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