T-Test Calculator
Perform a one-sample t-test to determine if a sample mean is significantly different from a known population mean. Returns t-statistic and p-value.
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How to use this calculator
The t-statistic measures how many standard errors the sample mean is from the hypothesised population mean. Large |t| → small p-value → reject null hypothesis.
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Enter the sample mean, the hypothesised population mean (μ₀), sample standard deviation, and sample size.
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Set the significance level (α) — commonly 0.05.
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If p < α, reject the null hypothesis: the sample mean is significantly different from μ₀.
Frequently asked questions
What is the null hypothesis for a one-sample t-test?
H₀ states that the sample comes from a population with mean μ₀. If the t-statistic is extreme enough (p < α), we reject this claim.
What does p-value < 0.05 mean?
There is less than a 5% probability of observing a test statistic as extreme as yours if the null hypothesis were true. By convention, this is considered statistically significant.
When should I use a t-test vs z-test?
Use a t-test when the population standard deviation is unknown (the usual case). Use a z-test only when σ is known and n is large (>30).
T-Test Calculator — Hypothesis Testing & P-Value
How to use the t-test
Use this t-test to perform a one-sample t-test to determine if a sample mean is significantly different from a known population mean. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the t-test works
The t-test calculator uses standard formulas used in statistical analysis, data science, and research. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
How the one-sample t-test works
The one-sample t-test compares a sample mean against a known or hypothesised population mean. The t-statistic measures the size of the difference relative to the variation in the sample. The resulting p-value tells you how likely that difference is due to chance.
Interpreting t-test results
A small p-value (< 0.05) indicates the sample mean is statistically significantly different from the hypothesised mean. A large p-value means the data is consistent with the null hypothesis — not that they are definitely equal. Always report confidence intervals alongside p-values for a fuller picture.
T-test: how it works
Statistical analysis underpins data science, research, quality control, and business intelligence. This tool applies established textbook formulas to your dataset and returns results instantly, eliminating manual calculation errors.
Who uses this tool?
Researchers, students, analysts, and business professionals use it to understand datasets quickly. Whether you are summarising survey responses or checking experiment results, this tool delivers the key figures instantly.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →