Introduction to Mathematical Statistics |
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Page 296
... significance level of this test . So if the observed data yield c1 < F < c2 and | T | ≥ c , we reject the hypothesis that the two normal distributions are the same because the two means seem to be unequal . Of course , if the two com ...
... significance level of this test . So if the observed data yield c1 < F < c2 and | T | ≥ c , we reject the hypothesis that the two normal distributions are the same because the two means seem to be unequal . Of course , if the two com ...
Page 302
... significance level . Example 2. A { x ; 0 < x < 1 } by { x ; ‡ < x ≤ 1 } , A3 probabilities p1 , i = point is to be selected a random process . Let A1 { x ; † < x ≤ 3 } , and А 1 , 2 , 3 , 4 , assigned to these = from the unit ...
... significance level . Example 2. A { x ; 0 < x < 1 } by { x ; ‡ < x ≤ 1 } , A3 probabilities p1 , i = point is to be selected a random process . Let A1 { x ; † < x ≤ 3 } , and А 1 , 2 , 3 , 4 , assigned to these = from the unit ...
Page 338
... significance level of this sequence μ1 = μ2 = ... = of tests of the equality of means is b - 1 α = 1 II ( 1 - α . ) . i = 1 με = This means that , if μ1 = μ2 is rejected , using W1 , at significance level a1 , then Ho : μ1 = μ2 = μ¿ is ...
... significance level of this sequence μ1 = μ2 = ... = of tests of the equality of means is b - 1 α = 1 II ( 1 - α . ) . i = 1 με = This means that , if μ1 = μ2 is rejected , using W1 , at significance level a1 , then Ho : μ1 = μ2 = μ¿ is ...
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Common terms and phrases
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