A Test of Equality of Two Normal Population Means and Variances

Abstract

Abstract Let X 1, …, X m and Y 1, …, Y n be two independent random samples from normal populations N(μ1, σ1 2) and N(μ2, σ2 2), respectively. The statistical problem is to test H 0: μ1 = μ2 and σ1 2 = σ2 2 against H a : μ1 ≠ μ2 or σ1 2 ≠ σ2 2. Using Fisher's method of combining two independent test statistics, we suggest a test and prove that it is asymptotically optimal in the sense of Bahadur efficiency.