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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 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.

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.

1 answer

To analyze the data using relative frequencies, let's calculate the proportions for each preference by grade.

  1. For 10th graders:

    • Total 10th graders: 165
    • Hip-Hop: 112 out of 165 = \( \frac{112}{165} \approx 0.6788 \) (or 67.88%)
    • Pop: 53 out of 165 = \( \frac{53}{165} \approx 0.3212 \) (or 32.12%)

  2. For 11th graders:

    • Total 11th graders: 245
    • Hip-Hop: 98 out of 245 = \( \frac{98}{245} \approx 0.4 \) (or 40.0%)
    • Pop: 147 out of 245 = \( \frac{147}{245} \approx 0.6 \) (or 60.0%)

Now, we can evaluate each of the statements:

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

    • For pop, 10th graders: 53 out of 200 = \( 0.265 \) (or 26.5%),
    • For pop, 11th graders: 147 out of 200 = \( 0.735 \) (or 73.5%).
    • This statement is false.

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

    • For hip-hop, 10th graders: 112 out of 210 = \( 0.533 \) (or 53.3%),
    • For hip-hop, 11th graders: 98 out of 210 = \( 0.466 \) (or 46.7%).
    • This statement is not true as the proportions are not equal and 10th graders are more likely.

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

    • As calculated, 10th graders prefer hip-hop (67.88%) over pop (32.12%).
    • This statement is false.

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

    • For 11th graders, 40% prefer hip-hop and 60% prefer pop.
    • Therefore, this statement is false.

Conclusion

None of the provided statements are true based on the relative frequencies calculated above.