When politicians make claims that we need to spend a large amount
of money to achieve a goal, the claim is often made without legitimate evidence to support a claim that a given program will have a particular result. 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.
What questions or comments would be relevant pertaining to the statistical claim made by the politician? Inquiries may be 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. Also based on this information would it be safe to conclude that the program will increase scores nation-wide?
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