# 08_03 - STAT 410 Examples for Summer 2009 Example 1 1 2...

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STAT 410 Examples for 08/03/2009 Summer 2009 Example 1 : 1 2 3 4 5 p 0 ( x ) 0.35 0.05 0.20 0.25 0.15 p 1 ( x ) 0.20 0.20 0.20 0.20 0.20 H 0 : X has p.m.f. p 0 ( x ) vs. H 1 : X has p.m.f. p 1 ( x ). 1 2 3 4 5 λ ( x ) 1.75 0.25 1 1.25 0.75 Reject H 0 if x = 2 α = 0.05, Power = 0.20. Reject H 0 if x = 2 or 5 α = 0.20, Power = 0.40. Reject H 0 if x = 2 Reject H 0 with probability 3 1 if x = 5 α = 0.10, Power = 15 4 .

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Example 2 : 1 2 3 4 5 p 0 ( x ) 0.05 0.10 0.20 0.25 0.40 p 1 ( x ) 0.20 0.20 0.40 0.10 0.10 H 0 : X has p.m.f. p 0 ( x ) vs. H 1 : X has p.m.f. p 1 ( x ). 1 2 3 4 5 λ ( x ) 0.25 0.5 0.5 2.5 4 Reject H 0 if x = 1 α = 0.05, Power = 0.20. Reject H 0 if x = 1 Reject H 0 with probability 2 1 if x = 2 α = 0.10, Power = 0.30. Reject H 0 if x = 1 Reject H 0 with probability 4 1 if x = 3 α = 0.10, Power = 0.30. Reject H 0 if x = 1 Reject H 0 with probability 4 1 if x = 2 Reject H 0 with probability 8 1 if x = 3 α = 0.10, Power = 0.30.
H 0 : θ Θ 0 vs. H 1 : θ Θ 1 Θ 0 Θ 1 = . Reject

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## This note was uploaded on 10/29/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Summer '08 term at University of Illinois at Urbana–Champaign.

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08_03 - STAT 410 Examples for Summer 2009 Example 1 1 2...

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