On a multiple-choice exam, if you think you have made a mistake, is it better to stick with your first choice or to erase and change your answer?
One of the authors instructed her students to change the answer if the second answer they got seemed better than the first (Change!). Her colleague told his students that their first answer was usually the best and they should avoid changing answers (Don't Change!). After both classes had taken several multiple-choice exams, the exams were studied to see whether answers were erased and replaced with different answers. The results are shown in the accompanying table. Complete parts a through c below.
| | | Instruction |
| :---------- | :----------- | :--------------- |
| | | Don't Change! | Change! |
| Behaviour | Changed | 208 | 122 |
| | Unchanged | 29,304 | 14,403 |
b. What is the percentage of answers that were changed for the students who were told to change their answers?
c. Compare the answers to parts a and b, and state whether you think the instruction had any effect on whether students changed their answers.
The percentage of answers that were changed for the students who were told to change their answers is the percentage for students who were told not to change their answers. This the idea that the instruction had an effect on whether students changed their answers.
Answer (1)
Calculate the percentage of changed answers for the 'Don't Change!' group: 208 + 29304 208 × 100 ≈ 0.705% .
The percentage of changed answers for the 'Change!' group is given as 0.840%.
Compare the two percentages: 0.840% > 0.705%.
The percentage of changed answers is greater for the 'Change!' group, supporting the idea that the instruction had an effect. greater than , supports
Explanation
Understand the problem and provided data We are given a table that shows the number of changed and unchanged answers for two groups of students. One group was instructed 'Don't Change!' their answers, while the other group was instructed 'Change!' their answers if they thought their second answer was better. We need to compare the percentage of answers changed in each group to determine if the instruction had any effect.
Calculate the total number of answers for the 'Don't Change!' group First, we need to calculate the percentage of answers that were changed for the students who were told 'Don't Change!' their answers. The number of changed answers is 208, and the number of unchanged answers is 29,304. The total number of answers is the sum of changed and unchanged answers, which is 208 + 29304 = 29512 .
Calculate the percentage of changed answers for the 'Don't Change!' group Now, we calculate the percentage of changed answers for the 'Don't Change!' group by dividing the number of changed answers by the total number of answers and multiplying by 100:
Calculate the percentage 29512 208 × 100 ≈ 0.705% The percentage of answers changed for the 'Don't Change!' group is approximately 0.705%.
Compare the percentages We are given that the percentage of answers changed for the 'Change!' group is 0.840%. Now we compare the two percentages.
State the conclusion Comparing the percentages, we see that 0.840% is greater than 0.705%. Therefore, the percentage of answers that were changed for the students who were told to change their answers is greater than the percentage for students who were told not to change their answers. This supports the idea that the instruction had an effect on whether students changed their answers.
Examples
Imagine you're advising students on test-taking strategies. This analysis helps determine whether encouraging students to reconsider their answers leads to more changes compared to advising them to stick with their initial choices. Understanding these effects can inform better test-taking advice and potentially improve student performance on multiple-choice exams. The key is to quantify how different instructions impact behavior and outcomes.
