## Introduction to mathematical statistics |

### From inside the book

Results 1-3 of 49

Page 260

8 = 1 if the

x2; 1) - 2 Here D = {8; 8 = 1,2}. Find the significance level of the test and the

power of the test when H0 is false. 10.4. Sketch, as in Figure 10.1, the graphs of

the ...

8 = 1 if the

**observed**values of X1, X2, say, x1, x2, are such that f(x1;2)f(x2;2) 1 l)f(x2; 1) - 2 Here D = {8; 8 = 1,2}. Find the significance level of the test and the

power of the test when H0 is false. 10.4. Sketch, as in Figure 10.1, the graphs of

the ...

Page 272

rejecting H0: 9 = % if and only if the

items 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

...

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 302

If H0 is true, Table II, with k -1=6-1 = i 5 degrees of freedom, shows that we have

Pr (Q6 > 11.1) = 0.05. Now suppose the experimental frequencies of A1,A2,...,A6

are respectively 13, 19, 11, 8, 5, and 4. The

If H0 is true, Table II, with k -1=6-1 = i 5 degrees of freedom, shows that we have

Pr (Q6 > 11.1) = 0.05. Now suppose the experimental frequencies of A1,A2,...,A6

are respectively 13, 19, 11, 8, 5, and 4. The

**observed**value of Q5 is (13 - 10)2 ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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