Question: In 2005, in response to various criticisms, the college board implemented changes to the SAT. In particular, the math portion eliminated quantitative comparisons and expanded the topics covered. A school admin. believed that the new math portion is more difficult and will result in lower scores on the math portion compared to the 2004 avg score of 516. A random sample of 25 students taking the new SAT test resulted in the following scores on the math portion. Test the hypothesis of that the scores are lower than 516 at the level of significance α = 0.05. For this data, X bar = 509 and s = 117.

410 720 480 560 590 340 430 400 440

540 480 450 720 570 380 740 640 600

320 580 450 480 550 470 380