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

1 answer

To determine which statement is true based on the relative frequencies of preferences for hip-hop and pop among 10th and 11th graders, let’s calculate the relevant relative frequencies from the data provided in the table.

Given Data

  1. 10th Grade:

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

  2. 11th Grade:

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

  3. Total:

    • Hip-Hop: 210
    • Pop: 200
    • Overall Total: 410

Relative Frequencies

  1. For 10th Graders:

    • Probability of preferring Hip-Hop: \[ P(\text{Hip-Hop | 10th}) = \frac{112}{165} \approx 0.6788 \]
    • Probability of preferring Pop: \[ P(\text{Pop | 10th}) = \frac{53}{165} \approx 0.3212 \]

    Conclusion: A 10th grader is more likely to prefer hip-hop than pop.

  2. For 11th Graders:

    • Probability of preferring Hip-Hop: \[ P(\text{Hip-Hop | 11th}) = \frac{98}{245} \approx 0.4 \]
    • Probability of preferring Pop: \[ P(\text{Pop | 11th}) = \frac{147}{245} \approx 0.6 \]

    Conclusion: A 11th grader is more likely to prefer pop than hip-hop.

  3. For Hip-Hop Fans (Total):

    • Probability of being a 10th grader: \[ P(\text{10th | Hip-Hop}) = \frac{112}{210} \approx 0.5333 \]
    • Probability of being an 11th grader:
      \[ P(\text{11th | Hip-Hop}) = \frac{98}{210} \approx 0.4667 \]

    Conclusion: If you like hip-hop, you are more likely to be a 10th grader.

  4. For Pop Fans (Total):

    • Probability of being a 10th grader: \[ P(\text{10th | Pop}) = \frac{53}{200} \approx 0.265 \]
    • Probability of being an 11th grader:
      \[ P(\text{11th | Pop}) = \frac{147}{200} \approx 0.735 \]

    Conclusion: If you like pop, you are more likely to be an 11th grader.

Answer Evaluation

Based on the analyses:

  1. If you are a 10th grader, you are more likely to prefer pop. - False (10th graders prefer hip-hop more)

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

  3. If you like pop, you are more likely to be a 10th grader. - False (pop fans are more likely to be 11th grade)

  4. If you are an 11th grader, you are more likely to prefer hip-hop. - False (11th graders prefer pop more)

The true statement based on the calculations from the data is: If you are a 10th grader, you are more likely to prefer hip-hop.

None of the options provided are true based on the data provided.

Please check if the options were correctly listed.