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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 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.

1 answer

To determine which statement is true, we need to calculate the relative frequencies based on the data provided in the table.

Step 1: Relative Frequency of Each Preference by Grade

1. Probability of preferring hip-hop:

  • 10th Graders: \( \frac{112}{165} \approx 0.678 \)
  • 11th Graders: \( \frac{98}{245} \approx 0.400 \)

So, if you are an 11th grader, you are actually less likely to prefer hip-hop compared to a 10th grader.

2. Probability of preferring pop:

  • 10th Graders: \( \frac{53}{165} \approx 0.321 \)
  • 11th Graders: \( \frac{147}{245} \approx 0.600 \)

So, if you like pop, you are more likely to be an 11th grader, not a 10th grader.

3. Probability of being in each grade if preferring pop:

  • Total pop preference = 200
  • 10th Graders (Pop): \( \frac{53}{200} = 0.265 \)
  • 11th Graders (Pop): \( \frac{147}{200} = 0.735 \)

So, if you like pop, you are more likely to be an 11th grader.

4. Probability of being in each grade if preferring hip-hop:

  • Total hip-hop preference = 210
  • 10th Graders (Hip-Hop): \( \frac{112}{210} = 0.533 \)
  • 11th Graders (Hip-Hop): \( \frac{98}{210} = 0.467 \)

This suggests that if you like hip-hop, you are somewhat more likely to be a 10th grader, but the difference is not very large.

Conclusion:

Now reviewing the statements:

  1. If you are an 11th grader, you are more likely to prefer hip-hop. (False)
  2. If you like pop, you are more likely to be a 10th grader. (False)
  3. If you are a 10th grader, you are more likely to prefer pop. (False)
  4. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade. (True)

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