## Introduction to mathematical statistics |

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Page 256

Among other things, this means that, if 9 = 75, the probability of rejecting the

hypothesis H0: 9 < 75 is \. That is, if 9 = 75 so that

rejecting this true hypothesis H0 is Many statisticians and research workers find it

very ...

Among other things, this means that, if 9 = 75, the probability of rejecting the

hypothesis H0: 9 < 75 is \. That is, if 9 = 75 so that

**H0 is true**, the probability ofrejecting this true hypothesis H0 is Many statisticians and research workers find it

very ...

Page 259

That is, the probability of rejecting H0 when

of rejecting H0 when H0 is false is 0.31. Since the significance level of this test (or

the size of the critical region) is the power of the test when

That is, the probability of rejecting H0 when

**H0 is true**is 0.05, and the probabilityof rejecting H0 when H0 is false is 0.31. Since the significance level of this test (or

the size of the critical region) is the power of the test when

**H0 is true**, the ...Page 265

The event 2 Xt > c is equivalent to the event _ i _ X > c/n = c1, say, so the test may

be based upon the statistic X. If

distribution that is «(0, 1/n). For a given positive integer n, the size of the sample,

and a ...

The event 2 Xt > c is equivalent to the event _ i _ X > c/n = c1, say, so the test may

be based upon the statistic X. If

**H0 is true**, that is, 9 = 8' = 0, then X has adistribution that is «(0, 1/n). For a given positive integer n, the size of the sample,

and a ...

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere