Introduction to Mathematical Statistics |
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Page 262
... great as the power of the test associated with each other A. Then C is defined as a best 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 ...
... great as the power of the test associated with each other A. Then C is defined as a best 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 ...
Page 268
... best 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 ... critical region should be a best critical 268 Statistical Hypotheses [ Ch . 10.
... best 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 ... critical region should be a best critical 268 Statistical Hypotheses [ Ch . 10.
Page 273
... best critical region for testing the simple hypothesis Ho : 01 01 , 02 02 > 0 , against the alternative simple hypothesis H1 : 01 = 0 < 01 , 02 = 021⁄2 > 02. Is this a uniformly most powerful critical 01 region for testing Ho : 01 01 ...
... best critical region for testing the simple hypothesis Ho : 01 01 , 02 02 > 0 , against the alternative simple hypothesis H1 : 01 = 0 < 01 , 02 = 021⁄2 > 02. Is this a uniformly most powerful critical 01 region for testing Ho : 01 01 ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²