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 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.
Learn more from an authoritative source:
WikipediaChi-Square Test Calculator
Calculate the chi-square (χ²) statistic for goodness-of-fit or independence tests. Enter observed and expected frequencies to get χ² and p-value.
Confidence Interval Calculator
Calculate the confidence interval for a population mean from sample data. Supports 90%, 95%, and 99% confidence levels.
Sample Size Calculator
Calculate the minimum sample size required for a statistically valid survey or experiment. Specify confidence level, margin of error, and population size.
Percentile Calculator
Find the percentile rank of a score in a dataset, or find the value at a given percentile. Enter up to 10 data values.
Poisson Distribution Calculator
Calculate Poisson probabilities for rare events. Find P(X = k), P(X ≤ k), and P(X > k) given an average rate λ.
Variance Calculator
Calculate variance and standard deviation for a set of numbers. Choose population variance (σ²) or sample variance (s²).
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →