## Introduction to mathematical statistics |

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Page 268

Robert V. Hogg, Allen Thornton Craig. n C = {(»j,..., xn); 2*1 ^ c) is a best critical

region for

find n and c. so that approximately Pr (| Xt < c; #0) = 0.10 and Pr (| Xt < c; ffj) =

0.80.

Robert V. Hogg, Allen Thornton Craig. n C = {(»j,..., xn); 2*1 ^ c) is a best critical

region for

**testing H0**: p = % i against H1 : p = J. Use the central limit theorem tofind n and c. so that approximately Pr (| Xt < c; #0) = 0.10 and Pr (| Xt < c; ffj) =

0.80.

Page 272

rejecting

items are such that 2 xt ^ 1. Find the power function K(8), i 0 < 8 < i, of this

10.17. Let X have a p.d.f. of the form/(x; 0) = 1/0, 0 < x < 8, zero elsewhere. Let Y1

...

rejecting

**H0**: 9 = % if and only if the observed values x1, x2 x10 of the 10 sampleitems are such that 2 xt ^ 1. Find the power function K(8), i 0 < 8 < i, of this

**test**.10.17. Let X have a p.d.f. of the form/(x; 0) = 1/0, 0 < x < 8, zero elsewhere. Let Y1

...

Page 293

In Example 1, let n = 10, and let the experimental'values of the 10 _ random

variables yield x = 0.6 and 2 (^i — x)2 = 3.6. If the

used, do we accept or reject

In Example 1, let n = 10, and let the experimental'values of the 10 _ random

variables yield x = 0.6 and 2 (^i — x)2 = 3.6. If the

**test**derived i in that example isused, do we accept or reject

**H0**: 8X = 0 at the 5 per cent significance level ? 11.2.### What people are saying - Write a review

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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