Applying what you have learned.... When politicians make claims that we need to

Question

Applying what you have learned.... 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.

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.

Explanation / Answer

Questions that can be asked are:

1. What is the average score before the program and after the implementation of program?

2. How many schools are present across the nation? Is a sample of 4 schools good representation of the entire nation ?

3. What is the Sampling method used to pick up the sample schools ? (There might be a chance that samples were picked from topmost increase in scores, giving us a false picture of effectiveness of program)

4. Are the number of schools same before and after the implementation of program (because a change in number of schools might disrupt the figures) ?

5. Is a single sample enough to give the picture? Why not create Sampling Distribution of mean? (Sampling Distribution of mean is a distribution of means of multiple samples picked from same population, example, pick a sample plot its mean , pick another sample , plot its mean and thus generate a distribution of means.)

6. What is the Median rise in score of program?

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