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Critique the following statements and determine if there is a significant difference between the treatments. Two high school teachers, Ms. Brown and Mr. Sorrentino, are preparing their students to take the state’s standardized testing for the school year. In the previous school year, Ms. Brown and Mr. Sorrentino followed the same curriculum and teaching methods. Based on last year’s score report to the teachers, the students in both classrooms yielded an average score of 83. This year, Ms. Brown and Mr. Sorrentino are following different curriculums to determine whether this will raise their class averages. Compared to last year, Ms. Brown’s students spent an additional week studying probability and two additional weeks studying inequalities. Here are her students’ scores from this year’s report: 71 79 93 75 88 72 91 80 71 90 Compared to last year, Mr. Sorrentino’s students spent an additional week studying probability and two additional weeks studying quadratic equations. Here are his students’ scores from this year’s report: 88 97 77 89 87 82 93 96 85 86 Determine the effectiveness of the new curriculum. (1 point) Responses Mr. Sorrentino’s curriculum was more effective. Mr. Sorrentino’s curriculum was more effective. Neither curriculum helped to improve scores. Neither curriculum helped to improve scores. Ms. Brown’s curriculum was more effective. Ms. Brown’s curriculum was more effective. Mr. Sorrentino’s and Ms. Brown’s curriculums increased the class averages by the same amount.

1 answer

To critique the statements and determine if there is a significant difference between the treatments (curricula), we should first analyze the provided scores for each teacher's class and calculate their averages, then compare the results.

1. Calculate Average Scores:

Ms. Brown's Scores: 71, 79, 93, 75, 88, 72, 91, 80, 71, 90

Sum of scores = 71 + 79 + 93 + 75 + 88 + 72 + 91 + 80 + 71 + 90 = 819

Number of students = 10

Average score = Total sum / Number of students = 819 / 10 = 81.9

Mr. Sorrentino's Scores: 88, 97, 77, 89, 87, 82, 93, 96, 85, 86

Sum of scores = 88 + 97 + 77 + 89 + 87 + 82 + 93 + 96 + 85 + 86 = 899

Number of students = 10

Average score = Total sum / Number of students = 899 / 10 = 89.9

2. Compare the Class Averages:

  • Ms. Brown's average score this year is 81.9.
  • Mr. Sorrentino's average score this year is 89.9.

3. Compare to Previous Year's Score: Last year, both classes had an average score of 83.

  • Ms. Brown's score of 81.9 indicates a decrease of 1.1 points.
  • Mr. Sorrentino's score of 89.9 indicates an increase of 6.9 points.

4. Effectiveness of the New Curricula:

  • Clearly, there is a significant difference between the effectiveness of the curricula as reflected in the students' scores this year. Mr. Sorrentino's curriculum led to an increase in the average score, while Ms. Brown's curriculum resulted in a decrease.

Conclusion: Given the calculations and comparisons, we can conclude that Mr. Sorrentino's curriculum was more effective in improving student scores, while Ms. Brown’s curriculum was less effective.

Critique of Responses:

  • "Mr. Sorrentino’s curriculum was more effective." This is accurate based on the data.
  • "Neither curriculum helped to improve scores." This is incorrect as Mr. Sorrentino's curriculum indeed improved the scores.
  • "Ms. Brown’s curriculum was more effective." This is incorrect, as her scores declined.
  • "Mr. Sorrentino’s and Ms. Brown’s curriculums increased the class averages by the same amount." This is incorrect because only Mr. Sorrentino's curriculum increased the average while Ms. Brown's decreased.

In summary, Mr. Sorrentino's curriculum was more effective based on the students' performance this year.