SAT Scores: Comparing Newtown High School to the Nation

1. SAT Scores: Comparing Newtown High School to the Nation

2. Background Information • Scholastic Assessment Test used for College Admissions • Developed by Carl Brigham • Takes approximately 3 hours and 45 minutes to complete • Introduced in 1901 The test was not multiple choice, but instead was evaluated based on essay responses as "excellent", "good", "doubtful", "poor" or "very poor". • Test has been changed several times with the newest change being the addition of the Writing section in 2005 • Scores range from 600-2400 composed of three 800 point sections (Math, Critical Reading, Writing)

3. What We Are Investigating • We are investigating whether or not there is a difference between SAT (out of 1600) scores at Newtown High School, and the SAT scores of the nation. To test this, we will compare the mean score of Newtown High school to the mean score of the Nation.

4. How We Gathered Our Data • We will use 50 scores out of the high school 2011 Senior class for our sample • Response Variable: Mean Score • Component: SAT Scores • We Will Use a Simple Random Sample • There were 367 pieces of data, which were labeled 0-366 • We Collected 50 numbers using RandInt(0,366,1) on the calculator • Ignored Repeats • Once we had 50 numbers, we matched them to the corresponding SAT scores for our sample data of SAT scores.

5. Data

6. Outcome of Sample • Mean of Newtown High: 1090.8 • Standard Deviation of NHS Data: 160.84 • Number of Sample Size: 50 • Standard Error: Sd/Sqrt(Number of sample size)= 160.84/Sqrt(50)= 22.75 • Degrees of Freedom: 50-1= 49 • National Mean: 1017 (researched) • This will be a one tailed one mean T-Test to see if the SAT scores at Newtown High School are higher than the national average

7. Assumptions and Conditions • Independence?- Yes, One student’s SAT score has no impact on another student’s SAT score. There are mechanisms in place to secure confidentiality, security and prevent cheating and sharing of information • 10% Condition?: Yes, Sample consists of less than 10% of total population • Random?: Yes, Samples collected randomly • There are two outliers in our data, so we can proceed with the test, but we must continue with caution • SAT scores at Newtown High School are independent of national scores • Sample of 50 SAT tests are a representative sample of the population of scores

8. Assumptions and Condiitons (cont.) • Normal?: Yes, Nearly Normal: Normal Probability Graph and histogram appear nearly normal, suggesting that a normal model is applicable.

10. Normal Probability Chart • Outliers? Yes, 2 outliers at data points 1510 and 740, that are more than two standard deviations away from the mean.

11. Mechanics • Ho: NHS Mean = 1017 • Ha: NHS Mean > 1017 • T-Score: (Sample Mean – National Mean) / Standard Error • T-Score: (1090.8 – 1017) / 22.75 • T-Score: 3.24 • Df= 49

12. Mechanics (cont.) • T-score= 3.24 • Df= 49 • P-Value= 0.001

13. P-value 0.001 Reject Null Hypothesis

14. Conclusion • After performing the one mean t-test, we conclude that there is sufficient evidence to suggest that there may be a difference between the mean SAT score of the Newtown High School Senior Class of 2011 and the National mean of SAT scores. The p-value of 0.001 is too low, below a reasonable alpha level of 0.05, to indicate that the difference between the two means is due to random sampling error. Therefore, we can reject the null hypothesis and conclude that there may be a difference, and that the SAT scores of Newtown High School Students may tend to be higher than the national average of SAT scores.

15. Improvements • Include all grade levels • Expand beyond Newtown High School to other districts in the county, state or region • Compare schools with one another