## Introduction to mathematical statistics |

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Page 262

Suppose there is one of these subsets, say C, such that when H1 is true, the

power of the test associated with C is at least as great as the power of the test

associated with each other A . Then C is defined as a

for ...

Suppose there is one of these subsets, say C, such that when H1 is true, the

power of the test associated with C is at least as great as the power of the test

associated with each other A . Then C is defined as a

**best critical region**of size afor ...

Page 268

Robert V. Hogg, Allen Thornton Craig. n C = {(»j,..., xn); 2*1 ^ c) is a

find n and c. so that approximately Pr (| Xt < c; #0) = 0.10 and Pr (| Xt < c; ffj) =

0.80.

Robert V. Hogg, Allen Thornton Craig. n C = {(»j,..., xn); 2*1 ^ c) is a

**best critical****region**for testing H0: p = % i against H1 : p = J. Use the central limit theorem tofind n and c. so that approximately Pr (| Xt < c; #0) = 0.10 and Pr (| Xt < c; ffj) =

0.80.

Page 273

is a uniformly most powerful critical region for testing H0: 9 = yg- against H1: 8 > -

fg. What is a, the ... Find a

91 = 9[, 82 = 8'2 > 0, against the alternative simple hypothesis H1. 81 = 8'[ < 9[ ...

is a uniformly most powerful critical region for testing H0: 9 = yg- against H1: 8 > -

fg. What is a, the ... Find a

**best critical region**for testing the simple hypothesis H0:91 = 9[, 82 = 8'2 > 0, against the alternative simple hypothesis H1. 81 = 8'[ < 9[ ...

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere