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Use the table to answer the question.

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

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.

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.

1 answer

To determine the correct statements based on relative frequencies, let's calculate the relative frequencies for each category.

  1. For 10th Graders:

    • Total 10th Graders: 165

    • Hip-Hop: 112

    • Pop: 53

    • Relative frequency for Hip-Hop among 10th Graders: \[ \frac{112}{165} \approx 0.6788 \text{ (or 67.88%)} \]

    • Relative frequency for Pop among 10th Graders: \[ \frac{53}{165} \approx 0.3212 \text{ (or 32.12%)} \]

  2. For 11th Graders:

    • Total 11th Graders: 245

    • Hip-Hop: 98

    • Pop: 147

    • Relative frequency for Hip-Hop among 11th Graders: \[ \frac{98}{245} \approx 0.4 \text{ (or 40%)} \]

    • Relative frequency for Pop among 11th Graders: \[ \frac{147}{245} \approx 0.6 \text{ (or 60%)} \]

Now let's analyze each option given in the question:

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

    • Pop preferences: 53 in 10th grade and 147 in 11th grade.
    • More students in 11th grade prefer pop music so this statement is false.

  2. 11th graders are more likely to prefer hip-hop over pop music.

    • Relative frequencies:
      • Hip-Hop: 40%
      • Pop: 60%
    • This statement is false since more 11th Graders prefer pop than hip-hop.

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

    • Hip-Hop Preferences: 112 (10th) vs. 98 (11th).
    • More students in 10th grade prefer hip-hop, so this statement is false.

  4. 10th graders are more likely to prefer hip-hop over pop music.

    • Relative frequencies: 67.88% like hip-hop and 32.12% like pop in 10th grade.
    • This statement is true.

Thus, the correct answer is:

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