In an experiment, the dependent variable is the variable whose behavior you are trying to explain or predict. It is called “dependent” because its value is supposed to depend on something else. That something is the independent variable. When the independent variable changes, the hypothesis is, the dependent variable will change as a result.
In the example that you have given us here, both the independent variable and the dependent variable are clear. The independent variable is the state. The dependent variable is the SAT scores of the students from public high schools who take the test. In this experiment, we are trying to determine which state produces the most intelligent students. We are implying that, as the state changes, the intelligence of the students will change. That means that the state is the independent variable. The intelligence of the students, as measured by SAT scores, is the dependent variable. We are hypothesizing that it will change as a result of the “change” in the state in which the students live.
Thus, in this experiment, the independent variable is clearly the state while the dependent variable is the SAT scores of the students.