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

1 answer

To analyze the given data and evaluate the statements using relative frequencies, let's calculate the probabilities based on the preferences for hip-hop and pop for both 10th and 11th graders.

Total Students

  • Total 10th graders = 165
  • Total 11th graders = 245
  • Overall total students = 410

Relative Frequencies

For Hip-Hop:

  • 10th graders who prefer hip-hop: 112
  • 11th graders who prefer hip-hop: 98

Relative frequency for 10th graders who prefer hip-hop: \[ \text{Relative Frequency (10th Hip-Hop)} = \frac{112}{165} \approx 0.6788 \]

Relative frequency for 11th graders who prefer hip-hop: \[ \text{Relative Frequency (11th Hip-Hop)} = \frac{98}{245} \approx 0.4 \]

For Pop:

  • 10th graders who prefer pop: 53
  • 11th graders who prefer pop: 147

Relative frequency for 10th graders who prefer pop: \[ \text{Relative Frequency (10th Pop)} = \frac{53}{165} \approx 0.3212 \]

Relative frequency for 11th graders who prefer pop: \[ \text{Relative Frequency (11th Pop)} = \frac{147}{245} \approx 0.6 \]

Analyzing the Statements

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

    • False. The relative frequency shows that a higher proportion of 10th graders prefer hip-hop compared to 11th graders.

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

    • False. Only about 40% of 11th graders prefer hip-hop, compared to about 68% of 10th graders.

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

    • True. 32% of 10th graders prefer pop versus 60% of 11th graders.

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

    • False. More 10th graders prefer hip-hop than pop.

Conclusion

The statement that is true based on the relative frequencies is:

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