## Introduction to Mathematical Statistics |

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10.2 Certain Best Tests In this section we require that both the hypothesis Ho,

which is to be tested, and the alternative ... Certainly, a test specifies a

10.2 Certain Best Tests In this section we require that both the hypothesis Ho,

which is to be tested, and the alternative ... Certainly, a test specifies a

**critical****region**; but it can also be said that a choice of a**critical region**defines a test.Page 267

In Example 1 of this section, let the simple hypotheses read Ho: 0 = 0 = 0 and H1:

6 = 9" = –1. Show that the best test of Ho ... Find a best

0.05 for testing Ho: a* = 1 against H1: g” = 2. Is this a best

In Example 1 of this section, let the simple hypotheses read Ho: 0 = 0 = 0 and H1:

6 = 9" = –1. Show that the best test of Ho ... Find a best

**critical region**of size a =0.05 for testing Ho: a* = 1 against H1: g” = 2. Is this a best

**critical region**of size ...Page 271

The first of these two expressions defines a best

9' against the hypothesis 0 = 8", provided 6" > 0", while the second expression

defines a best

The first of these two expressions defines a best

**critical region**for testing Ho: 6 =9' against the hypothesis 0 = 8", provided 6" > 0", while the second expression

defines a best

**critical region**for testing Ho: 0 = 0' against the hypothesis 0 = 0", ...### What people are saying - Write a review

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere