Abstract: For two normal populationsN（μ₁,σ₁²）andN（μ₂,σ₂²）, the current paper investigates the hypothesis test problem: H₀:μ₁=μ,σ₁²=σ₂² versus H₁:μ₁≠μ,σ₁²≠σ₂² The corresponding likelihood ratio statistic is derived and its distribution is discussed. We present the criteria table when a = 0.05 and a = 0.01. The strategy of calculating the criteria table is discussed in detail, and the corresponding SAS codes are shown also.