Use the table to answer the question.

Question

Finding patterns in the music tastes of 10th and 11th graders by analyzing the survey data.
Hip-Hop Pop Totals
10th Grade 112 53 165
11th Grade 98 147 245
Total 210 200 410
Examine the data from a survey of 10th and 11th graders about which music genre they prefer. Using relative frequencies, which of the following is true?

(1 point)
Responses

11th graders are more likely to prefer hip-hop over pop music.
11th graders are more likely to prefer hip-hop over pop music.

If you like hip-hop, you are more likely to be a 11th grader.
If you like hip-hop, you are more likely to be a 11th grader.

10th graders are more likely to prefer hip-hop over pop music.
10th graders are more likely to prefer hip-hop over pop music.

If you like pop music, you are more likely to be a 10th grader.
If you like pop music, you are more likely to be a 10th grader.

Answer 1

To analyze the survey data using relative frequencies, we first need to calculate the relative frequencies for the music preferences of both 10th and 11th graders.

Step 1: Calculate relative frequencies

For 10th Graders:

• Total = 165
• Hip-Hop: \( \frac{112}{165} \approx 0.6788 \)
• Pop: \( \frac{53}{165} \approx 0.3212 \)

For 11th Graders:

• Total = 245
• Hip-Hop: \( \frac{98}{245} \approx 0.4 \)
• Pop: \( \frac{147}{245} \approx 0.6 \)

Step 2: Compare preferences

1. 11th graders are more likely to prefer hip-hop over pop music.

   • Relative frequency for hip-hop (11th Grade) is 0.4; for pop, it's 0.6.
   • This statement is false.

2. If you like hip-hop, you are more likely to be an 11th grader.

   • Relative frequency for hip-hop (10th Grade) is approximately 0.6788; for 11th Grade, it's 0.4.
   • This statement is false.

3. 10th graders are more likely to prefer hip-hop over pop music.

   • Relative frequency for hip-hop (10th Grade) is approximately 0.6788; for pop, it’s approximately 0.3212.
   • This statement is true.

4. If you like pop music, you are more likely to be a 10th grader.

   • Relative frequency for pop (10th Grade) is approximately 0.3212; for 11th Grade, it’s approximately 0.6.
   • This statement is false.

Conclusion

The true statement is:

10th graders are more likely to prefer hip-hop over pop music.