Use the table to answer the question.

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 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 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.
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Answer 1

To evaluate the claims using relative frequencies, we can calculate the proportion of students in each grade who prefer hip-hop and pop.

1. For 10th Graders:

   • Total 10th Graders = 165
   • Hip-Hop preference = 112
   • Pop preference = 53

   Relative frequency for 10th Graders who like hip-hop: \[ \text{Relative frequency for hip-hop} = \frac{112}{165} \approx 0.6788 \text{ (or 67.88%)} \]

   Relative frequency for 10th Graders who like pop: \[ \text{Relative frequency for pop} = \frac{53}{165} \approx 0.3212 \text{ (or 32.12%)} \]

2. For 11th Graders:

   • Total 11th Graders = 245
   • Hip-Hop preference = 98
   • Pop preference = 147

   Relative frequency for 11th Graders who like hip-hop: \[ \text{Relative frequency for hip-hop} = \frac{98}{245} \approx 0.4 \text{ (or 40%)} \]

   Relative frequency for 11th Graders who like pop: \[ \text{Relative frequency for pop} = \frac{147}{245} \approx 0.6 \text{ (or 60%)} \]

Now, let's evaluate each statement:

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

   • Hip-Hop: Students = 112 (10th) and 98 (11th).
   • Proportion: \( \frac{112}{210} \) (10th) and \( \frac{98}{210} \) (11th) gives \(\approx 0.532\) for 10th and \(\approx 0.467\) for 11th. This statement is true.

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

   • Pop: Students = 53 (10th) and 147 (11th).
   • Proportion: \( \frac{53}{200} \) (10th) and \( \frac{147}{200} \) (11th). Clearly, 147 (11th) is greater. This statement is false.

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

   • Pop preference = 32.12% (10th) compared to 60% (11th). 10th graders are more likely to prefer hip-hop. This statement is false.

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

   • Hip-Hop preference for 11th Graders is 40%, and for pop, it is 60%. Therefore, 11th graders are more likely to prefer pop. This statement is false.

Conclusion:

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