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SAT Math Practice
Evaluating Statistical Claims

Distinguish correlation from causation and reason about limitations of observational studies.

18 original evaluating statistical claims questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.

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Sample question 1 · hard

A study finds a strong positive correlation between number of firefighters at a fire and size of the fire. Which choice best describes a limitation of concluding that number of firefighters at a fire directly causes size of the fire?

The correlation must be a coincidence and should be ignored entirely, whatever its strength and whatever the size of the study.
✓ Correlation alone does not establish causation; a third factor could explain why larger fires both require and are fought by more firefighters.
The study's sample size is automatically too small to be meaningful, since correlations of this kind need very large samples.
A strong correlation is sufficient by itself to prove that number of firefighters at a fire causes size of the fire, provided the study is large enough.

Correlation does not by itself establish causation; a confounding variable could explain the relationship (here, that larger fires both require and are fought by more firefighters), which is why the study alone can't prove direct causation.

Sample question 2 · hard

A study finds a strong positive correlation between hours spent studying and exam scores. Which choice best describes a limitation of concluding that hours spent studying directly causes exam scores?

✓ Correlation alone does not establish causation; a third factor could explain why study habits also correlate with other factors like sleep.
A strong correlation is sufficient by itself to prove that hours spent studying causes exam scores, provided the study is large enough.
The study's sample size is automatically too small to be meaningful, since correlations of this kind need very large samples.
The correlation must be a coincidence and should be ignored entirely, whatever its strength and whatever the size of the study.

Correlation does not by itself establish causation; a confounding variable could explain the relationship (here, that study habits also correlate with other factors like sleep), which is why the study alone can't prove direct causation.

Sample question 3 · hard

A study finds a strong positive correlation between household plant ownership and self-reported happiness. Which choice best describes a limitation of concluding that household plant ownership directly causes self-reported happiness?

A strong correlation is sufficient by itself to prove that household plant ownership causes self-reported happiness, provided the study is large enough.
The correlation must be a coincidence and should be ignored entirely, whatever its strength and whatever the size of the study.
The study's sample size is automatically too small to be meaningful, since correlations of this kind need very large samples.
✓ Correlation alone does not establish causation; a third factor could explain why people with more free time or income may have both.

Correlation does not by itself establish causation; a confounding variable could explain the relationship (here, that people with more free time or income may have both), which is why the study alone can't prove direct causation.

Sample question 4 · hard

A study finds a strong positive correlation between coffee consumption and reported alertness. Which choice best describes a limitation of concluding that coffee consumption directly causes reported alertness?

The study's sample size is automatically too small to be meaningful, since correlations of this kind need very large samples.
The correlation must be a coincidence and should be ignored entirely, whatever its strength and whatever the size of the study.
✓ Correlation alone does not establish causation; a third factor could explain why people who are already busier tend to drink more coffee.
A strong correlation is sufficient by itself to prove that coffee consumption causes reported alertness, provided the study is large enough.

Correlation does not by itself establish causation; a confounding variable could explain the relationship (here, that people who are already busier tend to drink more coffee), which is why the study alone can't prove direct causation.

Sample question 5 · hard

A study finds a strong positive correlation between time spent on social media and reported anxiety levels. Which choice best describes a limitation of concluding that time spent on social media directly causes reported anxiety levels?

The correlation must be a coincidence and should be ignored entirely, whatever its strength and whatever the size of the study.
✓ Correlation alone does not establish causation; a third factor could explain why people already prone to anxiety may use social media differently.
The study's sample size is automatically too small to be meaningful, since correlations of this kind need very large samples.
A strong correlation is sufficient by itself to prove that time spent on social media causes reported anxiety levels, provided the study is large enough.

Correlation does not by itself establish causation; a confounding variable could explain the relationship (here, that people already prone to anxiety may use social media differently), which is why the study alone can't prove direct causation.

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