The National Education Long survey (NELS) tracks a nationally representative sam

Question

The National Education Long survey (NELS) tracks a nationally representative sample at U.S. student from eightieth grade high school and voltage same reaction estimate the Sat of 265 NELS student who paid a tutor to help them improve their acres. 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 test 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 death.

Explanation / Answer

Standard deviation for SAT-Maths = std deviation/ Sqrt(n) = 65

Standard deviation for SAT-Verbal = std deviation/ Sqrt(n) = 49

We need to find the at how much confidence level (z-value), we can get increase of 180 points

For SAT-Maths, 180 = 19 + z * std deviation = 180 = 19 + z * 65

=> z = 2.476

For SAT-Verbal, 180 = 7 + z * std error = 180 = 7 + z * 49

=> z = 3.53

As, z-value of SAT-Maths, is lower than z-value of SAT-verbal, SAT- Math is most likely to have increase in 180 points, although the probability is very low.

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