Parents, caregivers and teachers: Explore this page for at-home or distance learning activities.

# Educational Attainment and Marriage Age - Testing a Correlation Coefficient's Significance

### Activity Description Students will develop, justify, and evaluate conjectures about the relationship between two quantitative variables over time in the United States: the median age (in years) when women first marry and the percentage of women aged 25–34 with a bachelor’s degree or higher. Students will write a regression equation for the data, interpret in context the linear model’s slope and y-intercept, and find the correlation coefficient (r), assessing the strength of the linear relationship and whether a significant relationship exists between the variables. Students will then summarize their conclusions and consider whether correlation implies causation.

11-12

60 minutes

### Learning Objectives

• Students will be able to predict and test the significance of the relationship between two quantitative variables.
• Students will be able to write a line of best fit and interpret the slope and y-intercept in the context of the data.
• Students will be able to assess the strength and direction of a linear association based on a correlation coefficient.
• Students will be able to compute a correlation coefficient and distinguish between correlation and causation.

### Materials Required

• The student version of this activity, 9 pages
• Graphing calculators (preferably TI-84 Plus) or graphing technology

### Activity Items

The following items are part of this activity. The items, their data sources, and any relevant instructions for viewing the source data online appear at the end of this teacher version.

• Data Table
• Optional Instructions for Calculating r on a TI-84 Plus
• Critical Values of r at a 5 Percent Significance Level

## Teacher Notes

#### Blooms Taxonomy

Evaluating Students will evaluate data by making and testing predictions using inference.

High School Math

#### Topics

• Correlation vs. causation
• Hypothesis testing
• Line of best fit
• Linear regression

#### Skills Taught

• Calculating and interpreting correlation coefficients
• Distinguishing between correlation and causation
• Testing the significance of a linear relationship
• Writing a regression equation that best models the data