Null Hypothesis Calculator: Quick & Accurate Statistical Analysis

This null hypothesis calculator helps you determine the statistical significance of your data set by calculating the probability of observing your results under the null hypothesis.

How to Use the Null Hypothesis Calculator

To use the null hypothesis calculator, enter the sample mean, hypothesized population mean, sample standard deviation, and sample size into their respective fields. Then press the “Calculate” button, and the calculator will display the test statistic used to determine if the null hypothesis can be rejected.

How It Calculates the Results

The calculator computes the test statistic by using the formula:

( z = frac{(bar{x} – mu_0)}{(sigma / sqrt{n})} )


  • ( bar{x} ) is the sample mean
  • ( mu_0 ) is the hypothesized population mean
  • ( sigma ) is the standard deviation of the sample
  • ( n ) is the sample size

This test statistic is then used in statistical hypothesis testing to determine if there is enough evidence to reject the null hypothesis at a certain significance level.


The calculator presumes that the sample data are representative of the population and that the sampling distribution of the mean is approximately normally distributed, especially as the sample size becomes large (Central Limit Theorem). It also assumes that an accurate standard deviation is known and that the sample is drawn randomly.

Be aware that for smaller sample sizes, particularly under 30, this calculator may not provide accurate results because the central limit theorem applies better to larger samples. For small samples, other techniques or adjustments (like t-tests) typically need to be used.

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