Bivariate Data Analysis & Probability Unit Test

Question

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Question
Use the table to answer the 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 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.

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.

Answer 1

To answer the question using relative frequencies, we will first calculate the relative frequencies for each preference (Hip-Hop and Pop) based on grade level.

1. For Hip-Hop:

   • Total students who prefer Hip-Hop: 210
   • 10th Grade students who prefer Hip-Hop: 112
   • 11th Grade students who prefer Hip-Hop: 98

   Relative frequency of 10th graders liking Hip-Hop: \[ \text{Relative Frequency (10th, Hip-Hop)} = \frac{112}{210} \approx 0.533 (53.3%) \]

   Relative frequency of 11th graders liking Hip-Hop: \[ \text{Relative Frequency (11th, Hip-Hop)} = \frac{98}{210} \approx 0.467 (46.7%) \]

2. For Pop:

   • Total students who prefer Pop: 200
   • 10th Grade students who prefer Pop: 53
   • 11th Grade students who prefer Pop: 147

   Relative frequency of 10th graders liking Pop: \[ \text{Relative Frequency (10th, Pop)} = \frac{53}{200} \approx 0.265 (26.5%) \]

   Relative frequency of 11th graders liking Pop: \[ \text{Relative Frequency (11th, Pop)} = \frac{147}{200} \approx 0.735 (73.5%) \]

Now we can analyze the statements:

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

   • This is incorrect since 73.5% of pop lovers are 11th graders.

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

   • This is incorrect; 61.2% of 11th graders prefer pop.

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

   • This is incorrect, as 53.3% are 10th graders while 46.7% are 11th graders.

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

   • This is correct, as 26.5% prefer pop compared to 53.3% who prefer hip-hop.

Based on this analysis, the true statement is: If you are a 10th grader, you are more likely to prefer pop.