Nearly all introductory statistics textbooks include a chapter on data collection methods that includes a detailed discussion of both random sampling methods and randomized experiments. But when statistical inference is introduced in subsequent chapters, its justification is nearly always based on principles of random sampling methods. From the language and notation that is used to the conditions that students are told to check, there is usually no mention of randomized experiments until an example that is a randomized experiment is encountered, at which point the author(s) may offer a statement to the effect of "the randomization allows us to view the groups as independent random samples." But a good student (or even an average one) should ask, "Why?" This paper shows, in a way easily accessible to students, why the usual inference procedures that are taught in an introductory course are often an appropriate approximation for randomized experiments even though the justification (the Central Limit Theorem) is based entirely on a random sampling model. (Contains 7 figures.)