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.

Explanation:

• Linear Association: Since for every 30 - minute (constant interval) increase in study time, the grade increase is 8 points (constant increase). The relationship can be modeled by a linear equation \(y = mx + b\) (where \(m=\frac{8}{0.5}=16\) if \(x\) is in hours). So, the data set has a linear association.
• Non - linear Association: A non - linear association would have a non - constant rate of change. Since the rate of change (8 points per 30 minutes) is constant, this is false.
• Positive Correlation: As the number of hours studied (\(x\)) increases, the grade (\(y\)) increases. In a linear relationship \(y=mx + b\) with \(m>0\), there is a positive correlation.
• Negative Correlation: A negative correlation would mean as \(x\) (study hours) increases, \(y\) (grade) decreases. This is false.
• Points per hour: If 30 minutes (\(0.5\) hours) gives an 8 - point increase, then for 1 hour (\(x = 1\)), using the unit - rate \(\frac{8}{0.5}=16\) points per hour.
• Study more, better grade: Given the positive correlation (as study time increases, grade increases), students who study more tend to earn better grades.

Answer:

• 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.