## Introduction to Mathematical Statistics |

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Page 170

Since the

of the test when Ho is true, the

the power of this test, when 6 = 4, is only 0.31, immediately suggests that a ...

Since the

**significance level**of a test (or the size of the critical region) is the powerof the test when Ho is true, the

**significance level**of this test is 0.05. The fact thatthe power of this test, when 6 = 4, is only 0.31, immediately suggests that a ...

Page 179

That is, the power function of the test which corresponds to this critical region

should be at least as great as the power function of any other test with the same

C ...

That is, the power function of the test which corresponds to this critical region

should be at least as great as the power function of any other test with the same

**significance level**for every simple hypothesis in H1. Definition. The critical regionC ...

Page 189

If the test derived in that exl ample is used, do we accept or reject Ho: 61 – 0 at

the 5 per cent

78.6, XCGr; – 3) = 71.2, 1 8 XCOy; — )* = 54.8. If we use the test derived in that ...

If the test derived in that exl ample is used, do we accept or reject Ho: 61 – 0 at

the 5 per cent

**significance level**? 9.22. In Example 2, let n = m = 8, £ = 75.2, j =78.6, XCGr; – 3) = 71.2, 1 8 XCOy; — )* = 54.8. If we use the test derived in that ...

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere