Introduction to Mathematical Statistics |
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Page 166
... null hypothesis Ho : 1 ( that is , accept the alternative hypothesis H1 : 0 = 2 ) if the experimentally determined point ( x1 , x2 ) plots in the shaded region of Figure 9-1 . Otherwise accept the null hypothesis Ho : 0 = 1 . x1 = 1 ...
... null hypothesis Ho : 1 ( that is , accept the alternative hypothesis H1 : 0 = 2 ) if the experimentally determined point ( x1 , x2 ) plots in the shaded region of Figure 9-1 . Otherwise accept the null hypothesis Ho : 0 = 1 . x1 = 1 ...
Page 176
... null simple hypothesis Ho : 01 = 0'1 = 0 , 1 02 0'2 1 against the alternative simple hypothesis H1 : 01 = 0 " 1 = 1 , 02 = 0 " 2 = 4 . 01 9.10 . Let X1 , Xn denote ... hypothesis H1 : 176 [ Ch . 9 STATISTICAL HYPOTHESES Composite Hypotheses.
... null simple hypothesis Ho : 01 = 0'1 = 0 , 1 02 0'2 1 against the alternative simple hypothesis H1 : 01 = 0 " 1 = 1 , 02 = 0 " 2 = 4 . 01 9.10 . Let X1 , Xn denote ... hypothesis H1 : 176 [ Ch . 9 STATISTICAL HYPOTHESES Composite Hypotheses.
Page 188
... null hypothesis Ho : 01 = 02 is true , the random variable T = nm √ n + m n - ( X − Ÿ ) Σ ( Y ; Σα Î ( X ; — X ) 2 ... null hypothesis is true . The reason is as follows : It was found that each of these tests could be based on some ...
... null hypothesis Ho : 01 = 02 is true , the random variable T = nm √ n + m n - ( X − Ÿ ) Σ ( Y ; Σα Î ( X ; — X ) 2 ... null hypothesis is true . The reason is as follows : It was found that each of these tests could be based on some ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²