Mathematics · Statistical Inference
Let X1, X2, ..., Xn be a random sample from a continuous distribution with the common probability density function: f(x|θ) = 2θθ / xθ+1, if x > 2, and 0 otherwise; where θ > 0 is an unknown parameter. Suppose P(Y > χ2m,β) = β, where Y ~ χ2m. For testing H0: θ = 1 against H1: θ > 1, a uniformly most powerful test of size α (0 < α < 1) will reject H0 if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Σi=1n ln Xi < χ2n,1-α + n ln 2
- 2Σi=1n ln Xi > χ2n,α + n ln 2
- 3Σi=1n ln Xi < 12χ22n,1-α + n ln 2
- 4Σi=1n ln Xi > 12χ22n,α + n ln 2✓
Correct answer
Σi=1n ln Xi > 12χ22n,α + n ln 2
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