Mathematics Standard • Year 12 • Module 5 • Lesson 4
Causation and Correlation, Master
Mastery Challenge for Causation and Correlation. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A dataset from several towns shows a positive association between ice-cream sales and swimming incidents. Give a plausible confounder, draw a simple causal explanation in words, and state a responsible conclusion. 3 marks
2. Use the idea
Design a study to test whether a new revision app improves quiz scores. State the explanatory variable, response variable and one feature that strengthens causal inference. 3 marks
3. Check your reasoning
A controlled study reports a higher average score for the app group, but only 12 students volunteered. Give a cautious conclusion and two limitations. 3 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
Temperature is a plausible confounder. Warmer weather can increase ice-cream sales and swimming activity, which may increase incidents. Conclude only that the variables are associated in the data; the association does not show ice-cream sales cause incidents.
2. Use the idea (3 marks)
Explanatory variable: app access/use (new app versus comparison condition). Response variable: quiz score measured with the same assessment. Randomly assign comparable students to the app and comparison groups, use equal study time, and keep assessment conditions consistent.
3. Check your reasoning (3 marks)
The study provides some evidence that app access may improve scores for these volunteers under the study conditions, but it does not prove the effect for all students. The sample is small and self-selected; chance variation, adherence or other design limitations may affect the result.