Question

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.

Answer 1

Solution

Methodology

From each of the 4 schools referred by the politician, take a sample of at least 20 students and obtain the sample averages and sample standard deviations.

Let these statistics pairs be: (X₁bar, s₁), (X₂bar, s₂), (X₃bar, s₃) and (X₄bar, s₄).

Test the hypotheses that the increases cited by the politician are significant, follow the following method:

Test statistic: [n = sample size]

For school 1: t₁ = √n (X₁bar – 70.5)/ s₁

For school 2: t₂ = √n (X₂bar – 71)/ s₂

For school 3: t₃ = √n (X₃bar – 72)/ s₃

For school 4: t₄ = √n (X₄bar – 72.5)/ s₄

Reject at α% level of significance, the politician’s claim of increase in scores if the calculated value of the respective t-statistic as given above is less than the upper α% point of t-distribution with degrees of freedom equal to n – 1.

DONE