Answer :
Sure, let's go through each part step by step.
### Part A: Percentage of students who failed the exam, given that they completed the exam review.
To determine the percentage of students who failed the exam given that they completed the exam review, we need to focus on the group that completed the exam review and find the proportion of that group who failed.
From the table:
- Completed exam review: 65%
- Passed the exam: 55%
- Did not pass the exam: 10%
The percentage of students who failed the exam, given that they completed the exam review can be calculated as follows:
[tex]\[ \text{Percentage failed given review} = \left( \frac{\text{Percentage who did not pass and completed the review}}{\text{Total percentage who completed the review}} \right) \times 100 \][/tex]
Substituting the given values,
[tex]\[ \text{Percentage failed given review} = \left( \frac{10\%}{65\%} \right) \times 100 \approx 15\% \][/tex]
So, the percentage of students who failed the exam, given that they completed the exam review is approximately \(15\%\).
### Part B: Percentage of students who failed the exam, given that they did not complete the exam review.
Similarly, we need to focus on the group that did not complete the exam review and find the proportion of that group who failed.
From the table:
- Did not complete the exam review: 35%
- Passed the exam: 20%
- Did not pass the exam: 15%
The percentage of students who failed the exam, given that they did not complete the exam review can be calculated as follows:
[tex]\[ \text{Percentage failed given no review} = \left( \frac{\text{Percentage who did not pass and did not complete the review}}{\text{Total percentage who did not complete the review}} \right) \times 100 \][/tex]
Substituting the given values,
[tex]\[ \text{Percentage failed given no review} = \left( \frac{15\%}{35\%} \right) \times 100 \approx 43\% \][/tex]
So, the percentage of students who failed the exam, given that they did not complete the exam review is approximately \(43\%\).
### Part C: Is there an association between failing the exam and completing the exam review? Justify your answer.
To determine if there is an association between failing the exam and completing the exam review, we compare the failure rates of students who completed the review and those who did not:
- Percentage failed given review: 15%
- Percentage failed given no review: 43%
Since there is a significant difference between the two percentages (15% vs. 43%), we can conclude that there is an association. The fact that the failure rate is much higher for students who did not complete the review (43%) compared to those who did complete the review (15%) suggests that completing the exam review is associated with a lower likelihood of failing the exam.
Hence, there is an association between failing the exam and completing the exam review.
### Part A: Percentage of students who failed the exam, given that they completed the exam review.
To determine the percentage of students who failed the exam given that they completed the exam review, we need to focus on the group that completed the exam review and find the proportion of that group who failed.
From the table:
- Completed exam review: 65%
- Passed the exam: 55%
- Did not pass the exam: 10%
The percentage of students who failed the exam, given that they completed the exam review can be calculated as follows:
[tex]\[ \text{Percentage failed given review} = \left( \frac{\text{Percentage who did not pass and completed the review}}{\text{Total percentage who completed the review}} \right) \times 100 \][/tex]
Substituting the given values,
[tex]\[ \text{Percentage failed given review} = \left( \frac{10\%}{65\%} \right) \times 100 \approx 15\% \][/tex]
So, the percentage of students who failed the exam, given that they completed the exam review is approximately \(15\%\).
### Part B: Percentage of students who failed the exam, given that they did not complete the exam review.
Similarly, we need to focus on the group that did not complete the exam review and find the proportion of that group who failed.
From the table:
- Did not complete the exam review: 35%
- Passed the exam: 20%
- Did not pass the exam: 15%
The percentage of students who failed the exam, given that they did not complete the exam review can be calculated as follows:
[tex]\[ \text{Percentage failed given no review} = \left( \frac{\text{Percentage who did not pass and did not complete the review}}{\text{Total percentage who did not complete the review}} \right) \times 100 \][/tex]
Substituting the given values,
[tex]\[ \text{Percentage failed given no review} = \left( \frac{15\%}{35\%} \right) \times 100 \approx 43\% \][/tex]
So, the percentage of students who failed the exam, given that they did not complete the exam review is approximately \(43\%\).
### Part C: Is there an association between failing the exam and completing the exam review? Justify your answer.
To determine if there is an association between failing the exam and completing the exam review, we compare the failure rates of students who completed the review and those who did not:
- Percentage failed given review: 15%
- Percentage failed given no review: 43%
Since there is a significant difference between the two percentages (15% vs. 43%), we can conclude that there is an association. The fact that the failure rate is much higher for students who did not complete the review (43%) compared to those who did complete the review (15%) suggests that completing the exam review is associated with a lower likelihood of failing the exam.
Hence, there is an association between failing the exam and completing the exam review.
