To analyze the data and determine which statement is true using relative frequencies, we first need to calculate the relative frequencies for each group based on their music preferences.
Step 1: Calculate the total number of students from each grade.
- Total 10th graders: 165
- Total 11th graders: 245
Step 2: Calculate the relative frequencies by genre and grade.
For 10th graders:
- Relative frequency of hip-hop: \( \frac{112}{165} \approx 0.6788 \)
- Relative frequency of pop: \( \frac{53}{165} \approx 0.3212 \)
For 11th graders:
- Relative frequency of hip-hop: \( \frac{98}{245} \approx 0.4000 \)
- Relative frequency of pop: \( \frac{147}{245} \approx 0.6000 \)
Step 3: Compare the statements.
-
If you like hip-hop, you are more likely to be an 11th grader.
- Hip-hop: 11th graders make up 0.4 (40%) vs. 10th grader's 0.6788 (67.88%). This is not true.
-
If you like pop music, you are more likely to be a 10th grader.
- Pop: 10th graders contribute 0.3212 (32.12%) vs. 11th graders' 0.6 (60%). This is not true.
-
11th graders are more likely to prefer hip-hop over pop music.
- 11th graders: hip-hop 0.4 (40%) vs. pop 0.6 (60%). This is not true.
-
10th graders are more likely to prefer hip-hop over pop music.
- 10th graders: hip-hop 0.6788 (67.88%) vs. pop 0.3212 (32.12%). This statement is true.
Conclusion: The correct statement is: "10th graders are more likely to prefer hip-hop over pop music."