Hypothesis Testing Tool
How to Use This Tool
  1. Select the appropriate test type (Z-test or T-test)
  2. Enter the hypothesized population mean (μ₀)
  3. Enter your sample mean (x̄)
  4. Enter the standard deviation (population σ for Z-test, sample s for T-test)
  5. Enter your sample size (n)
  6. Select your significance level (α) or enter a custom value
  7. Choose your alternative hypothesis type
  8. Click "Calculate" to see results
When to use Z-test vs T-test
  • Z-test: When population standard deviation is known OR sample size is large (n > 30)
  • T-test: When population standard deviation is unknown AND sample size is small (n ≤ 30)
Frequently Asked Questions

A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population parameter. It determines whether there's enough evidence in a sample to support a particular claim about the population.

Use a t-test when:
  • The population standard deviation is unknown
  • The sample size is small (typically n ≤ 30)
  • The population is normally distributed or approximately normal
Use a z-test when:
  • The population standard deviation is known
  • OR the sample size is large (typically n > 30)

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
  • If p-value ≤ α: Reject the null hypothesis
  • If p-value > α: Fail to reject the null hypothesis
A smaller p-value indicates stronger evidence against the null hypothesis.

  • Two-tailed (μ ≠ μ₀): Tests for any difference, without specifying direction
  • Left-tailed (μ < μ₀): Tests for a decrease or lower value
  • Right-tailed (μ > μ₀): Tests for an increase or higher value
Hypothesis Test Results
Test Statistic
-
Z-score
P-value
-
Significance
Conclusion
-
At α = 0.05
Test Details
Hypothesis

Null Hypothesis (H₀): μ = 50

Alternative Hypothesis (H₁): μ ≠ 50

Test Information

Test Type: Z-test

Significance Level (α): 0.05

Degrees of Freedom: -

Critical Values

-

Calculation
Formula Used
z = (x̄ - μ₀) / (σ/√n)
Calculation Steps

Enter values and click "Calculate" to see the calculation steps.

Visualization
The graph shows the distribution, test statistic, and critical region(s)

Hypothesis Testing Calculator

Perform Z-tests and T-tests to evaluate hypotheses about population means

Quick Start

Pre-filled example is ready to go. Just click "Calculate" to see results.

How to Use
  • Select test type (Z or T)
  • Enter your data values
  • Choose significance level
  • Select alternative hypothesis
  • Click "Calculate"
About This Tool

This calculator helps you perform hypothesis tests about population means using either Z-tests (when population standard deviation is known or sample size is large) or T-tests (when population standard deviation is unknown and sample size is small).

Common uses: Academic research, business analytics, quality control, medical studies.