(5 pts.) Suppose that eight observations X₁,..., X§ are drawn at random from a distribution with the following p.d.f. 9-

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5 Pts Suppose That Eight Observations X X Are Drawn At Random From A Distribution With The Following P D F 9 1 (53.13 KiB) Viewed 24 times

(5 pts.) Suppose that eight observations X₁,..., X§ are drawn at random from a distribution with the following p.d.f. 9-1 for 0 < x < 1 ƒ(x|0) = otherwise = Suppose also that the value of 0 is unknown (0 > 0), and it is desired to test the following hypotheses: Ho : 0 1 versus H₁ : 0 = 2. Use Neyman-Pearson lemma to show that the most powerful test (lowest 3) at the level of significance a = = 0.05 is to reject Họ if Σ;₁ ln X¿ > c and the critical value is c = -3.981. i=1 Hint: It can be shown that the distribution of Y = = -2 ln X is Xd.f.-2, Chi-squared with 2 d.f.