A researcher studied the effect of television violence on concentration of a particular blood chemical. In this study, 40 participants were measured over a period of an hour prior to watching a violent show and then immediately after. In the results section, the researcher writes: "There was a significant decline in blood concentration from a mean of 13.41 (SD = 2.48) to 12.38 (SD = 2.69), t(39) = 3.38, p < .01 (one tailed)."
Explain this result (including the underlying logic of the computations) to a person who understands hypothesis testing involving a single sample and a known population, but knows nothing about t tests.