Question
Bivariate Data Analysis & Probability Unit Test
11 of 1611 of 16 Items
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 are a 10th grader, you are more likely to prefer pop.
11 of 1611 of 16 Items
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 are a 10th grader, you are more likely to prefer pop.
Answers
GPT-4o mini
To analyze the data using relative frequencies, we will calculate the proportions given the total counts for each preference and grade level.
1. **Total Students who prefer Pop**:
- Total Pop = 200
2. **Relative frequency of 10th graders who prefer Pop**:
\[
\text{Relative Frequency (10th Graders Pop)} = \frac{\text{10th Graders who prefer Pop}}{\text{Total Students who prefer Pop}} = \frac{53}{200} = 0.265
\]
3. **Relative frequency of 11th graders who prefer Pop**:
\[
\text{Relative Frequency (11th Graders Pop)} = \frac{\text{11th Graders who prefer Pop}}{\text{Total Students who prefer Pop}} = \frac{147}{200} = 0.735
\]
This indicates that if you like pop, you are more likely to be an 11th grader since 73.5% of pop listeners are 11th graders compared to 26.5% who are 10th graders.
4. **Total Students who prefer Hip-Hop**:
- Total Hip-Hop = 210
5. **Relative frequency of 10th graders who prefer Hip-Hop**:
\[
\text{Relative Frequency (10th Graders Hip-Hop)} = \frac{\text{10th Graders who prefer Hip-Hop}}{\text{Total Students who prefer Hip-Hop}} = \frac{112}{210} \approx 0.533
\]
6. **Relative frequency of 11th graders who prefer Hip-Hop**:
\[
\text{Relative Frequency (11th Graders Hip-Hop)} = \frac{\text{11th Graders who prefer Hip-Hop}}{\text{Total Students who prefer Hip-Hop}} = \frac{98}{210} \approx 0.467
\]
This shows that if you are an 11th grader, you are less likely to prefer hip-hop (46.7%) compared to 10th graders (53.3%).
7. **Total Students**:
- The total number of students = 410.
Given this analysis, the true statement from the options given is:
**If you like pop, you are more likely to be a 11th grader.**
Therefore, none of the provided options are true as stated. If rephrased to "If you like pop, you are more likely to be an 11th grader," then that would be correct.
To summarize, none of the original options as presented accurately reflect the data based on the relative frequencies calculated.
1. **Total Students who prefer Pop**:
- Total Pop = 200
2. **Relative frequency of 10th graders who prefer Pop**:
\[
\text{Relative Frequency (10th Graders Pop)} = \frac{\text{10th Graders who prefer Pop}}{\text{Total Students who prefer Pop}} = \frac{53}{200} = 0.265
\]
3. **Relative frequency of 11th graders who prefer Pop**:
\[
\text{Relative Frequency (11th Graders Pop)} = \frac{\text{11th Graders who prefer Pop}}{\text{Total Students who prefer Pop}} = \frac{147}{200} = 0.735
\]
This indicates that if you like pop, you are more likely to be an 11th grader since 73.5% of pop listeners are 11th graders compared to 26.5% who are 10th graders.
4. **Total Students who prefer Hip-Hop**:
- Total Hip-Hop = 210
5. **Relative frequency of 10th graders who prefer Hip-Hop**:
\[
\text{Relative Frequency (10th Graders Hip-Hop)} = \frac{\text{10th Graders who prefer Hip-Hop}}{\text{Total Students who prefer Hip-Hop}} = \frac{112}{210} \approx 0.533
\]
6. **Relative frequency of 11th graders who prefer Hip-Hop**:
\[
\text{Relative Frequency (11th Graders Hip-Hop)} = \frac{\text{11th Graders who prefer Hip-Hop}}{\text{Total Students who prefer Hip-Hop}} = \frac{98}{210} \approx 0.467
\]
This shows that if you are an 11th grader, you are less likely to prefer hip-hop (46.7%) compared to 10th graders (53.3%).
7. **Total Students**:
- The total number of students = 410.
Given this analysis, the true statement from the options given is:
**If you like pop, you are more likely to be a 11th grader.**
Therefore, none of the provided options are true as stated. If rephrased to "If you like pop, you are more likely to be an 11th grader," then that would be correct.
To summarize, none of the original options as presented accurately reflect the data based on the relative frequencies calculated.