## Introduction to Mathematical Statistics |

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Page 285

Other Statistical Tests 11.1 Likelihood

magnitude of the

test or of a uniformly most powerful test can be modified, and made intuitively

appealing, ...

Other Statistical Tests 11.1 Likelihood

**Ratio**Tests The notion of using themagnitude of the

**ratio**of two probability density functions as the basis of a besttest or of a uniformly most powerful test can be modified, and made intuitively

appealing, ...

Page 286

Thus the

Suppose, however, we modify this

maximum of L(w) in w; that is, the maximum of L(a) with respect to 62. And we ...

Thus the

**ratio**of L(a) to L(Q) could not provide a basis for a test of Ho against H1.Suppose, however, we modify this

**ratio**in the following manner: We shall find themaximum of L(w) in w; that is, the maximum of L(a) with respect to 62. And we ...

Page 293

Show that the likelihood

simple hypothesis Ho against an alternative simple hypothesis H1, as that given

by the Neyman-Pearson theorem. Note that there only two points in Q. 11.4.

Show that the likelihood

**ratio**principle leads to the same test, when testing asimple hypothesis Ho against an alternative simple hypothesis H1, as that given

by the Neyman-Pearson theorem. Note that there only two points in Q. 11.4.

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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