Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 14
Page 267
... critical region of size α = 0.05 for testing Ho : 21 against H1 : o2 = 2. Is this a best critical region of size 0.05 for 02 testing Hoo2 = 1 against H1 : o2 = 4 ? Against H1 : o2 = o > 1 ? = 1 , 10.11 . If X1 , X2 , ... , X , is a ...
... critical region of size α = 0.05 for testing Ho : 21 against H1 : o2 = 2. Is this a best critical region of size 0.05 for 02 testing Hoo2 = 1 against H1 : o2 = 4 ? Against H1 : o2 = o > 1 ? = 1 , 10.11 . If X1 , X2 , ... , X , is a ...
Page 271
... critical region for testing the simple hypothesis against an alternative simple hypothesis , say , 0 = 0 ' + 1 , will not serve as a best critical region for testing Ho : 00 ' against the alternative simple hypothesis 00 ' 1 , say . By ...
... critical region for testing the simple hypothesis against an alternative simple hypothesis , say , 0 = 0 ' + 1 , will not serve as a best critical region for testing Ho : 00 ' against the alternative simple hypothesis 00 ' 1 , say . By ...
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 = L ( 0 ' ; x1 , ... , xn ) L ( 0 " ; x1 , ... , xn ) ≤ k provided the positive constant k is selected so ...
... critical region C so that max [ R ( 0 ' , C ) , R ( 0 ′′ , C ) ] is minimized . We shall show that the solution is the region C = L ( 0 ' ; x1 , ... , xn ) L ( 0 " ; x1 , ... , xn ) ≤ k provided the positive constant k is selected so ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