Mathematical Methods for Physics and Engineering : A Comprehensive Guide

31.7 HYPOTHESIS TESTING 0 0 0. 05 0. 10 10 20 30 40 λ(u) u λcrit ab Figure 31.12 The sampling distributionP(u|H 0 )forN= 10; thi ...

STATISTICS however, it is difficult to determineaandbfor a given significance levelα,soa slightly different rejection region, wh ...

31.7 HYPOTHESIS TESTING We now turn to Fisher’sF-test. Let us suppose that two independent samples of sizesN 1 andN 2 are drawn ...

STATISTICS distributionP(v^2 ,F|H 0 ) is obtained by requiring that P(v^2 ,F|H 0 )d(v^2 )dF=P(u^2 |H 0 )P(v^2 |H 0 )d(u^2 )d(v^2 ...

31.7 HYPOTHESIS TESTING Cn 1 ,n 2 (F) n 1 =12345678 n 2 =1 161 200 216 225 230 234 237 239 2 18.5 19.0 19.2 19.2 19.3 19.3 19.4 ...

STATISTICS
Suppose that two classes of students take the same mathematics examination and the following percentage marks are ob ...

31.7 HYPOTHESIS TESTING In the last equality, we rewrote the expression in matrix notation by defining the column vectorfwith el ...

STATISTICS number of degrees of freedom isn=N−M= 8. Settingn=8andα=0.05 in (31.127) we find from table 31.2 thatk=15.51. Hence o ...

31.8 EXERCISES 31.6 Prove that the sample mean is the bestlinear unbiased estimatorof the population meanμas follows. (a) If the ...

STATISTICS 31.10 This exercise is intended to illustrate the dangers of applying formalised estimator techniques to distribution ...

31.8 EXERCISES 31.13 A similar technique to that employed in exercise 31.12 can be used to test correlations between characteris ...

STATISTICS 31.16 The functiony(x) is known to be a quadratic function ofx. The following table gives the measured values and unc ...

31.9 HINTS AND ANSWERS 31.9 Hints and answers 31.1 Note that the reading of 9.28 m s−^2 is clearly in error, and should not be u ...

STATISTICS This gives aχ^2 of 1.2 for one d.o.f and no evidence for the claim. 31.15 As the distribution at each value ofsis Poi ...

Index Where the discussion of a topic runs over two consecutive pages, reference is made only to the first of these. For discuss ...

INDEX general properties,seeanti-Hermitian matrices antisymmetric tensors, 938, 941 antithetic variates, in Monte Carlo methods, ...

INDEX recurrence relations, 611–612 second kindYν(x), 607 graph of, 607 series, 604 ν= 0, 606 ν=± 1 /2, 605 sphericalj(x), 615, ...

INDEX central limit theorem, 1194–1196 central moments,seemoments, central centre of a group, 1069 centre of mass, 195 of hemisp ...

INDEX complement, 1121 probability for, 1125 complementary equation, 490 complementary error function, 640 complementary functio ...

INDEX consistency, of estimator, 1230 constant coefficients in ODE, 492–503 auxiliary equation, 493 constants of integration, 62 ...