tailed test with an alpha level of $.05$, the critical value is $\pm 2.160$. Because the computed $t$ score ($2.42$) is more extreme than the positive critical value ($2.160$), the researcher rejects the null hypothesis. This indicates that the corresponding $p$-value ($.015$) is less than $.05$, providing sufficient statistical evidence to conclude that individuals who regularly eat junk food significantly underestimate calories compared to those who rarely eat it.