Question
A teacher gathered data about the number of hours her students spent studying for a test and their resulting test grades. She found that on average, for every 30 minutes studied, the grade increased by 8 points. Which statements about this relationship are true? Check all that apply.
The data set would have a linear association.
The data set would have a nonlinear association.
The data set would have a positive correlation.
The data set would have a negative correlation.
Every student earns 16 more points for each additional hour they study.
Students that study more tend to earn better grades on the test.
The data set would have a linear association.
The data set would have a nonlinear association.
The data set would have a positive correlation.
The data set would have a negative correlation.
Every student earns 16 more points for each additional hour they study.
Students that study more tend to earn better grades on the test.
Answers
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Answered by
GPT-4o mini
Based on the information provided, let's analyze the statements one by one:
1. **The data set would have a linear association.**
- **True**: Since the relationship describes a consistent increase in grades with a consistent increase in study time (every 30 minutes corresponds to an 8-point increase), this indicates a linear association.
2. **The data set would have a nonlinear association.**
- **False**: The relationship is linear as described, so it does not have a nonlinear association.
3. **The data set would have a positive correlation.**
- **True**: There is a positive relationship between the number of hours studied and the test grades, meaning as study time increases, grades increase.
4. **The data set would have a negative correlation.**
- **False**: Since grades increase with more study time, this indicates a positive correlation rather than a negative one.
5. **Every student earns 16 more points for each additional hour they study.**
- **True**: If 30 minutes (or half an hour) of study leads to an 8-point increase, then studying an additional hour (which is 2 intervals of 30 minutes) would lead to an increase of 16 points (8 points per 30 minutes x 2).
6. **Students that study more tend to earn better grades on the test.**
- **True**: This statement accurately reflects the positive correlation established whereby more study time is associated with better grades.
In summary, the true statements are:
- The data set would have a linear association.
- The data set would have a positive correlation.
- Every student earns 16 more points for each additional hour they study.
- Students that study more tend to earn better grades on the test.
1. **The data set would have a linear association.**
- **True**: Since the relationship describes a consistent increase in grades with a consistent increase in study time (every 30 minutes corresponds to an 8-point increase), this indicates a linear association.
2. **The data set would have a nonlinear association.**
- **False**: The relationship is linear as described, so it does not have a nonlinear association.
3. **The data set would have a positive correlation.**
- **True**: There is a positive relationship between the number of hours studied and the test grades, meaning as study time increases, grades increase.
4. **The data set would have a negative correlation.**
- **False**: Since grades increase with more study time, this indicates a positive correlation rather than a negative one.
5. **Every student earns 16 more points for each additional hour they study.**
- **True**: If 30 minutes (or half an hour) of study leads to an 8-point increase, then studying an additional hour (which is 2 intervals of 30 minutes) would lead to an increase of 16 points (8 points per 30 minutes x 2).
6. **Students that study more tend to earn better grades on the test.**
- **True**: This statement accurately reflects the positive correlation established whereby more study time is associated with better grades.
In summary, the true statements are:
- The data set would have a linear association.
- The data set would have a positive correlation.
- Every student earns 16 more points for each additional hour they study.
- Students that study more tend to earn better grades on the test.
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