## Introduction to Mathematical Statistics |

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Page 260

The rejection of the hypothesis Ho when that hypothesis is true is, of course, an

incorrect decision or an error. ... To test the

the alternative

...

The rejection of the hypothesis Ho when that hypothesis is true is, of course, an

incorrect decision or an error. ... To test the

**simple hypothesis**Ho: 6 = 1 againstthe alternative

**simple hypothesis**H1: 0 = 2 use a random sample X1, X2 of size n...

Page 261

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

which is to be tested, and the alternative hypothesis H1 be

Thus, in all instances, the parameter space is a set that consists of exactly two

points.

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

which is to be tested, and the alternative hypothesis H1 be

**simple hypotheses**.Thus, in all instances, the parameter space is a set that consists of exactly two

points.

Page 271

That is, a best critical region for testing the

alternative

region for testing Ho: 6 = 9" against the alternative

say.

That is, a best critical region for testing the

**simple hypothesis**against analternative

**simple hypothesis**, say, 6 = 8' + 1, will not serve as a best criticalregion for testing Ho: 6 = 9" against the alternative

**simple hypothesis**0 = 0 – 1,say.

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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