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.
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)
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=σ√n
sˉx=17.0000√4
sˉx=8.5000
z=ˉx−μ0sˉx
z=317.5−310.00008.5000z=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
Share Share Tweet