# Hypotheses for 1-Sample Equivalence Test

For a 1-sample equivalence test, Minitab tests two separate null hypotheses.
Null hypotheses (default)
 H0: Δ ≤ δ1 The difference (Δ) between the mean of the test population and the target is less than or equal to the lower equivalence limit (δ1). H0: Δ ≥ δ2 The difference (Δ) between the mean of the test population and target is greater than or equal to the upper equivalence limit (δ2).
Alternative hypothesis (default)
 H1: δ1< Δ < δ2 The difference (Δ) between the mean of the test population and the target value is greater than the lower equivalence limit (δ1) and less than the upper equivalence limit (δ2).
If both null hypotheses are rejected, then the difference falls within your equivalence interval and you can claim that the test mean and the target are equivalent.
You can also test the following hypotheses by selecting a different option for the alternative hypothesis.
Option Hypotheses
Test mean > target H0: Test mean – target (Δ) ≤ 0

H1: Test mean – target (Δ) > 0

Test mean < target H0: Test mean – target (Δ) ≥ 0

H1: Test mean – target (Δ) < 0

Test mean - target > lower limit H0: Test mean – target (Δ) ≤ δ1

H1: Test mean – target (Δ) > δ1

Test mean - target < upper limit H0: Test mean – target (Δ) ≥ δ2

H1: Test mean – target (Δ) < δ2

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