Determine whether two groups differ significantly. Work through four real-world scenarios (one-sample, independent, paired, and proportion tests) with interactive data, assumption checks, and visual results.
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Scenario
A factory targets 500 units/hour. We sampled 30 hours of production. Is the true mean significantly different from the target?
H₀ (Null)
μ = 500
H₁ (Alternative)
μ ≠ 500
Factory data (n=30, x̄=504.33)
| Obs | Units/hr |
|---|---|
| 1 | 498 |
| 2 | 512 |
| 3 | 505 |
| 4 | 497 |
| 5 | 508 |
| 6 | 515 |
| 7 | 502 |
| 8 | 493 |
| 9 | 510 |
| 10 | 506 |
| …and 20 more observations | |
Assumption Check
Normality check: factory output data
Click "Run Assumption Check" to verify normality before running the test.
Formula
t = (x̄ − μ₀) / (s / √n)
degrees of freedom = n − 1 = 29
Quick Reference: When to Use Which Test
One-Sample t
Compare one group's mean to a known/target value
e.g. Is avg output = 500?
Independent t
Compare means of two separate, unrelated groups
e.g. Campaign A vs. B?
Paired t
Same subjects measured twice (before/after)
e.g. Training effect?
Proportion z
Compare two proportions (binary outcomes)
e.g. Conversion rate A vs. B?