The test statistic in the Neyman–Pearson Lemma and the likelihood ratio test statistic K are intimately related. Consider testing H₀: θ = θ₀ versus H_a: θ = θ_a, and let Λ* denote the test statistic in (9.6). Show that

Equation (9.6)

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f(x1,..., Xn; Oa) * ƒ ( x ₁ , . . . , x n ; 00 ) ≥ k {k} = ( R* x 1 , . . . , X, ,xn):