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.

Answer 1

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.