What is hypothesis testing?

Hypothesis testing is a statistical method to make decisions about populations based on sample data. It evaluates whether observed results are statistically significant.

What are null and alternative hypotheses?

The null hypothesis (H₀) states no effect or difference exists. The alternative hypothesis (H₁) claims an effect exists. We test whether to reject H₀.

The p-value is the probability of observing results at least as extreme as the sample, assuming H₀ is true. Small p-values provide evidence against H₀.

What is significance level (α)?

Alpha is the threshold for rejection, commonly 0.05 or 0.01. If p-value < α, reject H₀. Alpha represents acceptable Type I error probability.

When do I use z-test vs t-test?

Use z-test when population σ is known or n > 30. Use t-test when using sample standard deviation, especially for n < 30.

What's a Type I vs Type II error?

Type I (α): Rejecting H₀ when it's true (false positive). Type II (β): Failing to reject H₀ when it's false (false negative).

Hypothesis Testing Calculator

Q: When do I use z-test vs t-test?

Use z-test when population σ is known or n > 30. Use t-test when using sample standard deviation, especially for n < 30.

Q: What's a Type I vs Type II error?

Type I (α): Rejecting H₀ when it's true (false positive). Type II (β): Failing to reject H₀ when it's false (false negative).

Perform Z-tests, T-tests, proportion tests, and chi-square tests with step-by-step solutions

Test Parameters

Test Type

Test Direction

Significance Level (α)

Sample Mean (x̄)

Population Mean (μ₀)

Pop. Std Dev (σ)

Sample Size (n)

Results

Enter test parameters and click "Perform Test" to see results

Understanding Hypothesis Testing

When to Use Each Test

Z-Test: Population σ known, n ≥ 30
T-Test: Population σ unknown, uses sample s
Proportion: Testing population proportions
Chi-Square: Testing categorical data frequencies

Key Concepts

H₀: Null hypothesis (status quo)
H₁: Alternative hypothesis (claim)
α: Significance level (Type I error rate)
p-value: Probability of results if H₀ is true

Related Calculators

Normal CDF Inverse Normal Frequency Distribution

About Hypothesis Testing Calculator - Statistical Tests

Perform statistical hypothesis tests including z-tests, t-tests, and chi-square tests. Calculate p-values and make data-driven decisions.

Our **Hypothesis Testing Calculator** helps you conduct rigorous statistical tests to make evidence-based decisions. Perform one-sample and two-sample tests for means and proportions. For finding critical values, use our Inverse Normal Calculator.

Hypothesis testing is the foundation of statistical inference. This calculator guides you through formulating null and alternative hypotheses, calculating test statistics, and interpreting p-values.

Whether you're a student learning statistics, a researcher analyzing data, or a business professional making decisions, this tool provides step-by-step solutions with clear interpretations.

Key Features

Z-test for proportions

T-test for means

Chi-square tests

P-value calculation

Critical value lookup

Two-tailed and one-tailed tests

Why Use This Tool?

Make evidence-based decisions

Understand statistical significance

Learn hypothesis testing

Research applications

Quality control analysis

Common Use Cases

Research: Testing scientific hypotheses.

Business: A/B testing and marketing analysis.

Quality Control: Process improvement verification.

Medicine: Clinical trial analysis.

How to Use

Select test type (z, t, chi-square)

Enter sample statistics

Set significance level (α)

Choose one or two-tailed

View results and decision