Simple Hypothesis Testing

Perform one-sample and two-sample hypothesis tests with confidence intervals and effect sizes

Test Configuration
Compare a sample mean to a known population mean when population standard deviation is known
Determines the direction of the test
Probability of Type I error (typically 0.05)
Confidence level for the interval estimate (typically 0.95)
Test Parameters
Hypothesized population mean
Observed sample mean
Number of observations in the sample
Population standard deviation (must be known)
Sample standard deviation (used when σ is unknown)
Hypothesized population proportion
Number of successes in the sample
Number of trials in the sample
i Rule of thumb for z-approximation: n·p̂ and n·(1−p̂) ≥ 10.
Mean of the first sample
Mean of the second sample
Standard deviation of the first sample
Standard deviation of the second sample
Number of observations in the first sample
Number of observations in the second sample
i H₀: μ₁ − μ₂ = 0 (Welch’s t uses unequal variances by default).
Number of successes in the first sample
Number of trials in the first sample
Number of successes in the second sample
Number of trials in the second sample
i Approximation rule: nᵢ·p̂ᵢ and nᵢ·(1−p̂ᵢ) ≥ 10 for i=1,2.
Enter your test parameters and click "Run Test" to see results.

Notes: z critical values use a high-accuracy inverse-normal approximation. t-tests use numerical integration for the Student's t CDF and a robust inverse-t via bisection. Two-proportion test uses pooled SE for the hypothesis test and unpooled SE for the CI. Decisions are based on p-values (critical values shown for z-tests only).

For more information on hypothesis testing, visit Wikipedia or consult a statistics textbook.