Comprehensive Project 2024 Ap STATS

By: Erin Pietrasz & Izzy Rezzano

Purpose:

• This particular project was undertaken because millions of students in America take the SAT including us, and in the college search process it is important to look at the averages certain colleges accept for the SAT.
• The problem intended to be solved was if a certain section on the SAT produced higher mean scores.

The key issues that were raised consisted of:

• Colleges use student's SAT scores to determine if they will accept the student into colleges.
  
• Getting into a harder college requires them to be more selective in choosing students, they will require a higher SAT score and GPA.
  
• Also, having a higher SAT score can help you get scholarships.
  
• It is also one of the requirements to get a high school honors diploma.
  

Question:

• Is there a difference between the mean mathematics and mean writing scores for the SAT by school?

Background Research

• A 1200 is an above-average score that places you in approximately the 74th percentile of all high school students taking the exam.
• A score of 1200 makes it possible to apply to the vast majority of schools throughout the nation and be competitive for admission at a sizable number of colleges.
• Many studies have been done on this topic of SAT Scoring. Some studies took on the average SAT scores of ONLY private schools, while others took on just public schools.
• We collected our Data based on a Dataset on Kaggle, which combined both private and public school Math and Writing scores on the SAT.

Raw Data

Descriptive Statistics & Graphs

Descriptive Statistics & Graphs

Description of the means math section on the SAT: Skewed to the right, there is a gap of around 560, unimodal because there is one peak of around 400, cannot determine if there are any outliers, ranges from 354 to 673, mean: 436.886, standard deviation: 83.2967

Description of the means writing section on the SAT: Skewed to the right, unimodal because there is one peak of around 340 to 420, no gaps, cannot determine if there are any outliers

ranges from 314 to 642, mean:414.514, standard deviation: 75.0009

random sampling

• Our population was 387 and on Minitab, we took a random sample of 35 by using the random sampling of columns featured on Minitab.
  

Significance Test

• We decided to use a difference of paired means test for our data. We are using this test procedure because we want to compare the mean scores of the writing and mathematics portions of the SAT.
• μd: the true mean differences of scores of the math-writing of SAT scores from self-reported college-bound senior graduates per high school in 2010.

• Significant Level: 0.05

• Null Hypotheses: H0: μd = 0

• Alternative: Ha: μd ≠0
  

• Random sample: Our sample size was randomly selected from the population. Check
• Large Count Condition: nd number of pairs is 35. 35> 30 for both sets of data. Check
• 10% Condition: nd number of pairs is 35. The population is 387. 387(0.10)=38.7 so our number of pairs is less than our population.

Significance Test

Conclusion

We can reject the null hypothesis at the significance level of 0.05 since our p-value of 0.006 is less than our significance level. Therefore, we do have a significant amount of evidence to support the theory that the mean of differences shows a difference.

Discussion - Weaknesses

Our biggest weakness is that not all senior high school students reported their SAT test scores for their school, so we have some nonresponse problems. Students had to submit their scores for their school so they could determine the means of the writing and math sections on the SAT.

Discussion - Suggestions

SAT administrators would need to require the senior students to submit their test scores to help have more accurate data when comparing the means of writing and math on the SAT.