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# Test of the difference between two means, standard deviations known

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# Test of the difference between two means, standard deviations known

This test is used to determine whether the mean values obtained from two independent samples which provide the best estimate of two population means, μ1 and μ2, differ by a specified amount d, when the population standard deviation, σ, is known (or where a good estimate, s, is available based on a sample size n>30).

Assumptions: The sample is random and the population is Normally distributed

Hypothesis: H0: μ1-μ2=d; H1: μ1-μ2d

Test: Compute the z-statistic: z is distributed approximately N(0,1). If d=0 then the test is one of equality of the two mean values. If the two populations are finite, of size N1 and N2, the standard error components of the z-statistic should be replaced with the adjusted expressions: Note: if the samples are actually paired rather than independent, the difference between the pairs of values can be computed and then the mean of these differences tested using the z-test for a single mean.