Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 286
... significance level of this test ( or the size of the critical region ) is the power of the test when Ho is true , the significance level of this test is 0.05 . = = = = The fact that the power of this test , when 0 = 4 , is only 0.31 ...
... significance level of this test ( or the size of the critical region ) is the power of the test when Ho is true , the significance level of this test is 0.05 . = = = = The fact that the power of this test , when 0 = 4 , is only 0.31 ...
Page 289
... test of significance level a = 0.05 . That is , if x is 1.6450 / n greater than the mean = 30,000 , we would reject H1 and accept H , and the significance level would be equal to a = 0.05 . To test H0 30,000 against H , : 0 30,000 , let ...
... test of significance level a = 0.05 . That is , if x is 1.6450 / n greater than the mean = 30,000 , we would reject H1 and accept H , and the significance level would be equal to a = 0.05 . To test H0 30,000 against H , : 0 30,000 , let ...
Page 291
... significance level of the test is Pr ( Y≥ 3 ) = 1 – Pr ( Y ≤ 2 ) = 10.920 0.080 . 10 = If the critical region defined by Σx , ≥ 4 is used , the significance level is α = Pr ( Y≥ 4 ) = 1 − Pr ( Y ≤ 3 ) = 1 − 0.981 = 0.019 . 10 10 ...
... significance level of the test is Pr ( Y≥ 3 ) = 1 – Pr ( Y ≤ 2 ) = 10.920 0.080 . 10 = If the critical region defined by Σx , ≥ 4 is used , the significance level is α = Pr ( Y≥ 4 ) = 1 − Pr ( Y ≤ 3 ) = 1 − 0.981 = 0.019 . 10 10 ...
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Common terms and phrases
A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²