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z-Test

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 0.1 0.05 0.025 0.01 Zα 1.28 1.64 1.96 2.33

For samples less than 30 use the t-test.

 Analytical and descriptive statistics are covered in the MiC Quality online course Primer in Statistics. Try out our courses by taking the first module of the Primer in Statistics free of charge.
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