Introduction to Mathematical Statistics |
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Page 262
... critical region of size a for testing Ho against H1 . The definition of a best critical region of size a does not provide a systematic method of determining it . The following theorem , due to Neyman and Pearson , provides a solution to ...
... critical region of size a for testing Ho against H1 . The definition of a best critical region of size a does not provide a systematic method of determining it . The following theorem , due to Neyman and Pearson , provides a solution to ...
Page 268
... critical region for testing H 。: p = ↓ against H1 : p == 3. Use the central limit theorem to find n and c so that Σ n approximately Pr ( 1⁄2 X , ≤ c ; Ho ) ... critical region should be a best critical 268 Statistical Hypotheses [ Ch . 10.
... critical region for testing H 。: p = ↓ against H1 : p == 3. Use the central limit theorem to find n and c so that Σ n approximately Pr ( 1⁄2 X , ≤ c ; Ho ) ... critical region should be a best critical 268 Statistical Hypotheses [ Ch . 10.
Page 280
... critical region C so that max [ R ( 0 ' , C ) , R ( 0 " , C ) ] is minimized . We shall show that the solution is the region C = { ( x ...... xn ) ; L ( 0 ' ; x1 , ... , xn ) L ( 0 " ; x1 , ≤ k xn ) provided the positive constant k is ...
... critical region C so that max [ R ( 0 ' , C ) , R ( 0 " , C ) ] is minimized . We shall show that the solution is the region C = { ( x ...... xn ) ; L ( 0 ' ; x1 , ... , xn ) L ( 0 " ; x1 , ≤ k xn ) provided the positive constant k is ...
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A₁ A₂ accept accordance Accordingly alternative approximately assume called cent Chapter complete compute Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given H₁ Hence hypothesis inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics parameter probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