An iid sample of size n≥2 is used to test H₀:density (2π)^(−1/2)e^(−x²/2) against H₁:density e^(−|x|)/2. At level 0.05, the likelihood-ratio critical region has which form, for a suitable c?
The log alternative/null likelihood ratio is a constant plus Σ[x_i²/2−|x_i|]=(1/2)Σ(|x_i|−1)² plus another constant. Neyman–Pearson rejection for a large alternative/null ratio is therefore **C**.
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