Hypothesis Testing Calculator
Perform statistical hypothesis tests including z-tests and t-tests with comprehensive analysis and interpretation.
Test Parameters
Test Type
Sample Mean (x̄)
Population Mean (μ)
Sample Std Dev (s)
Sample Size (n)
Significance Level (α)
Hypothesis Type
How to Use
Step-by-Step Guide
- 1.Select test type (Z-test for large samples, T-test for small samples)
- 2.Enter sample statistics (mean, standard deviation, size)
- 3.Set population mean (hypothesized value)
- 4.Choose significance level and hypothesis type
- 5.Review test statistic, p-value, and conclusion
Test Selection Guide
- Z-Test: Large samples (n >= 30) or known population standard deviation
- T-Test: Small samples (n < 30) or unknown population standard deviation
- Two-tailed: Testing for difference (≠)
- One-tailed: Testing for direction (> or <)
Test Formulas
Z-Test Statistic
z = (x̄ - μ) / (σ/√n)
Standardized difference between sample and population means
T-Test Statistic
t = (x̄ - μ) / (s/√n)
Uses sample standard deviation for small samples
Effect Size (Cohen's d)
d = (x̄ - μ) / s
Standardized measure of effect magnitude
Statistical Power
Power = 1 - β
Probability of detecting true effect
Common Applications
Medical Research
Clinical trials, drug efficacy studies, and treatment comparisons with statistical significance testing.
Quality Control
Manufacturing process validation, product testing, and quality assurance with hypothesis testing.
Business Analytics
A/B testing, market research, and business decision making with statistical evidence.
Frequently Asked Questions
What is hypothesis testing?
Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data, helping determine if observed effects are statistically significant.
What does p-value represent?
The p-value represents the probability of observing results as extreme as, or more extreme than, the observed results if the null hypothesis is true.
When should I use one-tailed vs two-tailed test?
Use one-tailed tests when you have a specific direction hypothesis. Use two-tailed tests when you're testing for any difference without specifying direction.
What is statistical power?
Statistical power is the probability of correctly rejecting a false null hypothesis. Higher power means better ability to detect true effects.
Related Calculators
Key Takeaways
Statistical Evidence
Hypothesis testing provides objective evidence to support or reject claims about population parameters based on sample data.
Decision Making
Use p-values and effect sizes to make informed decisions with quantified uncertainty and statistical significance.
Research Validity
Proper hypothesis testing is essential for valid research conclusions and reproducible scientific findings.
Practical Application
Apply hypothesis testing across medicine, business, engineering, and science for data-driven decision making.