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Statistics

One Sample T-Test Calculator

Test a sample mean against a hypothesized population mean, with a t statistic and p-value.

Data stays on this deviceConvention explained below
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Data explorer

Check the dataset and sample convention before interpreting results.

See the method

Add your observations

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Your statistical summary

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter sample a, hypothesized mean, alternative hypothesis, significance level.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

t = (sample mean − hypothesized mean)/(sample SD/√n); df = n − 1.

A WORKED EXAMPLE

Using sample a = 8, 10, 9, 12, 11, hypothesized mean = 8, alternative hypothesis = two, significance level = 0.05, the result is 0.0474206556 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Independent observations. For small samples, the population should be approximately normal without influential outliers. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Reference: NIST: statistical methods handbook

Common questions

What does the hypothesized mean represent?

It is the population value specified by the null hypothesis, such as an established process target. It is not an additional sample observation.

Can I enter a single observation?

No. At least two observations and nonzero sample variation are required to estimate the standard error. More observations do not correct biased sampling.

Methodology maintained by ClarityKit. How these tools are built and checked.