The hypothesis testing calculator walks you through null vs alternative hypothesis testing step by step. Select the test type, enter your sample statistics, and get the test statistic, p-value, and decision with interpretation.
Hypothesis Test Setup
Interpretation
Step-by-Step
How to Use the Hypothesis Testing Calculator
Hypothesis testing is how statisticians decide whether data supports a claim. The null hypothesis H₀ is the default assumption; you're trying to gather evidence against it.
Step 1: Choose Test Type
Z-test (one-sample): use when population standard deviation σ is known. T-test: use when σ is unknown and you're using the sample standard deviation s. Proportion test: use when testing a proportion (e.g., "is the true proportion different from 0.5?").
Step 2: Set Up Hypotheses
H₀ is the null (e.g., μ = 50). H₁ is the alternative. Two-tailed: μ ≠ 50. Right-tailed: μ > 50 (one-directional claim). Left-tailed: μ < 50. Use two-tailed unless you have a specific direction in mind before seeing data.
Example: Z-test
A machine claims to fill bags at μ₀ = 50g. You sample n=30 bags and find x̄ = 52g with σ = 10g. Z = (52-50)/(10/√30) = 2/1.826 = 1.095. Two-tailed p-value = 2×(1-Φ(1.095)) ≈ 0.273. p > 0.05, fail to reject H₀.
FAQ
What is hypothesis testing?
Hypothesis testing is a statistical procedure to decide whether evidence supports a specific claim (alternative hypothesis H₁) against a default assumption (null hypothesis H₀). You calculate a test statistic, find the p-value, and reject H₀ if p < α (usually 0.05).
What is a p-value?
The p-value is the probability of observing results at least as extreme as your data, assuming H₀ is true. A small p-value (< 0.05) means your data is unlikely if H₀ were true, so you reject H₀. A large p-value means insufficient evidence to reject H₀.
What is the difference between one-tailed and two-tailed tests?
A two-tailed test checks for any difference (H₁: μ ≠ μ₀). A one-tailed test checks for a specific direction (H₁: μ > μ₀ or μ < μ₀). Two-tailed tests are more conservative; use one-tailed only when you have a strong prior reason to expect a specific direction.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
What is the significance level α?
The significance level α (commonly 0.05 or 5%) is the threshold for rejecting H₀. It equals the probability of a Type I error (false positive — rejecting H₀ when it's true). Lower α (0.01) is more stringent; higher α (0.10) is more lenient.