Example 1
\(\text{Test if class average (85) differs from school average (80)}\)
Calculatrice de test t
Effectuer des tests d'hypothèse statistiques avec des tests t à un échantillon, deux échantillons et appariés
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
T-Test
The t-test is used to determine if there is a significant difference between means. It is commonly used when sample sizes are small and the population standard deviation is unknown.
- One-Sample t-Test: Tests if a sample mean differs from a known population mean
- Two-Sample t-Test: Tests if two independent samples have different means
- Paired t-Test: Tests if matched pairs (before/after) have different means
- p-value: Probability of obtaining results at least as extreme, assuming null hypothesis is true
- Significance Level (α): Threshold for rejecting null hypothesis (commonly 0.05)
If p-value < α, we reject the null hypothesis and conclude there is a significant difference. If p-value ≥ α, we fail to reject the null hypothesis (insufficient evidence of difference).
\(t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}, t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}, t = \frac{\bar{d}}{s_d/\sqrt{n}}\)
Worked Examples
Example 2
\(\text{Compare two teaching methods to see which produces better test scores}\)