Question

Do students tend to improve their SAT math score the second time they take the test? A random sample of four students who took the test twice provided the given scores.

Student	1	2	3	4
First Score	450	520	720	600
Second Score	440	600	720	630

Assuming that the change in SAT Math score (second score—first score) for the population of all students taking the test twice is Normally distributed with mean μ , are we convinced that retaking the test improves scores? What is the P‑value for a test of H0:μ=μ0 versus Hα:μ≠μ0?

-less than 0.01

-more than 0.1

-more than 0.75

Answer 1

At 95% confidence pair wise 2 sample test excel report follows as