Mathematics Standard • Year 12 • Module 5 • Lesson 4
Causation and Correlation, Apply
Contextual Problem Set 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 council finds that suburbs with more public pools also have more hospital visits for sunburn. Identify a plausible confounder and explain how it could produce this association. 3 marks
2. Use the idea
Researchers randomly assign consenting volunteers to two exercise programmes, keep duration equal, and compare a measured fitness outcome after eight weeks. Explain why this design gives stronger evidence of a causal effect than a survey, and name one remaining limitation. 3 marks
3. Check your reasoning
A news headline says “More firefighters at a fire is associated with more damage, so firefighters cause damage.” Explain the direction-of-causation problem. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
Hotter/sunnier weather or a larger population could confound the association. More residents and more sunny days can increase pool use and the number of sunburn-related visits without pools causing sunburn by themselves.
2. Use the idea (3 marks)
Random assignment helps balance confounders between groups, so a difference in outcomes is more plausibly due to the programme. A limitation is that volunteers may not represent the wider population; adherence or measurement quality also matters.
3. Check your reasoning (2 marks)
Larger, more severe fires require more firefighters and also cause more damage. Fire severity can drive both variables; the observed association does not show firefighters caused the damage.