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Test for a Difference Between Two Means

• If both independent sample are large or both populations from which the sample is selected are drawn from a normal distributions with known standard deviations, use the normal distribution to test μ₁ − μ₂.

• If both independent sample are large or both populations from which the sample is selected are drawn from a normal distributions with unknown standard deviations, use the t-distribution with ν = n₁ + n₂ − 2 degrees of freedom to test μ₁ − μ₂ .

• If the sample size is large or the population of paired differences is normally distributed with unknown standard deviations, then use the t-distribution with ν = n − 1 degrees of freedom to test μ_d .