What is the null hypothesis in a one-sample t-test?

The null hypothesis states that the population mean equals the hypothesized value (H0: mu = mu0). The alternative hypothesis is that the mean is different (two-tailed), greater than, or less than that value depending on your chosen test direction.

How many data points do I need?

You need at least 2 values (so degrees of freedom >= 1). For reliable results the sample size is typically 5 or more, and the one-sample t-test assumes the population is approximately normally distributed or n >= 30.

How is the p-value computed here?

The p-value uses a numerical approximation of the Student t cumulative distribution function (CDF) with n-1 degrees of freedom. For two-tailed tests it is 2 * P(T > |t|); for one-tailed tests it is P(T > t) or P(T < t) depending on direction.

What does rejecting H0 mean?

Rejecting H0 means the sample evidence is strong enough (at your chosen alpha level) to conclude the population mean likely differs from the hypothesized value. It does not prove the alternative hypothesis is true — only that the data are inconsistent with H0.

What significance level should I use?

Alpha = 0.05 (5%) is the most common threshold in research and industry. Alpha = 0.01 is used when a stricter standard is required. Alpha = 0.10 is sometimes used in exploratory analysis.

Does this assume equal variances or normality?

The one-sample t-test assumes the data are drawn from a roughly normal distribution. It is robust to mild departures from normality, especially for n >= 30. No assumption about equal variances applies here since there is only one sample.

One Sample T-Test Calculator

Enter your sample data and a hypothesized mean to compute the t-statistic, degrees of freedom, p-value, and hypothesis test decision.

Sample Data & Parameters

Sample Values

Separate values with commas, spaces, or new lines.

Hypothesized Mean (μ₀)

Significance Level (α)

Test Direction

Two-tailed (H₁: μ ≠ μ₀) Left-tailed (H₁: μ < μ₀) Right-tailed (H₁: μ > μ₀)

Enter data and click Run T-Test to see results.

Summary

The one-sample t-test checks whether the mean of a single sample is statistically different from a known or hypothesized value. It uses the sample mean, sample standard deviation, and sample size to compute a t-statistic, then compares it against critical values (or a p-value) at your chosen significance level. This calculator handles all arithmetic client-side — no data ever leaves your browser.

How it works

Enter your data values separated by commas, spaces, or line breaks.
Set the hypothesized population mean (null hypothesis H0: mu = value).
Choose a significance level (alpha) and whether the test is two-tailed, left-tailed, or right-tailed.
The calculator computes the sample mean, standard deviation, and standard error.
The t-statistic is calculated as (sample mean - hypothesized mean) / standard error.
The p-value is derived from the t-distribution with n-1 degrees of freedom, and the result tells you whether to reject H0.

Use cases

Test whether a new drug changes a measurable biomarker from a known baseline.
Verify whether a manufacturing process produces parts at the specified target dimension.
Check if average student exam scores differ from a national standard.
Evaluate whether website load times meet a defined performance target.
Validate survey responses against a hypothesized population mean.
Quality control: determine if a batch mean is within tolerance.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu