PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS, 7TH EDITION

38217_App_p662-690.qxd

12/20/06

09:48

Page 663

Appendix Tables

663

38217_App_p662-690.qxd

664

12/20/06

09:48

Page 664

Appendix Tables

Table A.1

x

Cumulative Binomial Probabilities

B(x; n, p) b(y; n, p)

a. n 5

y0

p

x

0 1 2 3 4

0.01

0.05

0.10

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.75

0.80

0.90

0.95

0.99

.951 .999 1.000 1.000 1.000

.774 .977 .999 1.000 1.000

.590 .919 .991 1.000 1.000

.328 .737 .942 .993 1.000

.237 .633 .896 .984 .999

.168 .528 .837 .969 .998

.078 .337 .683 .913 .990

.031 .188 .500 .812 .969

.010 .087 .317 .663 .922

.002 .031 .163 .472 .832

.001 .016 .104 .367 .763

.000 .007 .058 .263 .672

.000 .000 .009 .081 .410

.000 .000 .001 .023 .226

.000 .000 .000 .001 .049

b. n 10 p

x

0.01

0.05

0.10

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.75

0.80

0.90

0.95

0.99

0 1 2 3 4

.904 .996 1.000 1.000 1.000

.599 .914 .988 .999 1.000

.349 .736 .930 .987 .998

.107 .376 .678 .879 .967

.056 .244 .526 .776 .922

.028 .149 .383 .650 .850

.006 .046 .167 .382 .633

.001 .011 .055 .172 .377

.000 .002 .012 .055 .166

.000 .000 .002 .011 .047

.000 .000 .000 .004 .020

.000 .000 .000 .001 .006

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

5 6 7 8 9

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.994 .999 1.000 1.000 1.000

.980 .996 1.000 1.000 1.000

.953 .989 .998 1.000 1.000

.834 .945 .988 .998 1.000

.623 .828 .945 .989 .999

.367 .618 .833 .954 .994

.150 .350 .617 .851 .972

.078 .224 .474 .756 .944

.033 .121 .322 .624 .893

.002 .013 .070 .264 .651

.000 .001 .012 .086 .401

.000 .000 .000 .004 .096

c. n 15 p

x

0.01

0.05

0.10

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.75

0.80

0.90

0.95

0.99

0 1 2 3 4

.860 .990 1.000 1.000 1.000

.463 .829 .964 .995 .999

.206 .549 .816 .944 .987

.035 .167 .398 .648 .836

.013 .080 .236 .461 .686

.005 .035 .127 .297 .515

.000 .005 .027 .091 .217

.000 .000 .004 .018 .059

.000 .000 .000 .002 .009

.000 .000 .000 .000 .001

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

5 6 7 8 9

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.998 1.000 1.000 1.000 1.000

.939 .982 .996 .999 1.000

.852 .943 .983 .996 .999

.722 .869 .950 .985 .996

.402 .610 .787 .905 .966

.151 .304 .500 .696 .849

.034 .095 .213 .390 .597

.004 .015 .050 .131 .278

.001 .004 .017 .057 .148

.000 .001 .004 .018 .061

.000 .000 .000 .000 .002

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

10 11 12 13 14

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.999 1.000 1.000 1.000 1.000

.991 .998 1.000 1.000 1.000

.941 .982 .996 1.000 1.000

.783 .909 .973 .995 1.000

.485 .703 .873 .965 .995

.314 .539 .764 .920 .987

.164 .352 .602 .833 .965

.013 .056 .184 .451 .794

.001 .005 .036 .171 .537

.000 .000 .000 .010 .140

(continued )

38217_App_p662-690.qxd

12/20/06

09:48

Page 665

Appendix Tables

Table A.1

665

x

Cumulative Binomial Probabilities (cont.)

B(x; n, p) b(y; n, p)

d. n 20

y0

p

x

0.01

0.05

0.10

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.75

0.80

0.90

0.95

0.99

0 1 2 3 4

.818 .983 .999 1.000 1.000

.358 .736 .925 .984 .997

.122 .392 .677 .867 .957

.012 .069 .206 .411 .630

.003 .024 .091 .225 .415

.001 .008 .035 .107 .238

.000 .001 .004 .016 .051

.000 .000 .000 .001 .006

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

5 6 7 8 9

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.989 .998 1.000 1.000 1.000

.804 .913 .968 .990 .997

.617 .786 .898 .959 .986

.416 .608 .772 .887 .952

.126 .250 .416 .596 .755

.021 .058 .132 .252 .412

.002 .006 .021 .057 .128

.000 .000 .001 .005 .017

.000 .000 .000 .001 .004

.000 .000 .000 .000 .001

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

10 11 12 13 14

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.999 1.000 1.000 1.000 1.000

.996 .999 1.000 1.000 1.000

.983 .995 .999 1.000 1.000

.872 .943 .979 .994 .998

.588 .748 .868 .942 .979

.245 .404 .584 .750 .874

.048 .113 .228 .392 .584

.014 .041 .102 .214 .383

.003 .010 .032 .087 .196

.000 .000 .000 .002 .011

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

15 16 17 18 19

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.994 .999 1.000 1.000 1.000

.949 .984 .996 .999 1.000

.762 .893 .965 .992 .999

.585 .775 .909 .976 .997

.370 .589 .794 .931 .988

.043 .133 .323 .608 .878

.003 .016 .075 .264 .642

.000 .000 .001 .017 .182

(continued )

38217_App_p662-690.qxd

666

12/20/06

09:48

Page 666

Appendix Tables

Table A.1

x

Cumulative Binomial Probabilities (cont.)

B(x; n, p) b(y; n, p)

e. n 25

y0

p

x

0.01

0.05

0.10

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.75

0.80

0.90

0.95

0.99

0 1 2 3 4

.778 .974 .998 1.000 1.000

.277 .642 .873 .966 .993

.072 .271 .537 .764 .902

.004 .027 .098 .234 .421

.001 .007 .032 .096 .214

.000 .002 .009 .033 .090

.000 .000 .000 .002 .009

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

5 6 7 8 9

1.000 1.000 1.000 1.000 1.000

.999 1.000 1.000 1.000 1.000

.967 .991 .998 1.000 1.000

.617 .780 .891 .953 .983

.378 .561 .727 .851 .929

.193 .341 .512 .677 .811

.029 .074 .154 .274 .425

.002 .007 .022 .054 .115

.000 .000 .001 .004 .013

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

10 11 12 13 14

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.994 .998 1.000 1.000 1.000

.970 .980 .997 .999 1.000

.902 .956 .983 .994 .998

.586 .732 .846 .922 .966

.212 .345 .500 .655 .788

.034 .078 .154 .268 .414

.002 .006 .017 .044 .098

.000 .001 .003 .020 .030

.000 .000 .000 .002 .006

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

15 16 17 18 19

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.987 .996 .999 1.000 1.000

.885 .946 .978 .993 .998

.575 .726 .846 .926 .971

.189 .323 .488 .659 .807

.071 .149 .273 .439 .622

.017 .047 .109 .220 .383

.000 .000 .002 .009 .033

.000 .000 .000 .000 .001

.000 .000 .000 .000 .000

20 21 22 23 24

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

1.000 1.000 1.000 1.000 1.000

.991 .998 1.000 1.000 1.000

.910 .967 .991 .998 1.000

.786 .904 .968 .993 .999

.579 .766 .902 .973 .996

.098 .236 .463 .729 .928

.007 .034 .127 .358 .723

.000 .000 .002 .026 .222

x

e y F(x; ) y0 y!

