Understanding a Z Hypothesis Test
A z hypothesis test compares a sample result with a claimed population value. It is used when the population standard deviation is known, or when the sample is large enough for a normal approximation. This calculator supports one sample mean tests and one sample proportion tests.
Why the Test Direction Matters
The tool asks for the null value, sample evidence, sample size, alpha, and test direction. It then computes the standard error, z statistic, p value, critical value, confidence interval, and decision. These values help you decide whether the sample gives strong evidence against the null hypothesis.
A left tailed test checks whether the population value may be lower. A right tailed test checks whether it may be higher. A two tailed test checks whether it may be different in either direction. Choosing the correct direction matters before data is reviewed.
Mean and Proportion Options
For means, the calculator uses the known population standard deviation. For proportions, it uses the null proportion in the test standard error. The confidence interval uses the observed estimate, so it describes likely values for the population parameter.
Power and Planning
Advanced fields add planning support. You can enter an alternative value and target power. The calculator then estimates test power and an approximate required sample size. These estimates are useful for study planning, audits, surveys, quality checks, and A/B testing.
Reading the Decision
The decision should not be read alone. A tiny p value shows strong statistical evidence, but it does not prove practical importance. Always review the estimate, confidence interval, sample size, and context. Also check that observations are independent and sampling is suitable.
Good Practice
Use the example table to compare common cases. Export results when you need records for reports or classroom work. The CSV file is useful for spreadsheets. The PDF report is useful for sharing a quick summary.
For best results, keep units consistent and enter positive sample sizes. In mean mode, standard deviation must be greater than zero. In proportion mode, counts must match the chosen sample size. If your sample is small, or data is highly skewed, a different test may fit better. The result is a guide for evidence. It is not a substitute for research design, domain knowledge, or professional statistical review. Document assumptions when results support business or scientific choices.