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Two Sample z-Test

The Two Sample z Test is a hypothesis test used to to compare the means of two samples to see if it is feasible that they come from the same population. The test is used where the standard deviation is known or where the sample size is large (greater than 30). The test requires that the population conforms to a normal distribution. The hypothesis is:

H0 the population means are equal
H1 the popular means are different

The test is:

 sample means n1, n2 sample sizes s1, s2 sample standard deviations

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 with less than 30 items see the Two Sample 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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