## Introduction to Mathematical Statistics |

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Page 173

That is, the test with critical region C has a power, when 6 = 6", that is at least as

great as the power of the test that has A for the critical region. Thus, as asserted

in the theorem, C is a

That is, the test with critical region C has a power, when 6 = 6", that is at least as

great as the power of the test that has A for the critical region. Thus, as asserted

in the theorem, C is a

**best critical region**of size a for testing the null simple ...Page 179

Example 2 of the preceding section afforded an illustration of a test of a null

simple hypothesis Ho that is a

the alternative composite hypothesis H1. In this section we define a

, ...

Example 2 of the preceding section afforded an illustration of a test of a null

simple hypothesis Ho that is a

**best**test of Ho against every simple hypothesis inthe alternative composite hypothesis H1. In this section we define a

**critical region**, ...

Page 180

The set C = {(xi, z2, ..., zn); Xoz,” - cł is then a

null simple hypothesis Ho: 0 = 0' against the simple hypothesis 0 = 6”. It remains

to determine c so that this critical region has the desired size o. If Ho is true, the ...

The set C = {(xi, z2, ..., zn); Xoz,” - cł is then a

**best critical region**for testing the 1null simple hypothesis Ho: 0 = 0' against the simple hypothesis 0 = 6”. It remains

to determine c so that this critical region has the desired size o. If Ho is true, the ...

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere