Given a scatterplot showing a positive linear relationship between hours studied and exam scores, which statement is an inference that can be made by using the graph?

• A. All students who study less than $2$ hours will fail the exam.
• B. There is a negative correlation between hours studied and exam scores.
• C. Studying has no effect on exam performance.
• D. Students who study more hours tend to achieve higher exam scores.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand what a scatterplot represents. A scatterplot displays individual data points for two variables—in this case, hours studied (independent variable) and exam scores (dependent variable)—to visualize their relationship.
2. Step 2: Identify the type of relationship shown in the scatterplot. A positive linear relationship means that as the value of one variable increases, the other variable tends to increase as well.
3. Step 3: Recognize that correlation describes the direction and strength of a linear relationship between two variables. A positive correlation indicates that higher values of one variable are associated with higher values of the other.
4. Step 4: Evaluate the given statements against the scatterplot's positive linear trend. Statements claiming negative correlation or no effect contradict the observed positive relationship.
5. Step 5: Conclude that the appropriate inference from the scatterplot is that students who study more hours tend to achieve higher exam scores, reflecting the positive association between the two variables.