Let's say that a politician wants to implement a nation-wide education program. The politician gave four examples of schools that used the program: scores at the schools increased 0.5, 1, 2, and 2.5...

Let's say that a politician wants to implement a nation-wide education program.  The politician gave four examples of schools that used the program: scores at the schools increased 0.5, 1, 2, and 2.5 points respectively (the nation-wide average of the scores is 70).  The politician gave no additional evidence about the effectiveness of the program.

Your task: What questions or comments would you have pertaining to the statistical claim made by the politician? You might inquire about the sample, the sampling methods, the full population, the sampling distribution of the mean, and whatever would be useful to more accurately or precisely describe the effectiveness of the program.  At the end of your post, state whether you would conclude that the program will increase scores nation-wide.

Note that it is a separate question of whether it is "worth it" to effect change by taking money from people in the form of taxes to pay for a program.  Other than (optionally) saying that you think the statistics can or can not answer such a question, the "worth it" question is not part of this discussion.