Introduction to Mathematical Statistics |
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Results 1-3 of 14
Page 166
... 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- √0.05 x2 = 1- √0.05 ( 0,0 ) Figure ...
... 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- √0.05 x2 = 1- √0.05 ( 0,0 ) Figure ...
Page 170
... accept H1 : 0 = 1 if the observed values of X1 , X2 , say , X1 , X2 , are such that f ( x1 ; 2 ) f ( x2 ; 2 ) f ( x1 ; 1 ) f ( x2 ; 1 ) 1 < 2 Find the significance level of the test and the power of the test when H。 is false . 0 9.2 ...
... accept H1 : 0 = 1 if the observed values of X1 , X2 , say , X1 , X2 , are such that f ( x1 ; 2 ) f ( x2 ; 2 ) f ( x1 ; 1 ) f ( x2 ; 1 ) 1 < 2 Find the significance level of the test and the power of the test when H。 is false . 0 9.2 ...
Page 178
... accept H1 : 01 if either y1 ≤ 1⁄2 or y1 ≥ 1 . 00 , of the test . 4 9.14 . Consider a normal distribution of the form n ( x ; 0 , 4 ) . The null simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 ...
... accept H1 : 01 if either y1 ≤ 1⁄2 or y1 ≥ 1 . 00 , of the test . 4 9.14 . Consider a normal distribution of the form n ( x ; 0 , 4 ) . The null simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 ...
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