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. 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).

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To evaluate the claim made by the politician, we need to analyze the evidence provided regarding the impact of the program on improving school scores. Let's break it down step-by-step:

1. Start by identifying the main claim: The politician suggests that spending a large amount of money on the program will lead to positive results.

2. Analyze the evidence provided: The evidence given is the improvement in scores at four different schools: 0.5, 1, 2, and 2.5 points respectively.

3. Consider the nationwide average score: The nationwide average score is stated to be 70.

4. Compare the improvements to the national average: Given the average score of 70 and the improvement scores provided, we can see that the improvements range from relatively small (0.5 points) to more substantial (2.5 points).

5. Assess the significance of the improvements: In order to determine if the improvements are meaningful, we need to consider the scale of the scoring system. If the scoring system has a high range, such as 0-100, then improvements of 0.5 or 1 point may not have a significant impact. However, if the scale is more limited, such as 0-10, then these improvements could be quite substantial.

6. Consider the sample size: It is important to note that the evidence provided only includes scores from four schools. In statistical terms, this would be considered a small sample size, which may not be representative of the wider population.

7. Evaluate if the evidence supports the claim: Based on the information provided, it is difficult to determine if the program will have a particular result or justify the need for a large amount of money. The scores vary across the four schools, and without additional information, it is challenging to make generalizations about the program's effectiveness.

In conclusion, to assess the claim made by politicians, it is necessary to critically examine the evidence provided, consider the scale of improvements, and evaluate the sample size. Without legitimate evidence that shows a consistent positive impact on a larger scale, it becomes difficult to support the claim that spending a large amount of money on the program will achieve the desired results.