Table A.2 Cumulative Poisson Probabilities

x

0 1 2 3 4 5 6

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.0

.905 .995 1.000

.819 .982 .999 1.000

.741 .963 .996 1.000

.670 .938 .992 .999 1.000

.607 .910 .986 .998 1.000

.549 .878 .977 .997 1.000

.497 .844 .966 .994 .999 1.000

.449 .809 .953 .991 .999 1.000

.407 .772 .937 .987 .998 1.000

.368 .736 .920 .981 .996 .999 1.000 (continued )

38217_App_p662-690.qxd

12/20/06

09:48

Page 667

Appendix Tables

Table A.2

667

x

Cumulative Poisson Probabilities (cont.)

e y F(x; ) y0 y!

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

15.0

20.0

0 1 2 3 4

.135 .406 .677 .857 .947

.050 .199 .423 .647 .815

.018 .092 .238 .433 .629

.007 .040 .125 .265 .440

.002 .017 .062 .151 .285

.001 .007 .030 .082 .173

.000 .003 .014 .042 .100

.000 .001 .006 .021 .055

.000 .000 .003 .010 .029

.000 .000 .000 .000 .001

.000 .000 .000 .000 .000

5 6 7 8 9

.983 .995 .999 1.000

.916 .966 .988 .996 .999

.785 .889 .949 .979 .992

.616 .762 .867 .932 .968

.446 .606 .744 .847 .916

.301 .450 .599 .729 .830

.191 .313 .453 .593 .717

.116 .207 .324 .456 .587

.067 .130 .220 .333 .458

.003 .008 .018 .037 .070

.000 .000 .001 .002 .005

1.000

.997 .999 1.000

.986 .995 .998 .999 1.000

.957 .980 .991 .996 .999

.901 .947 .973 .987 .994

.816 .888 .936 .966 .983

.706 .803 .876 .926 .959

.583 .697 .792 .864 .917

.118 .185 .268 .363 .466

.011 .021 .039 .066 .105

.999 1.000

.998 .999 1.000

.992 .996 .998 .999 1.000

.978 .989 .995 .998 .999

.951 .973 .986 .993 .997

.568 .664 .749 .819 .875

.157 .221 .297 .381 .470

1.000

.998 .999 1.000

.917 .947 .967 .981 .989

.559 .644 .721 .787 .843

.994 .997 .998 .999 1.000

.888 .922 .948 .966 .978

10 11 12 13 14

x

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

.987 .992 .995 .997 .999

35 36

.999 1.000

38217_App_p662-690.qxd

668

12/20/06

09:48

Page 668

Appendix Tables

Table A.3

Standard Normal Curve Areas

Φ(z) P(Z z) Standard normal density function Shaded area = Φ(z)

0

z

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

3.4 3.3 3.2 3.1 3.0

.0003 .0005 .0007 .0010 .0013

.0003 .0005 .0007 .0009 .0013

.0003 .0005 .0006 .0009 .0013

.0003 .0004 .0006 .0009 .0012

.0003 .0004 .0006 .0008 .0012

.0003 .0004 .0006 .0008 .0011

.0003 .0004 .0006 .0008 .0011

.0003 .0004 .0005 .0008 .0011

.0003 .0004 .0005 .0007 .0010

.0002 .0003 .0005 .0007 .0010

2.9 2.8 2.7 2.6 2.5

.0019 .0026 .0035 .0047 .0062

.0018 .0025 .0034 .0045 .0060

.0017 .0024 .0033 .0044 .0059

.0017 .0023 .0032 .0043 .0057

.0016 .0023 .0031 .0041 .0055

.0016 .0022 .0030 .0040 .0054

.0015 .0021 .0029 .0039 .0052

.0015 .0021 .0028 .0038 .0051

.0014 .0020 .0027 .0037 .0049

.0014 .0019 .0026 .0036 .0038

2.4 2.3 2.2 2.1 2.0

.0082 .0107 .0139 .0179 .0228

.0080 .0104 .0136 .0174 .0222

.0078 .0102 .0132 .0170 .0217

.0075 .0099 .0129 .0166 .0212

.0073 .0096 .0125 .0162 .0207

.0071 .0094 .0122 .0158 .0202

.0069 .0091 .0119 .0154 .0197

.0068 .0089 .0116 .0150 .0192

.0066 .0087 .0113 .0146 .0188

.0064 .0084 .0110 .0143 .0183

1.9 1.8 1.7 1.6 1.5

.0287 .0359 .0446 .0548 .0668

.0281 .0352 .0436 .0537 .0655

.0274 .0344 .0427 .0526 .0643

.0268 .0336 .0418 .0516 .0630

.0262 .0329 .0409 .0505 .0618

.0256 .0322 .0401 .0495 .0606

.0250 .0314 .0392 .0485 .0594

.0244 .0307 .0384 .0475 .0582

.0239 .0301 .0375 .0465 .0571

.0233 .0294 .0367 .0455 .0559

1.4 1.3 1.2 1.1 1.0

.0808 .0968 .1151 .1357 .1587

.0793 .0951 .1131 .1335 .1562

.0778 .0934 .1112 .1314 .1539

.0764 .0918 .1093 .1292 .1515

.0749 .0901 .1075 .1271 .1492

.0735 .0885 .1056 .1251 .1469

.0722 .0869 .1038 .1230 .1446

.0708 .0853 .1020 .1210 .1423

.0694 .0838 .1003 .1190 .1401

.0681 .0823 .0985 .1170 .1379

0.9 0.8 0.7 0.6 0.5

.1841 .2119 .2420 .2743 .3085

.1814 .2090 .2389 .2709 .3050

.1788 .2061 .2358 .2676 .3015

.1762 .2033 .2327 .2643 .2981

.1736 .2005 .2296 .2611 .2946

.1711 .1977 .2266 .2578 .2912

.1685 .1949 .2236 .2546 .2877

.1660 .1922 .2206 .2514 .2843

.1635 .1894 .2177 .2483 .2810

.1611 .1867 .2148 .2451 .2776

0.4 0.3 0.2 0.1 0.0

.3446 .3821 .4207 .4602 .5000

.3409 .3783 .4168 .4562 .4960

.3372 .3745 .4129 .4522 .4920

.3336 .3707 .4090 .4483 .4880

.3300 .3669 .4052 .4443 .4840

.3264 .3632 .4013 .4404 .4801

.3228 .3594 .3974 .4364 .4761

.3192 .3557 .3936 .4325 .4721

.3156 .3520 .3897 .4286 .4681

.3121 .3482 .3859 .4247 .4641 (continued )

