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 z = 0.882353
p-value (One-tailed) = 0.188793
p-value (Two-tailed) = 0.377586
Population mean is not significantly different from a hypothesized value at 5% significance level(One-tailed)
Population mean is not significantly different from a hypothesized value at 5% significance level(Two-tailed)

Step by Step Calculation

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

$s_{\bar{x}} =\frac{17.0000}{\sqrt{4}}$
$s_{\bar{x}} =8.5000$
$z = \frac{\bar{x}-\mu{}_{0}}{s_{\bar{x}}}$
$z = \frac{317.5-310.0000}{8.5000}$ $z = 0.882353$

$\mu_{0}$ : 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