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Use the table to answer the question.

This table displays the number of 10th and 11th-grade students who prefer either hip-hop or pop.
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 are an 11th grader, you are more likely to prefer hip-hop.
If you are an 11th grader, you are more likely to prefer hip-hop.

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

If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

If you are a 10th grader, you are more likely to prefer pop.
If you are a 10th grader, you are more likely to prefer pop.
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1 answer

To answer the question, we need to calculate the relative frequencies for the preferences of hip-hop and pop among 10th and 11th graders. Let's break it down.

Data Summary

  • 10th Grade:

    • Hip-Hop: 112
    • Pop: 53
    • Total: 165

  • 11th Grade:

    • Hip-Hop: 98
    • Pop: 147
    • Total: 245

Relative Frequencies

  1. For 10th Graders:

    • Proportion who prefer Hip-Hop: \( \frac{112}{165} \approx 0.6788 \) (or 67.88%)
    • Proportion who prefer Pop: \( \frac{53}{165} \approx 0.3212 \) (or 32.12%)

  2. For 11th Graders:

    • Proportion who prefer Hip-Hop: \( \frac{98}{245} \approx 0.4 \) (or 40%)
    • Proportion who prefer Pop: \( \frac{147}{245} \approx 0.6 \) (or 60%)

Evaluating the Statements

  1. If you are an 11th grader, you are more likely to prefer hip-hop.

    • False: 40% prefer hip-hop compared to 60% who prefer pop.

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

    • Let's calculate this:
      • Total pop preference: 200
      • 10th graders who like pop: 53
      • 11th graders who like pop: 147
      • Proportion who are 10th graders: \( \frac{53}{200} = 0.265 \) (26.5%)
      • Proportion who are 11th graders: \( \frac{147}{200} = 0.735 \) (73.5%)
    • False: 10th graders are less likely to prefer pop.

  3. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

    • Hip-Hop total preference: 210
    • Proportion from 10th grade: \( \frac{112}{210} \approx 0.533 \) (53.3%)
    • Proportion from 11th grade: \( \frac{98}{210} \approx 0.4667 \) (46.7%)
    • False: More hip-hop fans are from 10th grade.

  4. If you are a 10th grader, you are more likely to prefer pop.

    • False: 32.12% prefer pop compared to 67.88% who prefer hip-hop.

Conclusion

None of the statements provided in the options are true based on the calculated relative frequencies. It appears there may have been an oversight in the interpretation of the statements. If we had to summarize the preference distributions, the trends would suggest that 10th graders prefer hip-hop more than 11th graders.

Thus, if required to select a statement, it would be based on comparing the ratios but in this context provided, all statements appear to be incorrect.