Hypotheses for 2 Variances

For a 2 variances test, the hypotheses are as follows.

Null hypothesis

H₀: σ₁ / σ₂ = K	The ratio between the first population standard deviation (σ₁) and the second population standard deviation (σ₂) is equal to the hypothesized ratio (K).

Alternative hypothesis

Select one of the following alternative hypotheses.

H₁: σ₁ / σ₂ ≠ K	The ratio between the first population standard deviation (σ₁) and the second population standard deviation (σ₂) does not equal the hypothesized ratio (K).
H₁: σ₁ / σ₂ > K	The ratio between the first population standard deviation (σ₁) and the second population standard deviation (σ₂) is greater than the hypothesized ratio (K).
H₁: σ₁ / σ₂ < K	The ratio between the first population standard deviation (σ₁) and the second population standard deviation (σ₂) is less than the hypothesized ratio (K).

If you are testing the ratio of variances, substitute variance (σ²) for standard deviation (σ) in the hypotheses.