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
  • Enter Summary Data

Enter Raw Data

Paste data below from MS Excel or Notepad.
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

sˉx=σn

sˉx=17.00004
sˉx=8.5000
z=ˉxμ0sˉx
z=317.5310.00008.5000z=0.882353

μ0 : Hypothesized value
ˉx : Sample mean
n : Sample size
σ : Population standard deviation
sˉx : 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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