Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is =350 and =35. The 100 students who completed the tutoring program had an average score of 385 points.

a. Is the students' average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama's claim of at least a 50-point increase in the SAT score?

b. Is the Tutor O-Rama students' average score of 385 points significantly differentat the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama's tutoring?