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?
Answer (2)
Calculate the total number of answers: 208 + 29304 = 29512 .
Calculate the percentage of changed answers: 29512 208 × 100 .
The result of the calculation is 0.7047987 .
Round the percentage to three decimal places: 0.705% .
Explanation
Understand the problem and provided data We are given a table that shows how many students changed their answers on a multiple-choice exam, and how many did not. The table is broken down by whether the students were instructed to change their answers if they thought they made a mistake, or to stick with their first answer. We want to find the percentage of answers that were changed for the students who were told not to change their answers.
Calculate the total number of answers First, we need to find the total number of answers for the students who were told not to change their answers. From the table, we see that 208 answers were changed and 29,304 answers were unchanged. So, the total number of answers is 208 + 29304 .
Sum the values 208 + 29304 = 29512
Calculate the percentage of changed answers Next, we need to find the percentage of answers that were changed. To do this, we divide the number of changed answers by the total number of answers, and then multiply by 100. So, the percentage of changed answers is 29512 208 × 100 .
Perform the division and multiplication 29512 208 × 100 = 0.007047987 × 100 = 0.7047987
Round to three decimal places Finally, we need to round the percentage to three decimal places. So, the percentage of changed answers is approximately 0.705% .
State the final answer Therefore, the percentage of answers that were changed for the students who were told not to change their answers is 0.705% .
Examples
This type of calculation is useful in educational research to analyze the effectiveness of different teaching strategies. For example, if we wanted to know whether encouraging students to review and potentially change their answers on tests leads to better overall scores, we could compare the performance of students who were instructed to change their answers with those who were not. By calculating the percentage of changed answers and analyzing the corresponding score changes, we can gain insights into the impact of this strategy. This helps educators make informed decisions about how to advise students on test-taking strategies.
The percentage of changed answers for students instructed not to change their answers is approximately 0.705%. This was calculated by dividing the number of changed answers by the total number of answers and converting it into a percentage. After rounding, the final answer is 0.705%.
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