Hypothesis Tests on the Variance

Hypothesis Tests on the Variance of a Normally Distributed Population

Hypothesis
H0: σ² = σ₀² , or σ² ≥σ₀² , or σ² ≤ σ₀²
H1: σ² ≠σ₀² , or σ² < σ₀² , or σ² > σ₀²

Test statistic : χ² = (n – 1)*s² / σ₀2
Where:
n = sample size
s² = sample variance
σ₀² = population variance from hypothesis

Sample variance s² is referred to as the square sum of deviations between observed values and sample mean, degrees of freedom, or n – 1
Use Chi-squared test

Critical value comes from chi-squared table. It is an asymmetrical distribution and approaches to a normal distribution when degree of freedom increase, but bound below by zero, i.e. cannot be -ve.
{Look up df=n-1, p=significance for 1-sided test or p=significance/2 for 2-sided test}.