To analyze the data and determine the relative frequencies for each of the music genres by grade, we can calculate the proportions of 10th and 11th graders who prefer hip-hop and pop music.
Total Counts from the Table:
- 10th Grade Hip-Hop: 112
- 10th Grade Pop: 53
- 11th Grade Hip-Hop: 98
- 11th Grade Pop: 147
Total Students:
- 10th Graders: 165
- 11th Graders: 245
- Overall Total: 410
Relative Frequencies Calculation:
-
For 10th Graders:
- Proportion who prefer Hip-Hop: \( \frac{112}{165} \approx 0.6788 \)
- Proportion who prefer Pop: \( \frac{53}{165} \approx 0.3212 \)
-
For 11th Graders:
- Proportion who prefer Hip-Hop: \( \frac{98}{245} \approx 0.4 \)
- Proportion who prefer Pop: \( \frac{147}{245} \approx 0.6 \)
Now, let's analyze the statements:
-
If you like pop music, you are more likely to be a 10th grader.
- 10th Graders: \( 0.3212 \) for Pop
- 11th Graders: \( 0.6 \) for Pop
- Not true (11th graders prefer pop more).
-
If you like hip-hop, you are more likely to be a 11th grader.
- 10th Graders: \( 0.6788 \) for Hip-Hop
- 11th Graders: \( 0.4 \) for Hip-Hop
- Not true (10th graders prefer hip-hop more).
-
10th graders are more likely to prefer hip-hop over pop music.
- Proportion Hip-Hop (10th Graders): \( 0.6788 \)
- Proportion Pop (10th Graders): \( 0.3212 \)
- True (10th graders prefer hip-hop more).
-
11th graders are more likely to prefer hip-hop over pop music.
- Proportion Hip-Hop (11th Graders): \( 0.4 \)
- Proportion Pop (11th Graders): \( 0.6 \)
- Not true (11th graders prefer pop).
Conclusion: The statement that is true is: 10th graders are more likely to prefer hip-hop over pop music.