To examine the data and analyze the relative frequencies of music genre preferences among 10th and 11th graders, we can calculate the proportions of students who prefer hip-hop and pop music for each grade.
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Hip-Hop Preference:
- 10th Grade: \( \frac{112}{165} \)
- 11th Grade: \( \frac{98}{245} \)
Calculating these values:
- \( \frac{112}{165} \approx 0.6788 \)
- \( \frac{98}{245} \approx 0.4 \)
This means about 67.88% of 10th graders prefer hip-hop compared to about 40% of 11th graders.
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Pop Music Preference:
- 10th Grade: \( \frac{53}{165} \)
- 11th Grade: \( \frac{147}{245} \)
Calculating these values:
- \( \frac{53}{165} \approx 0.3212 \)
- \( \frac{147}{245} \approx 0.6 \)
This means about 32.12% of 10th graders prefer pop compared to about 60% of 11th graders.
Now let's assess the statements based on our calculations:
-
If you like hip-hop, you are more likely to be a 11th grader.
False (more 10th graders prefer hip-hop). -
If you like pop music, you are more likely to be a 10th grader.
False (more 11th graders prefer pop). -
11th graders are more likely to prefer hip-hop over pop music.
False (less than 40% of 11th graders prefer hip-hop, and 60% prefer pop). -
10th graders are more likely to prefer hip-hop over pop music.
True (about 67.88% prefer hip-hop vs. 32.12% for pop).
Thus, the correct answer is:
10th graders are more likely to prefer hip-hop over pop music.