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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 grader: 98 | 147 | 245
total: 210 | 200 | 410

examine the data from a survey of 1th and 11th graders about which music genre they prefer.

using relative frequencies, which of the following is true?

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 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

1 answer

To analyze the statements, we can first calculate the relative frequencies for each grade and music genre based on the provided data.

Given Data:

  • 10th Grade:

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

  • 11th Grade:

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

  • Grand Totals:

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

Relative Frequencies Calculation:

  1. For Pop:

    • 10th Graders who like Pop: \( \frac{53}{165} \approx 0.3212 \)
    • 11th Graders who like Pop: \( \frac{147}{245} \approx 0.6 \)

    So, if you like Pop, the relative frequency of being a 10th grader is about 32.12%, and for an 11th grader, it is 60%.

  2. For Hip-hop:

    • 10th Graders who like Hip-hop: \( \frac{112}{165} \approx 0.6788 \)
    • 11th Graders who like Hip-hop: \( \frac{98}{245} \approx 0.4 \)

    So, if you like Hip-hop, the relative frequency of being a 10th grader is about 67.88%, and for an 11th grader, it is 40%.

Evaluation of Statements:

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

    • False. About 32.12% are 10th graders, and 60% are 11th graders who like Pop.

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

    • False. 67.88% are 10th graders and 40% are 11th graders who like Hip-hop. This is not almost equal.

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

    • False. 67.88% of 10th graders prefer Hip-hop, while only about 32.12% prefer Pop.

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

    • False. 40% of 11th graders prefer Hip-hop, while 60% prefer Pop.

Conclusion:

None of the given statements are true based on the relative frequencies calculated from the data provided.