Hypothesis Testing Calculator
Evaluate a one-sample z-test by providing sample summary statistics, selecting a tail, and setting a significance level.
Standard error: 0.7500
Z-statistic: 3.2000
p-value: 0.001374
Decision: Reject the null hypothesis.
How to Use This Calculator
- Define the null hypothesis mean and provide sample statistics.
- Select a tail direction matching your alternative hypothesis.
- Review the z-statistic, p-value, and decision at your chosen α.
- Combine results with confidence intervals or practical significance as needed.
Formula
Z = (x̄ − μ₀) / (σ / √n)
Two-tailed p = 2 × (1 − Φ(|Z|))
Right-tailed p = 1 − Φ(Z), Left-tailed p = Φ(Z)
Φ denotes the standard normal cumulative distribution function. This calculator assumes a known population standard deviation.
Full Description
Hypothesis testing compares observed sample evidence against a null hypothesis. With known population standard deviation, the z-test provides exact p-values from the normal distribution. Choose the tail based on your alternative hypothesis to focus on increases, decreases, or any change.
Frequently Asked Questions
When should I use a t-test instead?
If the population standard deviation is unknown or sample size is small, use a t-test with sample standard deviation.
Can I run a two-sample test here?
No. This calculator focuses on one-sample z-tests. Use dedicated two-sample or proportion test tools for comparisons.
What if my p-value equals α?
Conventionally, you reject H₀ when p < α. If p equals α exactly, the decision is borderline; report the value and context.
How do I interpret the decision?
Rejecting H₀ implies evidence supports the alternative hypothesis. Failing to reject means insufficient evidence—not proof that H₀ is true.