Question

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?
Hip Hop Pop
Totals
10円
110
50
160
Grade
11%h
99
150
249
Grade
Total
209
200
409
A. If you like pop, you are more likely to be a 10th grader.
B. If you are a 10th grader, you are more likely to prefer pop.
C. If you are an 11th grader, you are more likely to prefer hip-hop.
D. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

Answer 1

To analyze the preferences of music genres among 10th and 11th graders in terms of relative frequencies, we first need to clarify and summarize the data presented in your survey results. The totals are outlined in a way that specifies both the number of students preferring each genre and their grade levels.

Based on the provided data:

1. **Total number of students surveyed: 409**
2. **Total preferences:**
- Hip Hop: 209 students
- Pop: 200 students

3. **Breakdown by grades:**
- **10th Grade:**
- Hip Hop: 110
- Pop: 50
- *Total 10th Graders: 160*

- **11th Grade:**
- Hip Hop: 99
- Pop: 150
- *Total 11th Graders: 249*

Now, we can calculate the relative frequencies for each scenario provided in the options A, B, C, and D:

**A. If you like pop, you are more likely to be a 10th grader.**
- Pop Preferences:
- 10th Graders: 50 (out of 200 total Pop)
- Relative frequency for 10th graders preferring Pop: \( \frac{50}{200} = 0.25\) (or 25%)
- 11th Graders: 150 (out of 200 total Pop)
- Relative frequency for 11th graders preferring Pop: \( \frac{150}{200} = 0.75\) (or 75%)

*Conclusion: This statement is false.*

**B. If you are a 10th grader, you are more likely to prefer pop.**
- Total 10th Graders: 160
- Preference Breakdown:
- Hip Hop: 110
- Pop: 50
- Relative frequency for 10th graders preferring Pop: \( \frac{50}{160} = 0.3125\) (or 31.25%)
- Relative frequency for 10th graders preferring Hip Hop: \( \frac{110}{160} = 0.6875\) (or 68.75%)

*Conclusion: This statement is false.*

**C. If you are an 11th grader, you are more likely to prefer hip-hop.**
- Total 11th Graders: 249
- Preference Breakdown:
- Hip Hop: 99
- Pop: 150
- Relative frequency for 11th graders preferring Hip Hop: \( \frac{99}{249} \approx 0.3984\) (or 39.84%)
- Relative frequency for 11th graders preferring Pop: \( \frac{150}{249} \approx 0.6016\) (or 60.16%)

*Conclusion: This statement is false.*

**D. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.**
- Total Hip Hop Preferences: 209
- Breakdown by Grades:
- 10th Graders: 110
- 11th Graders: 99
- Relative frequency for 10th graders preferring Hip Hop: \( \frac{110}{209} \approx 0.5263\) (or 52.63%)
- Relative frequency for 11th graders preferring Hip Hop: \( \frac{99}{209} \approx 0.4737\) (or 47.37%)

Both distributions are fairly close, indicating that a student who likes hip-hop could indeed be from either grade relatively equally.

*Conclusion: This statement is true.*

So, the only true statement based on the given data is **D**.