Question

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 μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points. 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? (2 pts) Is the Tutor O-Rama students’ average score of 385 points significantly different at 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? (2 pts)

Answer 1

Answer:

See below

Step-by-step explanation:

The score increase was 35 points. They claimed an increase of at least 50 points.  For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645.  For a significance level of 1%, the z-score needs to be smaller than -2.325

The z score for our situation:  z = (385 - 350)/50 = 0.7

The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores.  The evidence doesn't support their claim of being effective tutoring.