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:

Step1: Analyze Linear Association

A linear association means the relationship between two variables (study hours and test grades here) can be approximated by a straight line. Since for every 30 minutes (a constant time interval) studied, the grade increases by 8 points (a constant rate), the relationship is linear. So "The data set would have a linear association" is true, and the nonlinear one is false.

Step2: Analyze Correlation Direction

Positive correlation means as one variable (study hours) increases, the other (test grades) also increases. Here, more study hours lead to higher grades, so it's a positive correlation. Thus "The data set would have a positive correlation" is true, and negative is false.

Step3: Analyze Points per Hour

30 minutes is 0.5 hours. For 0.5 hours, grade increases by 8 points. So per hour, it's \( \frac{8}{0.5}=16 \) points. So "Every student earns 16 more points for each additional hour they study" is true (assuming the average holds, as the problem says "on average").

Step4: Analyze Study - Grade Trend

Since more study (higher hours) leads to better grades (higher scores), "Students that study more tend to earn better grades on the test" is true.

Answer:

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.