One Sample Z-Test Calculator

One Sample z-test is used to check whether the population mean is statistically significantly different from a hypothesized value. It is used when the population standard deviation is known.

In the calculation below you have two options - either to enter raw data or you can enter summary information which is required to calculate one sample z-test.

Under raw data tab, you can enter values separated by comma, space, tab spaces or new line.

Enter Raw Data

Paste data below from MS Excel or Notepad.

Enter Summary Data


Step by Step Calculation

$$ s_{\bar{x}} = \frac{\sigma}{\sqrt{n}} $$

\(\mu_{0}\) : Hypothesized value
\(\bar{x}\) : Sample mean
\(n\) : Sample size
\(\sigma_{}\) : Population standard deviation
\(s_{\bar{x}}\) : Estimated standard error of the mean

Assumptions of One Sample Z-Test
  • Data must be normally distributed
  • One-sample z-test assumes that the standard deviation of the population is already known.
  • Sample must be picked randomly from population
  • Data must be continuous
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