Scatter Plots & Data Analysis Online Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
14 of 1514 of 15 Items

Question
Use the table to answer the question.

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

11th graders are more likely to prefer hip-hop over pop music.
11th 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.
If you like hip-hop, you are more likely to be a 11th grader.

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 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.

Answer 1

To evaluate the statements, we will calculate the relative frequencies from the data provided in the table.

Given Data:

• 10th Grade:

  • Hip-Hop: 112
  • Pop: 53
  • Total: 165

• 11th Grade:

  • Hip-Hop: 98
  • Pop: 147
  • Total: 245

• Overall Totals:

  • Hip-Hop: 210
  • Pop: 200
  • Total: 410

Ask for Relative Frequencies:

Relative frequency is calculated as: \[ \text{Relative Frequency} = \frac{\text{Frequency of Interest}}{\text{Total Frequency}} \]

Calculate Relative Frequencies for Each Statement:

1. 11th graders are more likely to prefer hip-hop over pop music.

   • Relative frequency for hip-hop (11th Grade) = \( \frac{98}{245} \approx 0.40 \)
   • Relative frequency for pop (11th Grade) = \( \frac{147}{245} \approx 0.60 \)
   • Since 0.40 < 0.60, this statement is FALSE.

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

   • Relative frequency of being a 11th grader among hip-hop listeners = \( \frac{98}{210} \approx 0.47 \)
   • Relative frequency of being a 10th grader among hip-hop listeners = \( \frac{112}{210} \approx 0.53 \)
   • Since 0.47 < 0.53, this statement is FALSE.

3. 10th graders are more likely to prefer hip-hop over pop music.

   • Relative frequency for hip-hop (10th Grade) = \( \frac{112}{165} \approx 0.68 \)
   • Relative frequency for pop (10th Grade) = \( \frac{53}{165} \approx 0.32 \)
   • Since 0.68 > 0.32, this statement is TRUE.

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

   • Relative frequency of being a 10th grader among pop listeners = \( \frac{53}{200} = 0.265 \)
   • Relative frequency of being an 11th grader among pop listeners = \( \frac{147}{200} = 0.735 \)
   • Since 0.265 < 0.735, this statement is FALSE.

Conclusion:

The only true statement is:

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