The TIMMS Exam The Trends in International Mathematics and Science (TIMMS) is a mathematics and science achievement exam given internationally. On each exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in TIMMS, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.79. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean.

Verified step by step guidance

1. Step 1: Understand what the correlation coefficient represents. The correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate a strong linear relationship, and values near 0 indicate little to no linear relationship.
2. Step 2: Identify the given correlation value. Here, the correlation between the percentage of items answered (student task persistence) and mean exam score is \(r = 0.79\).
3. Step 3: Interpret the magnitude and sign of the correlation. Since \$0.79$ is a positive value close to 1, it suggests a strong positive linear relationship between task persistence and achievement score. This means that as task persistence increases, the achievement score tends to increase as well.
4. Step 4: Consider the context and limitations. While a correlation of 0.79 indicates a strong association, it does not imply causation. Other factors might influence the relationship, and further analysis would be needed to establish cause and effect.
5. Step 5: Formulate a clear explanatory sentence. For example, you might say: "The correlation of 0.79 suggests that there is a strong positive linear relationship between student task persistence and achievement score on the TIMMS exam, indicating that students who persist more tend to have higher scores."

Key Concepts

Correlation Coefficient

The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1. A value of 0.79 indicates a strong positive linear association, meaning as one variable increases, the other tends to increase as well.

Linear Relationship

A linear relationship implies that changes in one variable are associated with proportional changes in another, forming a straight-line pattern when graphed. A high correlation suggests such a relationship, but it does not prove causation or rule out other types of relationships.

Interpretation of Statistical Results

Interpreting statistical results involves understanding what the numbers imply about real-world phenomena. Here, a correlation of 0.79 suggests a strong link between task persistence and achievement scores, but it should be explained carefully, noting that correlation does not imply causation.