38217_App_p662-690.qxd

12/20/06

09:48

Page 669

Appendix Tables

669

(z) P(Z z)

Table A.3 Standard Normal Curve Areas (cont.) z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0 0.1 0.2 0.3 0.4

.5000 .5398 .5793 .6179 .6554

.5040 .5438 .5832 .6217 .6591

.5080 .5478 .5871 .6255 .6628

.5120 .5517 .5910 .6293 .6664

.5160 .5557 .5948 .6331 .6700

.5199 .5596 .5987 .6368 .6736

.5239 .5636 .6026 .6406 .6772

.5279 .5675 .6064 .6443 .6808

.5319 .5714 .6103 .6480 .6844

.5359 .5753 .6141 .6517 .6879

0.5 0.6 0.7 0.8 0.9

.6915 .7257 .7580 .7881 .8159

.6950 .7291 .7611 .7910 .8186

.6985 .7324 .7642 .7939 .8212

.7019 .7357 .7673 .7967 .8238

.7054 .7389 .7704 .7995 .8264

.7088 .7422 .7734 .8023 .8289

.7123 .7454 .7764 .8051 .8315

.7157 .7486 .7794 .8078 .8340

.7190 .7517 .7823 .8106 .8365

.7224 .7549 .7852 .8133 .8389

1.0 1.1 1.2 1.3 1.4

.8413 .8643 .8849 .9032 .9192

.8438 .8665 .8869 .9049 .9207

.8461 .8686 .8888 .9066 .9222

.8485 .8708 .8907 .9082 .9236

.8508 .8729 .8925 .9099 .9251

.8531 .8749 .8944 .9115 .9265

.8554 .8770 .8962 .9131 .9278

.8577 .8790 .8980 .9147 .9292

.8599 .8810 .8997 .9162 .9306

.8621 .8830 .9015 .9177 .9319

1.5 1.6 1.7 1.8 1.9

.9332 .9452 .9554 .9641 .9713

.9345 .9463 .9564 .9649 .9719

.9357 .9474 .9573 .9656 .9726

.9370 .9484 .9582 .9664 .9732

.9382 .9495 .9591 .9671 .9738

.9394 .9505 .9599 .9678 .9744

.9406 .9515 .9608 .9686 .9750

.9418 .9525 .9616 .9693 .9756

.9429 .9535 .9625 .9699 .9761

.9441 .9545 .9633 .9706 .9767

2.0 2.1 2.2 2.3 2.4

.9772 .9821 .9861 .9893 .9918

.9778 .9826 .9864 .9896 .9920

.9783 .9830 .9868 .9898 .9922

.9788 .9834 .9871 .9901 .9925

.9793 .9838 .9875 .9904 .9927

.9798 .9842 .9878 .9906 .9929

.9803 .9846 .9881 .9909 .9931

.9808 .9850 .9884 .9911 .9932

.9812 .9854 .9887 .9913 .9934

.9817 .9857 .9890 .9916 .9936

2.5 2.6 2.7 2.8 2.9

.9938 .9953 .9965 .9974 .9981

.9940 .9955 .9966 .9975 .9982

.9941 .9956 .9967 .9976 .9982

.9943 .9957 .9968 .9977 .9983

.9945 .9959 .9969 .9977 .9984

.9946 .9960 .9970 .9978 .9984

.9948 .9961 .9971 .9979 .9985

.9949 .9962 .9972 .9979 .9985

.9951 .9963 .9973 .9980 .9986

.9952 .9964 .9974 .9981 .9986

3.0 3.1 3.2 3.3 3.4

.9987 .9990 .9993 .9995 .9997

.9987 .9991 .9993 .9995 .9997

.9987 .9991 .9994 .9995 .9997

.9988 .9991 .9994 .9996 .9997

.9988 .9992 .9994 .9996 .9997

.9989 .9992 .9994 .9996 .9997

.9989 .9992 .9994 .9996 .9997

.9989 .9992 .9995 .9996 .9997

.9990 .9993 .9995 .9996 .9997

.9990 .9993 .9995 .9997 .9998

38217_App_p662-690.qxd

670

12/20/06

09:48

Page 670

Appendix Tables

Table A.4

The Incomplete Gamma Function

F(x; )

