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. Sample X Population Standard Deviation ($ \sigma_{} $) Hypothesized population mean ($ \mu_{0} $)

Enter Summary Data

Sample mean ($ \bar{x} $) Population Standard Deviation (s) Sample Size (n) Hypothesized population mean ($ \mu_{0} $)

Solution

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