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The z-test is a hypothesis test used to test the mean against a specified value. The z-test is used where the standard deviation is known or the sample is large (greater than about 30). The population must also conform to a normal distribution. The hypothesis is:
H0 the population mean equals a specified value
H1 the popular mean is [equal to/less than/greater than] a specified value
The test is:
where:
 |
sample mean |
| μ 0 |
specified value |
| s |
sample standard deviation |
| n |
sample size |
The p-value can be obtained from Excel using the function:
one-tail test: = 1 - NORMSDIST(Z0)
two-tail test: = (1 - NORMSDIST(Z0))/2
Alternatively the critical values of the z statistic can be found from tables. For a one sided test:
| α |
0.10
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0.05
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0.025
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0.01
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| Zα |
1.28
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1.64
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1.96
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2.33
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For samples less than 30 use the t-test.
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