(1)y x

1 y

e

dy

0

x

1

2

3

4

5

6

7

8

9

10

1 2 3 4

.632 .865 .950 .982

.264 .594 .801 .908

.080 .323 .577 .762

.019 .143 .353 .567

.004 .053 .185 .371

.001 .017 .084 .215

.000 .005 .034 .111

.000 .001 .012 .051

.000 .000 .004 .021

.000 .000 .001 .008

5 6 7 8 9

.993 .998 .999 1.000

.960 .983 .993 .997 .999

.875 .938 .970 .986 .994

.735 .849 .918 .958 .979

.560 .715 .827 .900 .945

.384 .554 .699 .809 .884

.238 .394 .550 .687 .793

.133 .256 .401 .547 .676

.068 .153 .271 .407 .544

.032 .084 .170 .283 .413

1.000

.997 .999 1.000

.990 .995 .998 .999 1.000

.971 .985 .992 .996 .998

.933 .962 .980 .989 .994

.870 .921 .954 .974 .986

.780 .857 .911 .946 .968

.667 .768 .845 .900 .938

.542 .659 .758 .834 .891

.999

.997

.992

.982

.963

.930

10 11 12 13 14 15

38217_App_p662-690.qxd

12/20/06

09:48

Page 671

671

Appendix Tables

Table A.5 Critical Values for t Distributions

t density curve Shaded area = 0

t ,

v

.10

.05

.025

.01

.005

.001

.0005

1 2 3 4

3.078 1.886 1.638 1.533

6.314 2.920 2.353 2.132

12.706 4.303 3.182 2.776

31.821 6.965 4.541 3.747

63.657 9.925 5.841 4.604

318.31 22.326 10.213 7.173

636.62 31.598 12.924 8.610

5 6 7 8 9

1.476 1.440 1.415 1.397 1.383

2.015 1.943 1.895 1.860 1.833

2.571 2.447 2.365 2.306 2.262

3.365 3.143 2.998 2.896 2.821

4.032 3.707 3.499 3.355 3.250

5.893 5.208 4.785 4.501 4.297

6.869 5.959 5.408 5.041 4.781

10 11 12 13 14

1.372 1.363 1.356 1.350 1.345

1.812 1.796 1.782 1.771 1.761

2.228 2.201 2.179 2.160 2.145

2.764 2.718 2.681 2.650 2.624

3.169 3.106 3.055 3.012 2.977

4.144 4.025 3.930 3.852 3.787

4.587 4.437 4.318 4.221 4.140

15 16 17 18 19

1.341 1.337 1.333 1.330 1.328

1.753 1.746 1.740 1.734 1.729

2.131 2.120 2.110 2.101 2.093

2.602 2.583 2.567 2.552 2.539

2.947 2.921 2.898 2.878 2.861

3.733 3.686 3.646 3.610 3.579

4.073 4.015 3.965 3.922 3.883

20 21 22 23 24

1.325 1.323 1.321 1.319 1.318

1.725 1.721 1.717 1.714 1.711

2.086 2.080 2.074 2.069 2.064

2.528 2.518 2.508 2.500 2.492

2.845 2.831 2.819 2.807 2.797

3.552 3.527 3.505 3.485 3.467

3.850 3.819 3.792 3.767 3.745

25 26 27 28 29

1.316 1.315 1.314 1.313 1.311

1.708 1.706 1.703 1.701 1.699

2.060 2.056 2.052 2.048 2.045

2.485 2.479 2.473 2.467 2.462

2.787 2.779 2.771 2.763 2.756

3.450 3.435 3.421 3.408 3.396

3.725 3.707 3.690 3.674 3.659

30 32 34 36 38

1.310 1.309 1.307 1.306 1.304

1.697 1.694 1.691 1.688 1.686

2.042 2.037 2.032 2.028 2.024

2.457 2.449 2.441 2.434 2.429

2.750 2.738 2.728 2.719 2.712

3.385 3.365 3.348 3.333 3.319

3.646 3.622 3.601 3.582 3.566

40 50 60 120 ∞

1.303 1.299 1.296 1.289 1.282

1.684 1.676 1.671 1.658 1.645

2.021 2.009 2.000 1.980 1.960

2.423 2.403 2.390 2.358 2.326

2.704 2.678 2.660 2.617 2.576

3.307 3.262 3.232 3.160 3.090

3.551 3.496 3.460 3.373 3.291

32.019 8.380 5.369 4.275 3.712 3.369 3.136 2.967 2.839 2.737 2.655 2.587 2.529 2.480 2.437 2.400 2.366 2.337 2.310 2.208 2.140 2.090 2.052 2.021 1.996 1.958 1.929 1.907 1.889 1.874 1.825 1.798 1.780 1.767 1.645

37.674 9.916 6.370 5.079 4.414 4.007 3.732 3.532 3.379 3.259 3.162 3.081 3.012 2.954 2.903 2.858 2.819 2.784 2.752 2.631 2.549 2.490 2.445 2.408 2.379 2.333 2.299 2.272 2.251 2.233 2.175 2.143 2.121 2.106 1.960

95%

% of Population Captured 90%

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Sample Size n 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 150 200 250 300

95%

48.430 12.861 8.299 6.634 5.775 5.248 4.891 4.631 4.433 4.277 4.150 4.044 3.955 3.878 3.812 3.754 3.702 3.656 3.615 3.457 3.350 3.272 3.213 3.165 3.126 3.066 3.021 2.986 2.958 2.934 2.859 2.816 2.788 2.767 2.576

99% 160.193 18.930 9.398 6.612 5.337 4.613 4.147 3.822 3.582 3.397 3.250 3.130 3.029 2.945 2.872 2.808 2.753 2.703 2.659 2.494 2.385 2.306 2.247 2.200 2.162 2.103 2.060 2.026 1.999 1.977 1.905 1.865 1.839 1.820 1.645

90%

Two-sided Intervals

188.491 22.401 11.150 7.855 6.345 5.488 4.936 4.550 4.265 4.045 3.870 3.727 3.608 3.507 3.421 3.345 3.279 3.221 3.168 2.972 2.841 2.748 2.677 2.621 2.576 2.506 2.454 2.414 2.382 2.355 2.270 2.222 2.191 2.169 1.960

95%

99%

242.300 29.055 14.527 10.260 8.301 7.187 6.468 5.966 5.594 5.308 5.079 4.893 4.737 4.605 4.492 4.393 4.307 4.230 4.161 3.904 3.733 3.611 3.518 3.444 3.385 3.293 3.225 3.173 3.130 3.096 2.983 2.921 2.880 2.850 2.576

99%

Tolerance Critical Values for Normal Population Distributions

20.581 6.156 4.162 3.407 3.006 2.756 2.582 2.454 2.355 2.275 2.210 2.155 2.109 2.068 2.033 2.002 1.974 1.949 1.926 1.838 1.777 1.732 1.697 1.669 1.646 1.609 1.581 1.559 1.542 1.527 1.478 1.450 1.431 1.417 1.282

90% 26.260 7.656 5.144 4.203 3.708 3.400 3.187 3.031 2.911 2.815 2.736 2.671 2.615 2.566 2.524 2.486 2.453 2.423 2.396 2.292 2.220 2.167 2.126 2.092 2.065 2.022 1.990 1.965 1.944 1.927 1.870 1.837 1.815 1.800 1.645

95%

95%

37.094 10.553 7.042 5.741 5.062 4.642 4.354 4.143 3.981 3.852 3.747 3.659 3.585 3.520 3.464 3.414 3.370 3.331 3.295 3.158 3.064 2.995 2.941 2.898 2.863 2.807 2.765 2.733 2.706 2.684 2.611 2.570 2.542 2.522 2.326

99% 103.029 13.995 7.380 5.362 4.411 3.859 3.497 3.241 3.048 2.898 2.777 2.677 2.593 2.522 2.460 2.405 2.357 2.314 2.276 2.129 2.030 1.957 1.902 1.857 1.821 1.764 1.722 1.688 1.661 1.639 1.566 1.524 1.496 1.476 1.282

90%

One-sided Intervals

131.426 17.370 9.083 6.578 5.406 4.728 4.285 3.972 3.738 3.556 3.410 3.290 3.189 3.102 3.028 2.963 2.905 2.854 2.808 2.633 2.516 2.430 2.364 2.312 2.269 2.202 2.153 2.114 2.082 2.056 1.971 1.923 1.891 1.868 1.645

95%

99%

185.617 23.896 12.387 8.939 7.335 6.412 5.812 5.389 5.074 4.829 4.633 4.472 4.337 4.222 4.123 4.037 3.960 3.892 3.832 3.601 3.447 3.334 3.249 3.180 3.125 3.038 2.974 2.924 2.883 2.850 2.741 2.679 2.638 2.608 2.326

