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 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 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 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.

Answer 1

To determine the accuracy of the statements based on the data from the table, we will calculate the relative frequencies for preferences of hip-hop and pop among 10th and 11th graders.

Total Students

• Total 10th graders: 165
• Total 11th graders: 245

Relative Frequencies for Preferences

1. Pop Preference:

   • 10th graders preferring pop: 53

   • 11th graders preferring pop: 147

   • Relative frequency of pop preference:

     • For 10th graders: \( \frac{53}{165} \approx 0.321 \) (32.1%)
     • For 11th graders: \( \frac{147}{245} \approx 0.600 \) (60.0%)

   This indicates that if you like pop, you are more likely to be an 11th grader.

2. Hip-Hop Preference:

   • 10th graders preferring hip-hop: 112

   • 11th graders preferring hip-hop: 98

   • Relative frequency of hip-hop preference:

     • For 10th graders: \( \frac{112}{165} \approx 0.678 \) (67.9%)
     • For 11th graders: \( \frac{98}{245} \approx 0.400 \) (40.0%)

   This indicates that if you like hip-hop, you are more likely to be a 10th grader.

3. 10th Graders' Overall Preferences:

   • 10th graders prefer hip-hop more (112 out of 165) than pop (53 out of 165).

4. 11th Graders' Overall Preferences:

   • 11th graders prefer pop more (147 out of 245) than hip-hop (98 out of 245).

Assessing the Statements:

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

   • False (more likely to be an 11th grader).

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

   • False (more likely to be 10th grader).

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

   • False (10th graders prefer hip-hop more).

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

   • False (11th graders prefer pop more).

Conclusion:

None of the statements are true based on the relative frequencies from the data provided.