Question

increasing test scores (option 4 of 4)
a school claims that their new tutoring program improved math test scores by 5%. they tested 30 students and saw an average score increase from 70 to 74.
does this prove the program works? what else would you want to know?

Explanation:

Just because the average score increased from 70 to 74 (an increase of about 5.71%, calculated as $\frac{74 - 70}{70}\times100\%\approx5.71\%$) for 30 students does not mean the program is the cause. There could be confounding variables. For example, we would want to know if the same test was used before and after (different tests could have different difficulty levels). We would also want to know if there was a control group (students who did not participate in the tutoring program) to compare against. Additionally, information about the variability (standard deviation) of the scores before and after could help - if the scores were very spread out (high standard deviation) before and after, the increase might not be as meaningful as if the scores were tightly clustered (low standard deviation). Also, knowing if the students were randomly selected for the tutoring program and if there were any external factors (like a school - wide initiative to focus more on math around the same time as the tutoring program) would be important.

Answer:

No, it does not prove the program works.