99%

672

Confidence Level

Table A.6

38217_App_p662-690.qxd 12/20/06 09:48 Page 672

Appendix Tables

38217_App_p662-690.qxd

12/20/06

09:48

Page 673

673

Appendix Tables

Table A.7

2 density curve

Critical Values for Chi-Squared Distributions

Shaded area =

0

2,

.995

.99

.975

.95

.90

.10

.05

.025

.01

.005

1 2 3 4 5

0.000 0.010 0.072 0.207 0.412

0.000 0.020 0.115 0.297 0.554

0.001 0.051 0.216 0.484 0.831

0.004 0.103 0.352 0.711 1.145

0.016 0.211 0.584 1.064 1.610

2.706 4.605 6.251 7.779 9.236

3.843 5.992 7.815 9.488 11.070

5.025 7.378 9.348 11.143 12.832

6.637 9.210 11.344 13.277 15.085

7.882 10.597 12.837 14.860 16.748

6 7 8 9 10

0.676 0.989 1.344 1.735 2.156

0.872 1.239 1.646 2.088 2.558

1.237 1.690 2.180 2.700 3.247

1.635 2.167 2.733 3.325 3.940

2.204 2.833 3.490 4.168 4.865

10.645 12.017 13.362 14.684 15.987

12.592 14.067 15.507 16.919 18.307

14.440 16.012 17.534 19.022 20.483

16.812 18.474 20.090 21.665 23.209

18.548 20.276 21.954 23.587 25.188

11 12 13 14 15

2.603 3.074 3.565 4.075 4.600

3.053 3.571 4.107 4.660 5.229

3.816 4.404 5.009 5.629 6.262

4.575 5.226 5.892 6.571 7.261

5.578 6.304 7.041 7.790 8.547

17.275 18.549 19.812 21.064 22.307

19.675 21.026 22.362 23.685 24.996

21.920 23.337 24.735 26.119 27.488

24.724 26.217 27.687 29.141 30.577

26.755 28.300 29.817 31.319 32.799

16 17 18 19 20

5.142 5.697 6.265 6.843 7.434

5.812 6.407 7.015 7.632 8.260

6.908 7.564 8.231 8.906 9.591

7.962 8.682 9.390 10.117 10.851

9.312 10.085 10.865 11.651 12.443

23.542 24.769 25.989 27.203 28.412

26.296 27.587 28.869 30.143 31.410

28.845 30.190 31.526 32.852 34.170

32.000 33.408 34.805 36.190 37.566

34.267 35.716 37.156 38.580 39.997

21 22 23 24 25

8.033 8.643 9.260 9.886 10.519

8.897 9.542 10.195 10.856 11.523

10.283 10.982 11.688 12.401 13.120

11.591 12.338 13.090 13.848 14.611

13.240 14.042 14.848 15.659 16.473

29.615 30.813 32.007 33.196 34.381

32.670 33.924 35.172 36.415 37.652

35.478 36.781 38.075 39.364 40.646

38.930 40.289 41.637 42.980 44.313

41.399 42.796 44.179 45.558 46.925

26 27 28 29 30

11.160 11.807 12.461 13.120 13.787

12.198 12.878 13.565 14.256 14.954

13.844 14.573 15.308 16.147 16.791

15.379 16.151 16.928 17.708 18.493

17.292 18.114 18.939 19.768 20.599

35.563 36.741 37.916 39.087 40.256

38.885 40.113 41.337 42.557 43.773

41.923 43.194 44.461 45.772 46.979

45.642 46.962 48.278 49.586 50.892

48.290 49.642 50.993 52.333 53.672

31 32 33 34 35

14.457 15.134 15.814 16.501 17.191

15.655 16.362 17.073 17.789 18.508

17.538 18.291 19.046 19.806 20.569

19.280 20.072 20.866 21.664 22.465

21.433 22.271 23.110 23.952 24.796

41.422 42.585 43.745 44.903 46.059

44.985 46.194 47.400 48.602 49.802

48.231 49.480 50.724 51.966 53.203

52.190 53.486 54.774 56.061 57.340

55.000 56.328 57.646 58.964 60.272

36 37 38 39 40

17.887 18.584 19.289 19.994 20.706

19.233 19.960 20.691 21.425 22.164

21.336 22.105 22.878 23.654 24.433

23.269 24.075 24.884 25.695 26.509

25.643 26.492 27.343 28.196 29.050

47.212 48.363 49.513 50.660 51.805

50.998 52.192 53.384 54.572 55.758

54.437 55.667 56.896 58.119 59.342

58.619 59.891 61.162 62.426 63.691

61.581 62.880 64.181 65.473 66.766

2 For 40, 2, 1 z 9

2 9

3

38217_App_p662-690.qxd

674

12/20/06

09:48

Page 674

Appendix Tables

Table A.8

t Curve Tail Areas t curve

Area to the right of t 0 t

t

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

0.0 0.1 0.2 0.3 0.4 0.5

.500 .468 .437 .407 .379 .352

.500 .465 .430 .396 .364 .333

.500 .463 .427 .392 .358 .326

.500 .463 .426 .390 .355 .322

.500 .462. .425 .388 .353 .319

.500 .462 .424 .387 .352 .317

.500 .462 .424 .386 .351 .316

.500 .461 .423 .386 .350 .315

.500 .461 .423 .386 .349 .315

.500 .461 .423 .385 .349 .314

.500 .461 .423 .385 .348 .313

.500 .461 .422 .385 .348 .313

