Suppose that eight observationsX1, ,X8 are drawn at random from a distribution with the following p d f Suppose also that the value of is unknown ( 0), and it is desired to test the following hypotheses H0 1, H1 1 Show that the UMP test at the level of significance 0 0 05 specifies rejecting H0 if log Xi 3 981 6 1 for 0

Question: Suppose that eight observationsX1, . . . ,X8 are drawn at random from a distribution with the following p.d.f.: Suppose also that the value of

Suppose that eight observationsX1, . . . ,X8 are drawn at random from a distribution with the following p.d.f.:

Suppose also that the value of Î¸ is unknown (Î¸ > 0), and it is desired to test the following hypotheses:
H0: Î¸ ‰¤ 1,
H1: Î¸ >1.
Show that the UMP test at the level of significance Î±0 = 0.05 specifies rejecting H0 if
log Xi ‰¥ˆ’3.981.

[ 6-1 for 0

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