QM210
The Small Sample Trap
When does your sample size critically affect which test to use and what conclusion to draw? Navigate 10 hypothesis testing scenarios and find out.
How It Works
- Each round presents a hypothesis testing scenario with business context
- Answer three questions in sequence: test type, critical value, and decision
- All three correct earns 10 points; two correct earns 6; one correct earns 3; zero earns 0
- After each round, see the full hypothesis test laid out step by step
- Score out of 100 — earn a letter grade at the end
Game Over!
You scored out of 100
Round-by-Round Summary
Key Insight: Why Sample Size Matters
Small samples force you to use the T-distribution, which has heavier tails than the Z-distribution. This means critical values are larger, making it harder to reject H0. As n grows, the T-distribution converges toward Z — but when σ is unknown, you still technically use T. The "trap" is assuming a large sample automatically means Z-test, or that a small sample automatically means you will fail to reject. The test choice depends on whether σ is known, and the critical value depends on degrees of freedom (n − 1) and the significance level.