.500 .461 .422 .384 .348 .313

.500 .461 .422 .384 .347 .312

.500 .461 .422 .384 .347 .312

.500 .461 .422 .384 .347 .312

.500 .461 .422 .384 .347 .312

.500 .461 .422 .384 .347 .312

0.6 0.7 0.8 0.9 1.0

.328 .306 .285 .267 .250

.305 .278 .254 .232 .211

.295 .267 .241 .217 .196

.290 .261 .234 .210 .187

.287 .258 .230 .205 .182

.285 .255 .227 .201 .178

.284 .253 .225 .199 .175

.283 .252 .223 .197 .173

.282 .251 .222 .196 .172

.281 .250 .221 .195 .170

.280 .249 .220 .194 .169

.280 .249 .220 .193 .169

.279 .248 .219 .192 .168

.279 .247 .218 .191 .167

.279 .247 .218 .191 .167

.278 .247 .218 .191 .166

.278 .247 .217 .190 .166

.278 .246 .217 .190 .165

1.1 1.2 1.3 1.4 1.5

.235 .221 .209 .197 .187

.193 .177 .162 .148 .136

.176 .158 .142 .128 .115

.167 .148 .132 .117 .104

.162 .142 .125 .110 .097

.157 .138 .121 .106 .092

.154 .135 .117 .102 .089

.152 .132 .115 .100 .086

.150 .130 .113 .098 .084

.149 .129 .111 .096 .082

.147 .128 .110 .095 .081

.146 .127 .109 .093 .080

.146 .126 .108 .092 .079

.144 .124 .107 .091 .077

.144 .124 .107 .091 .077

.144 .124 .106 .090 .077

.143 .123 .105 .090 .076

.143 .123 .105 .089 .075

1.6 1.7 1.8 1.9 2.0

.178 .169 .161 .154 .148

.125 .116 .107 .099 .092

.104 .094 .085 .077 .070

.092 .082 .073 .065 .058

.085 .075 .066 .058 .051

.080 .070 .061 .053 .046

.077 .065 .057 .050 .043

.074 .064 .055 .047 .040

.072 .062 .053 .045 .038

.070 .060 .051 .043 .037

.069 .059 .050 .042 .035

.068 .057 .049 .041 .034

.067 .056 .048 .040 .033

.065 .055 .046 .038 .032

.065 .055 .046 .038 .032

.065 .054 .045 .038 .031

.064 .054 .045 .037 .031

.064 .053 .044 .037 .030

2.1 2.2 2.3 2.4 2.5

.141 .136 .131 .126 .121

.085 .079 .074 .069 .065

.063 .058 .052 .048 .044

.052 .046 .041 .037 .033

.045 .040 .035 .031 .027

.040 .035 .031 .027 .023

.037 .032 .027 .024 .020

.034 .029 .025 .022 .018

.033 .028 .023 .020 .017

.031 .026 .022 .019 .016

.030 .025 .021 .018 .015

.029 .024 .020 .017 .014

.028 .023 .019 .016 .013

.027 .022 .018 .015 .012

.027 .022 .018 .015 .012

.026 .021 .018 .014 .012

.025 .021 .017 .014 .011

.025 .021 .017 .014 .011

2.6 2.7 2.8 2.9 3.0

.117 .113 .109 .106 .102

.061 .057 .054 .051 .048

.040 .037 .034 .031 .029

.030 .027 .024 .022 .020

.024 .021 .019 .017 .015

.020 .018 .016 .014 .012

.018 .015 .013 .011 .010

.016 .014 .012 .010 .009

.014 .012 .010 .009 .007

.013 .011 .009 .008 .007

.012 .010 .009 .007 .006

.012 .010 .008 .007 .006

.011 .009 .008 .006 .005

.010 .008 .007 .005 .004

.010 .008 .007 .005 .004

.010 .008 .006 .005 .004

.009 .008 .006 .005 .004

.009 .007 .006 .005 .004

3.1 3.2 3.3 3.4 3.5

.099 .096 .094 .091 .089

.045 .043 .040 .038 .036

.027 .025 .023 .021 .020

.018 .016 .015 .014 .012

.013 .012 .011 .010 .009

.011 .009 .008 .007 .006

.009 .008 .007 .006 .005

.007 .006 .005 .005 .004

.006 .005 .005 .004 .003

.006 .005 .004 .003 .003

.005 .004 .004 .003 .002

.005 .004 .003 .003 .002

.004 .003 .003 .002 .002

.004 .003 .002 .002 .002

.004 .003 .002 .002 .002

.003 .003 .002 .002 .001

.003 .003 .002 .002 .001

.003 .002 .002 .002 .001

3.6 3.7 3.8 3.9 4.0

.086 .084 .082 .080 .078

.035 .033 .031 .030 .029

.018 .017 .016 .015 .014

.011 .010 .010 .009 .008

.008 .007 .006 .006 .005

.006 .005 .004 .004 .004

.004 .004 .003 .003 .003

.004 .003 .003 .002 .002

.003 .002 .002 .002 .002

.002 .002 .002 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .001 .001 .001 .001

.001 .001 .001 .001 .001

.001 .001 .001 .001 .001

.001 .001 .001 .001 .001

.001 .001 .001 .001 .000

.001 .001 .001 .001 .000

(continued )

38217_App_p662-690.qxd

12/20/06

09:48

Page 675

Appendix Tables

Table A.8

675

t Curve Tail Areas (cont.) t curve

Area to the right of t 0 t

19

20

21

22

23

24

25

26

27

28

29

30

35

40

60

120

( z)

