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

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

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