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Let Xij denote the observation of the primary toxicological endpoint for the jth experimentalunit in theith group, i = 0, 1 and j = 1,... ,Ni. Assume Xij to be i.i.d. ~ N(μi, σ2i) withμ0 denoting the toxicological effect for the control group and μ1 denoting the effect for thenew substance group. The traditional approach to prove the hazard of a new substance isformulated as follows: