## Introduction to mathematical statistics |

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Page 256

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

hypothesis

very ...

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

**rejecting**thehypothesis

**H0**: 9 < 75 is \. That is, if 9 = 75 so that**H0**is true, the probability of**rejecting**this true hypothesis**H0**is Many statisticians and research workers find itvery ...

Page 260

The

incorrect decision or an error. This incorrect decision is often called a Type-I error

; accordingly, the significance level of the test is the probability of committing an ...

The

**rejection**of the hypothesis**H0**when that hypothesis is true is, of course, anincorrect decision or an error. This incorrect decision is often called a Type-I error

; accordingly, the significance level of the test is the probability of committing an ...

Page 378

CHAPTER 11 11.1 t = 3 > 2.262,

11.13 No. 11.14 q3 = x2\& > 7.81,

a) ...

CHAPTER 11 11.1 t = 3 > 2.262,

**reject H0**. 11.2 \t\ = 2.27 > 2.145,**reject H0**.11.13 No. 11.14 q3 = x2\& > 7.81,

**reject H0**. CHAPTER 12 12.5 F = 7.6 > 3.89,**reject H0**. 12.8 r + 8, 2r + 49. 12.9 r2(d + r1)/[ri(r2 - 2)], r2 > 2. CHAPTER 13 13.3 (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