1. The Correlation between Relative Frequencies of Roman Numerals in Practice AP Questions and their Answers
Joshua Smith

2. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III

3. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III

4. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

5. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

6. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

7. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

8. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

9. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

10. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

11. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

12. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

13. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
I and II
I and III
II and III

14. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
II 3 I and II
III 2 I II
I and II
I and III
II and III

15. Which of these statements are true. I. 1 + 2 = 3 II. 1 + 3 = 2 III
II 3 I and II
III 2 I II
I and II
I and III
II and III

16. Rationale
When accurate Roman numeral statements have higher relative frequencies, test takers are required to know the validity of more statements (and more information).
The goal of test makers is to assess students on as much information as possible on the given subject.
By putting accurate statements in more answer choices, test makers require test takers to know more information.

17. Hypotheses Hypothesis
The use of relative frequencies as a means of answering Roman numeral practice AP questions will result in a statistically significant difference from random choice.
Null Hypothesis
The use of relative frequencies as a means of answering Roman numeral practice AP questions will not result in a statistically significant difference from random choice.

18. Significance The rejection of the null hypothesis would result in:
an advantage for test takers in answering questions.
feedback for test makers on how they can improve.
information on the difference between knowing the material for a test and having test taking skills.

23. Results 156 Questions (out of ≈ 14000) 33 Effectively Answered
123 Not Effectively Answered
116 Not The Correct Answer Choice
7 Not An Answer Choice
Randomized Choice Control
156 5 =31.2≈31

24. Results 2-PropZTest Conditions x1: 31 n1: 156 x2: 33 n2: 156 p1: ≠ p2
α-value = .05

25. Conclusion p > α (.779 > .05) NO STATISTICAL SIGNIFICANCE
The experiment failed to reject the null hypothesis.

26. THANKS
Mr. Dulmage
My Parents
The Audience