0.0 0.1 0.2 0.3 0.4 0.5

.500 .461 .422 .384 .347 .311

.500 .461 .422 .384 .347 .311

.500 .461 .422 .384 .347 .311

.500 .461 .422 .383 .347 .311

.500 .461 .422 .383 .346 .311

.500 .461 .422 .383 .346 .311

.500 .461 .422 .383 .346 .311

.500 .461 .422 .383 .346 .311

.500 .461 .421 .383 .346 .311

.500 .461 .421 .383 .346 .310

.500 .461 .421 .383 .346 .310

.500 .461 .421 .383 .346 .310

.500 .460 .421 .383 .346 .310

.500 .460 .421 .383 .346 .310

.500 .460 .421 .383 .345 .309

.500 .460 .421 .382 .345 .309

.500 .460 .421 .382 .345 .309

0.6 0.7 0.8 0.9 1.0

.278 .246 .217 .190 .165

.278 .246 .217 .189 .165

.278 .246 .216 .189 .164

.277 .246 .216 .189 .164

.277 .245 .216 .189 .164

.277 .245 .216 .189 .164

.277 .245 .216 .188 .163

.277 .245 .215 .188 .163

.277 .245 .215 .188 .163

.277 .245 .215 .188 .163

.277 .245 .215 .188 .163

.277 .245 .215 .188 .163

.276 .244 .215 .187 .162

.276 .244 .214 .187 .162

.275 .243 .213 .186 .161

.275 .243 .213 .185 .160

.274 .242 .212 .184 .159

1.1 1.2 1.3 1.4 1.5

.143 .122 .105 .089 .075

.142 .122 .104 .089 .075

.142 .122 .104 .088 .074

.142 .121 .104 .088 .074

.141 .121 .103 .087 .074

.141 .121 .103 .087 .073

.141 .121 .103 .087 .073

.141 .120 .103 .087 .073

.141 .120 .102 .086 .073

.140 .120 .102 .086 .072

.140 .120 .102 .086 .072

.140 .120 .102 .086 .072

.139 .119 .101 .085 .071

.139 .119 .101 .085 .071

.138 .117 .099 .083 .069

.137 .116 .098 .082 .068

.136 .115 .097 .081 .067

1.6 1.7 1.8 1.9 2.0

.063 .053 .044 .036 .030

.063 .052 .043 .036 .030

.062 .052 .043 .036 .029

.062 .052 .043 .035 .029

.062 .051 .042 .035 .029

.061 .051 .042 .035 .028

.061 .051 .042 .035 .028

.061 .051 .042 .034 .028

.061 .050 .042 .034 .028

.060 .050 .041 .034 .028

.060 .050 .041 .034 .027

.060 .050 .041 .034 .027

.059 .049 .040 .033 .027

.059 .048 .040 .032 .026

.057 .047 .038 .031 .025

.056 .046 .037 .030 .024

.055 .045 .036 .029 .023

2.1 2.2 2.3 2.4 2.5

.025 .020 .016 .013 .011

.024 .020 .016 .013 .011

.024 .020 .016 .013 .010

.024 .019 .016 .013 .010

.023 .019 .015 .012 .010

.023 .019 .015 .012 .010

.023 .019 .015 .012 .010

.023 .018 .015 .012 .010

.023 .018 .015 .012 .009

.022 .018 .015 .012 .009

.022 .018 .014 .012 .009

.022 .018 .014 .011 .009

.022 .017 .014 .011 .009

.021 .017 .013 .011 .008

.020 .016 .012 .010 .008

.019 .015 .012 .009 .007

.018 .014 .011 .008 .006

2.6 2.7 2.8 2.9 3.0

.009 .007 .006 .005 .004

.009 .007 .006 .004 .004

.008 .007 .005 .004 .003

.008 .007 .005 .004 .003

.008 .006 .005 .004 .003

.008 .006 .005 .004 .003

.008 .006 .005 .004 .003

.008 .006 .005 .004 .003

.007 .006 .005 .004 .003

.007 .006 .005 .004 .003

.007 .006 .005 .004 .003

.007 .006 .004 .003 .003

.007 .005 .004 .003 .002

.007 .005 .004 .003 .002

.006 .004 .003 .003 .002

.005 .004 .003 .002 .002

.005 .003 .003 .002 .001

3.1 3.2 3.3 3.4 3.5

.003 .002 .002 .002 .001

.003 .002 .002 .001 .001

.003 .002 .002 .001 .001

.003 .002 .002 .001 .001

.003 .002 .002 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .002 .001 .001 .001

.002 .001 .001 .001 .001

.002 .001 .001 .001 .001

.001 .001 .001 .001 .000

.001 .001 .001 .000 .000

.001 .001 .000 .000 .000

3.6 3.7 3.8 3.9 4.0

.001 .001 .001 .000 .000

.001 .001 .001 .000 .000

.001 .001 .001 .000 .000

.001 .001 .000 .000 .000

.001 .001 .000 .000 .000

.001 .001 .000 .000 .000

.001 .001 .000 .000 .000

.001 .001 .000 .000 .000

.001 .000 .000 .000 .000

.001 .000 .000 .000 .000

.001 .000 .000 .000 .000

.001 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

.000 .000 .000 .000 .000

t

38217_App_p662-690.qxd

676

12/20/06

09:48

Page 676

Appendix Tables

Table A.9 Critical Values for F Distributions

2 denominator df

1 numerator df

1

2

3

4

5

6

7

8

9

1

.100 .050 .010 .001

39.86 161.45 4052.2 405284

49.50 199.50 4999.5 500000

53.59 215.71 5403.4 540379

55.83 224.58 5624.6 562500

57.24 230.16 5763.6 576405

58.20 233.99 5859.0 585937

58.91 236.77 5928.4 592873

59.44 238.88 5981.1 598144

59.86 240.54 6022.5 602284

2

.100 .050 .010 .001

8.53 18.51 98.50 998.50

9.00 19.00 99.00 999.00

9.16 19.16 99.17 999.17

9.24 19.25 99.25 999.25

9.29 19.30 99.30 999.30

9.33 19.33 99.33 999.33

9.35 19.35 99.36 999.36

9.37 19.37 99.37 999.37

9.38 19.38 99.39 999.39

3

.100 .050 .010 .001

5.54 10.13 34.12 167.03

5.46 9.55 30.82 148.50

5.39 9.28 29.46 141.11

5.34 9.12 28.71 137.10

5.31 9.01 28.24 134.58

5.28 8.94 27.91 132.85

5.27 8.89 27.67 131.58

5.25 8.85 27.49 130.62

5.24 8.81 27.35 129.86

4

.100 .050 .010 .001

4.54 7.71 21.20 74.14

4.32 6.94 18.00 61.25

4.19 6.59 16.69 56.18

4.11 6.39 15.98 53.44

4.05 6.26 15.52 51.71

4.01 6.16 15.21 50.53

3.98 6.09 14.98 49.66

3.95 6.04 14.80 49.00

3.94 6.00 14.66 48.47

5

.100 .050 .010 .001

4.06 6.61 16.26 47.18

3.78 5.79 13.27 37.12

3.62 5.41 12.06 33.20

3.52 5.19 11.39 31.09

3.45 5.05 10.97 29.75

3.40 4.95 10.67 28.83

3.37 4.88 10.46 28.16

3.34 4.82 10.29 27.65

3.32 4.77 10.16 27.24

6

.100 .050 .010 .001

3.78 5.99 13.75 35.51

3.46 5.14 10.92 27.00

3.29 4.76 9.78 23.70

3.18 4.53 9.15 21.92

3.11 4.39 8.75 20.80

3.05 4.28 8.47 20.03

3.01 4.21 8.26 19.46

2.98 4.15 8.10 19.03

2.96 4.10 7.98 18.69

7

.100 .050 .010 .001

3.59 5.59 12.25 29.25

3.26 4.74 9.55 21.69

3.07 4.35 8.45 18.77

2.96 4.12 7.85 17.20

2.88 3.97 7.46 16.21

2.83 3.87 7.19 15.52

2.78 3.79 6.99 15.02

2.75 3.73 6.84 14.63

2.72 3.68 6.72 14.33

8

.100 .050 .010 .001

3.46 5.32 11.26 25.41

3.11 4.46 8.65 18.49

2.92 4.07 7.59 15.83

2.81 3.84 7.01 14.39

2.73 3.69 6.63 13.48

2.67 3.58 6.37 12.86

2.62 3.50 6.18 12.40

2.59 3.44 6.03 12.05

2.56 3.39 5.91 11.77

9

.100 .050 .010 .001

3.36 5.12 10.56 22.86

3.01 4.26 8.02 16.39

2.81 3.86 6.99 13.90

2.69 3.63 6.42 12.56

2.61 3.48 6.06 11.71

2.55 3.37 5.80 11.13

2.51 3.29 5.61 10.70

2.47 3.23 5.47 10.37

2.44 3.18 5.35 10.11

10

.100 .050 .010 .001

3.29 4.96 10.04 21.04

2.92 4.10 7.56 14.91

2.73 3.71 6.55 12.55

2.61 3.48 5.99 11.28

2.52 3.33 5.64 10.48

2.46 3.22 5.39 9.93

2.41 3.14 5.20 9.52

2.38 3.07 5.06 9.20

2.35 3.02 4.94 8.96

11

.100 .050 .010 .001

3.23 4.84 9.65 19.69

2.86 3.98 7.21 13.81

2.66 3.59 6.22 11.56

2.54 3.36 5.67 10.35

2.45 3.20 5.32 9.58

2.39 3.09 5.07 9.05

2.34 3.01 4.89 8.66

2.30 2.95 4.74 8.35

2.27 2.90 4.63 8.12

12

.100 .050 .010 .001

3.18 4.75 9.33 18.64

2.81 3.89 6.93 12.97

2.61 3.49 5.95 10.80

2.48 3.26 5.41 9.63

2.39 3.11 5.06 8.89

2.33 3.00 4.82 8.38

2.28 2.91 4.64 8.00

2.24 2.85 4.50 7.71

2.21 2.80 4.39 7.48 (continued )

