Hypothesis Test

z- and t-tests with p-value and rejection region

z = (x̄ − μ₀)/(σ/√n) = (52 − 50)/(10/√100)

Decision

Reject H₀

Statistically significant at α = 0.05: the evidence favors the alternative.

Hypotheses

H₀: μ = 50

H₁: μ ≠ 50

Test statistic (z)

p-value

0.0455

Critical value

±1.96

Sample mean (x̄)

Standard error

Rejection region

Reject H₀ if |z| > 1.96

Distribution

Standard normal (z)

p = 0.0455 vs α = 0.05

About this calculator

The Hypothesis Test Calculator runs a one-sample z-test or t-test for a mean, or a z-test for a proportion, with a two-sided or one-tailed alternative. It reports the test statistic, the exact p-value, the critical value and rejection region, the standard error, and the reject / fail-to-reject decision at your chosen significance level α. A shaded density curve shows where the statistic falls relative to the rejection region, making the decision easy to see. Useful for statistics coursework, A/B testing, and quality control.