The National Education Longitudinal Survey (NELS) tracks a nationally representa

Question

The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S students from eighth grade through high school and college. Some research examined the SAT scores of 265 NELs students who paid a private tutor to help them improve their score. The table summarizes the changes in both the SAT-Mathematics and SAT-verbal scores for these students. Suppose the selected student's score increased on one of the SAT tests by 180 points, which test, the SAT-Math or AST-verbal, is the one most likely to have had the 180-point increase? Explain with details.

Explanation / Answer

SAT-Math is most likely as it's standard deviation is higher than the standard deviation of the SAT-Verbal and also its mean is the higher of the two.

Detailed explanation using Confidence interval:
Lets take a 99.7% CI, i.e. 3 standard deviations away from the mean
For SAT-Math 99.7% CI(19-65*3, 19 + 65*3) = (-176, 214)

For SAT-Verbal 99.7% CI(7-49*3,7+49*3) = (-140,154)

Only the interval of the SAT-Math has the value 180 and therefore is the most likely

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