Question

Question
Use the table to answer the question.

Finding patterns in the music tastes of 10th and 11th graders by analyzing the survey data.
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 pop music, you are more likely to be a 10th grader.
If you like pop music, you are more likely to be a 10th grader.

11th graders are more likely to prefer hip-hop over pop music.
11th graders are more likely to prefer hip-hop over pop music.

10th graders are more likely to prefer hip-hop over pop music.
10th graders are more likely to prefer hip-hop over pop music.

If you like hip-hop, you are more likely to be a 11th grader.

Answer 1

To analyze the music preferences of 10th and 11th graders using relative frequencies, let's calculate the relative frequencies for each group and genre.

First, we need to calculate the total number of students in each grade:

- Total 10th graders = 165
- Total 11th graders = 245

Next, let’s calculate the relative frequencies for each genre in each grade.

### 10th Grade:
- **Hip-Hop**:
\[
\text{Relative frequency} = \frac{112}{165} \approx 0.6788 \text{ (or 67.88\%)}
\]

- **Pop**:
\[
\text{Relative frequency} = \frac{53}{165} \approx 0.3212 \text{ (or 32.12\%)}
\]

### 11th Grade:
- **Hip-Hop**:
\[
\text{Relative frequency} = \frac{98}{245} \approx 0.4 \text{ (or 40\%)}
\]

- **Pop**:
\[
\text{Relative frequency} = \frac{147}{245} \approx 0.6 \text{ (or 60\%)}
\]

Now, let's analyze the statements provided based on these relative frequencies:

1. **If you like pop music, you are more likely to be a 10th grader.**
- The relative frequency of pop in 10th grade is 32.12%; in 11th grade, it is 60%. Therefore, this statement is false.

2. **11th graders are more likely to prefer hip-hop over pop music.**
- The relative frequency of hip-hop in 11th grade is 40%, while the relative frequency of pop is 60%. This statement is false.

3. **10th graders are more likely to prefer hip-hop over pop music.**
- The relative frequency of hip-hop in 10th grade is 67.88%, while the relative frequency of pop is 32.12%. This statement is true.

4. **If you like hip-hop, you are more likely to be an 11th grader.**
- The relative frequency of hip-hop for 10th graders is 67.88% (112 out of 165) compared to 40% (98 out of 245) for 11th graders. This statement is false.

Based on this analysis, the true statement is:
**10th graders are more likely to prefer hip-hop over pop music.**