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? 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?

A

a. The average score of 385 points should be compared to the score of 400 points, considering that the tutor claims that their services will increase the average score of 350 by at least 50.

z = ((x-μ)/√(σ2/N)) = ((385-400)/√(352/100)) = -4.285

The p-value for the z-score is 0.000009, which implies that the students’ average score of 385 is significant at both 5% and 1% levels. Thus, the null hypothesis stating that the average score of tutored students is 400 should be rejected.

b. The extremely high value of the z-score means that the score of 385 significantly differs at 5% and 1% levels from the average score of 350. It is possible to conclude that the tutor’s services significantly raise SAT math scores, yet this increase is less than 50 points.

z = ((385-350)/√(352/100)) = 10

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Academic.Tips. (2021) '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? 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'. 16 July.

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Academic.Tips. (2021, July 16). 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? 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? Retrieved from https://academic.tips/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-%CE%BC350-and-%CF%8335-the-100-students-who-comple/

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Academic.Tips. 2021. "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? 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?" July 16, 2021. https://academic.tips/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-%CE%BC350-and-%CF%8335-the-100-students-who-comple/.

1. Academic.Tips. "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? 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?" July 16, 2021. https://academic.tips/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-%CE%BC350-and-%CF%8335-the-100-students-who-comple/.


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Academic.Tips. "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? 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?" July 16, 2021. https://academic.tips/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-%CE%BC350-and-%CF%8335-the-100-students-who-comple/.

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"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? 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?" Academic.Tips, 16 July 2021, academic.tips/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-%CE%BC350-and-%CF%8335-the-100-students-who-comple/.

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