AP Statistics Multiple Choice Investigation Ashvin Nagarajan & Joshua Kohler
Which answer would you pick?
Summary Our Statistical Analysis will analyze the distribution of answer choices for the past 5 years of the AP Statistics Multiple Choice Exam. We choose this project because we are curious if one answer choice is more likely than any other. Perhaps this information will provide future students with helpful insight.
Observation Design We tabulated the number of each answer choice per year. We then compiled a two way table for the data. In order to test significance, we performed a χ2 test for homogeneity.
Study Design This is an observational study because we did not impose any treatment on the samples. We chose this study design because we wanted to interpret the most recent data. These samples were from the five latest multiple choice exams.
Observed Data Test 1 Test 2 Test 3 Test 4 Test 5 Total A 4 5 7 8 32 B 13 40 C 6 9 36 D 12 15 10 53 E 39 200
Expected Data Test 1 Test 2 Test 3 Test 4 Test 5 Total A 8 40 B C D E 200
State Our objective is to determine if there is a difference in the distribution of multiple choice answer choices for the AP Statistics Exams from 2012-2016. We will use the following hypotheses. Ho = There is no difference in the true distribution of answer choices for the AP Statistics Exam. HA = There is a difference in the true distribution of answer choices for the AP Statistics Exam. We assigned a value of alpha a=.05 for this test.
Plan We will perform a Chi Squared Test for Homogeneity if conditions are met. Random: The data comes from an observational study for the 5 most recent multiple choice exams. 10%: The data is not from a SRS so we will proceed without the 10% condition with caution. Large Counts: If correct answers are evenly distributed across all choices, then the expected value is 8 which is greater than 5 so the Large Counts condition is met.
Do Using technology, the calculator’s χ2 test gives Degrees of Freedom = 16 χ2 = 13.4053 P-value = 0.6429
Graph
Conclude Since our p-value, 0.6429, is greater than alpha= 0.05, we fail to reject the null hypothesis. We do not having convincing evidence that there is a difference in the true distribution of answer choices for the AP Statistics Exam from 2012 to 2016.
What does this mean Since we do not have convincing evidence that any specific answer choice is more likely than any other, every answer choice is equally likely to be correct. Moreover, this data suggests that since all answers are equally likely it would be unwise to predict your answer based on previous answer choices. Although this data suggests this, there were significant outliers. For example, in test 2 there were 15 Ds and only 5 As. This is very different from the expected values however this distribution is still probable through random chance.
Pictures
Thank you for listening!