Sampling distribution of two independent samples mean with known population variances, (Xˉ1−Xˉ2)∼N(μ1−μ2,n1σ12+n2σ22) where z=n1σ12+n2σ22(Xˉ1−Xˉ2)−(μ1−μ2) Sampling distribution of two independent samples mean with unknown population variances and n1 and n2≥30 (Xˉ1−Xˉ2)∼N(μ1−μ2n1s12+n2s22)Z=n1s12+n2s22(Xˉ1−Xˉ2)−(μ1−μ2) where Sampling distribution of two independent samples proportion (p^1−p^2)∼N(p1−p2,n1p1(1−p1)+n2p2(1−p2))Z=n1p1(1−p1)+n2p2(1−p2)(p^1−p^2)−(p1−p2)
