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?
| | | Instruction |
|-----------|-----------|--------------------|
| | | Don't Change! | Change! |
| Behaviour | Changed | 208 | 122 |
| | Unchanged | 29,304 | 14,403 |
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.
a. What is the percentage of answers that were changed for the students who were told not to change their answers?
[tex]$0.705 \%$[/tex]
(Round to three decimal places as needed.)
b. What is the percentage of answers that were changed for the students who were told to change their answers?
$\square$ \%
(Round to three decimal places as needed.)
Answer (2)
Calculate the total number of answers: 122 + 14403 = 14525 .
Calculate the percentage of changed answers: 14525 122 × 100 .
The percentage of changed answers is approximately 0.840% .
The percentage of answers that were changed for the students who were told to change their answers is 0.840% .
Explanation
Understand the problem and provided data We are given a table that shows how students behaved on a multiple-choice exam based on the instructions they received. The instructions were either "Don't Change!" or "Change!". The behavior was either "Changed" or "Unchanged". We are asked to find the percentage of answers that were changed for the students who were told to change their answers.
Outline the solution To find the percentage of answers changed by students who were instructed to change their answers, we need to divide the number of answers changed by the total number of answers for that group of students, and then multiply by 100. From the table, we see that 122 answers were changed and 14,403 answers were unchanged.
Calculate the total number of answers First, calculate the total number of answers for the students who were told to change their answers: T o t a l = C han g e d + U n c han g e d = 122 + 14403 = 14525
Calculate the percentage of changed answers Next, calculate the percentage of answers that were changed for the students who were told to change their answers: P erce n t a g e = T o t a l C han g e d × 100 = 14525 122 × 100
State the result The result of the calculation is approximately 0.840%.
Present the final answer Therefore, the percentage of answers that were changed for the students who were told to change their answers is approximately 0.840 % .
Examples
Understanding how students perform when changing answers on multiple-choice exams can help educators refine their test-taking advice. For instance, if changing answers leads to a higher percentage of correct answers, instructors might encourage students to reconsider their initial choices. Conversely, if sticking with the first answer proves more beneficial, students could be advised against second-guessing themselves. This analysis provides valuable insights into optimizing test-taking strategies.
The percentage of answers changed by students who were instructed to change their answers is approximately 0.840%.
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