## Introduction to Mathematical Statistics |

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Page 176

Find a best test of the null simple

the alternative simple

specify numerical values for each of these parameters is called a

Find a best test of the null simple

**hypothesis**Ho: 61 = 6'1 = 0, 6, = 6'2 = 1 againstthe alternative simple

**hypothesis**H1: 61 ... A statistical**hypothesis**that does notspecify numerical values for each of these parameters is called a

**composite**...Page 179

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 in

the alternative

, ...

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 in

the alternative

**composite hypothesis**H1. In this section we define a critical region, ...

Page 182

Let the null

is a subset of Q and Wils be called the subspace specified by the null hypothesis

Ho ...

Let the null

**composite hypothesis**be Ho: 6 = 0, 0, P 0, and let the alternative**composite hypothesis**be Hi: 6, #4 0, à, SU. The set a = {(0, 0.); 61 = 0, 0 < 0, 3 oois a subset of Q and Wils be called the subspace specified by the null hypothesis

Ho ...

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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