38217_App_p662-690.qxd

12/20/06

09:48

Page 677

Appendix Tables

Table A.9

677

Critical Values for F Distributions (cont.) 1 numerator df

10

12

15

20

25

30

40

50

60

120

1000

60.19 241.88 6055.8 605621

60.71 243.91 6106.3 610668

61.22 245.95 6157.3 615764

61.74 248.01 6208.7 620908

62.05 249.26 6239.8 624017

62.26 250.10 6260.6 626099

62.53 251.14 6286.8 628712

62.69 251.77 6302.5 630285

62.79 252.20 6313.0 631337

63.06 253.25 6339.4 633972

63.30 254.19 6362.7 636301

9.39 19.40 99.40 999.40

9.41 19.41 99.42 999.42

9.42 19.43 99.43 999.43

9.44 19.45 99.45 999.45

9.45 19.46 99.46 999.46

9.46 19.46 99.47 999.47

9.47 19.47 99.47 999.47

9.47 19.48 99.48 999.48

9.47 19.48 99.48 999.48

9.48 19.49 99.49 999.49

9.49 19.49 99.50 999.50

5.23 8.79 27.23 129.25

5.22 8.74 27.05 128.32

5.20 8.70 26.87 127.37

5.18 8.66 26.69 126.42

5.17 8.63 26.58 125.84

5.17 8.62 26.50 125.45

5.16 8.59 26.41 124.96

5.15 8.58 26.35 124.66

5.15 8.57 26.32 124.47

5.14 8.55 26.22 123.97

5.13 8.53 26.14 123.53

3.92 5.96 14.55 48.05

3.90 5.91 14.37 47.41

3.87 5.86 14.20 46.76

3.84 5.80 14.02 46.10

3.83 5.77 13.91 45.70

3.82 5.75 13.84 45.43

3.80 5.72 13.75 45.09

3.80 5.70 13.69 44.88

3.79 5.69 13.65 44.75

3.78 5.66 13.56 44.40

3.76 5.63 13.47 44.09

3.30 4.74 10.05 26.92

3.27 4.68 9.89 26.42

3.24 4.62 9.72 25.91

3.21 4.56 9.55 25.39

3.19 4.52 9.45 25.08

3.17 4.50 9.38 24.87

3.16 4.46 9.29 24.60

3.15 4.44 9.24 24.44

3.14 4.43 9.20 24.33

3.12 4.40 9.11 24.06

3.11 4.37 9.03 23.82

2.94 4.06 7.87 18.41

2.90 4.00 7.72 17.99

2.87 3.94 7.56 17.56

2.84 3.87 7.40 17.12

2.81 3.83 7.30 16.85

2.80 3.81 7.23 16.67

2.78 3.77 7.14 16.44

2.77 3.75 7.09 16.31

2.76 3.74 7.06 16.21

2.74 3.70 6.97 15.98

2.72 3.67 6.89 15.77

2.70 3.64 6.62 14.08

2.67 3.57 6.47 13.71

2.63 3.51 6.31 13.32

2.59 3.44 6.16 12.93

2.57 3.40 6.06 12.69

2.56 3.38 5.99 12.53

2.54 3.34 5.91 12.33

2.52 3.32 5.86 12.20

2.51 3.30 5.82 12.12

2.49 3.27 5.74 11.91

2.47 3.23 5.66 11.72

2.54 3.35 5.81 11.54

2.50 3.28 5.67 11.19

2.46 3.22 5.52 10.84

2.42 3.15 5.36 10.48

2.40 3.11 5.26 10.26

2.38 3.08 5.20 10.11

2.36 3.04 5.12 9.92

2.35 3.02 5.07 9.80

2.34 3.01 5.03 9.73

2.32 2.97 4.95 9.53

2.30 2.93 4.87 9.36

2.42 3.14 5.26 9.89

2.38 3.07 5.11 9.57

2.34 3.01 4.96 9.24

2.30 2.94 4.81 8.90

2.27 2.89 4.71 8.69

2.25 2.86 4.65 8.55

2.23 2.83 4.57 8.37

2.22 2.80 4.52 8.26

2.21 2.79 4.48 8.19

2.18 2.75 4.40 8.00

2.16 2.71 4.32 7.84

2.32 2.98 4.85 8.75

2.28 2.91 4.71 8.45

2.24 2.85 4.56 8.13

2.20 2.77 4.41 7.80

2.17 2.73 4.31 7.60

2.16 2.70 4.25 7.47

2.13 2.66 4.17 7.30

2.12 2.64 4.12 7.19

2.11 2.62 4.08 7.12

2.08 2.58 4.00 6.94

2.06 2.54 3.92 6.78

2.25 2.85 4.54 7.92

2.21 2.79 4.40 7.63

2.17 2.72 4.25 7.32

2.12 2.65 4.10 7.01

2.10 2.60 4.01 6.81

2.08 2.57 3.94 6.68

2.05 2.53 3.86 6.52

2.04 2.51 3.81 6.42

2.03 2.49 3.78 6.35

2.00 2.45 3.69 6.18

1.98 2.41 3.61 6.02

2.19 2.75 4.30 7.29

2.15 2.69 4.16 7.00

2.10 2.62 4.01 6.71

2.06 2.54 3.86 6.40

2.03 2.50 3.76 6.22

2.01 2.47 3.70 6.09

1.99 2.43 3.62 5.93

1.97 2.40 3.57 5.83

1.96 2.38 3.54 5.76

1.93 2.34 3.45 5.59

1.91 2.30 3.37 5.44 (continued )

38217_App_p662-690.qxd

678

12/20/06

09:48

Page 678

Appendix Tables

Table A.9

Critical Values for F Distributions (cont.)

2 denominator df

1 numerator df

1

2

3

4

5

6

7

8

9

13

.100 .050 .010 .001

3.14 4.67 9.07 17.82

2.76 3.81 6.70 12.31

2.56 3.41 5.74 10.21

2.43 3.18 5.21 9.07

2.35 3.03 4.86 8.35

2.28 2.92 4.62 7.86

2.23 2.83 4.44 7.49

2.20 2.77 4.30 7.21

2.16 2.71 4.19 6.98

14

.100 .050 .010 .001

3.10 4.60 8.86 17.14

2.73 3.74 6.51 11.78

2.52 3.34 5.56 9.73

2.39 3.11 5.04 8.62

2.31 2.96 4.69 7.92

2.24 2.85 4.46 7.44

2.19 2.76 4.28 7.08

2.15 2.70 4.14 6.80

2.12 2.65 4.03 6.58

15

.100 .050 .010 .001

3.07 4.54 8.68 16.59

2.70 3.68 6.36 11.34

2.49 3.29 5.42 9.34

2.36 3.06 4.89 8.25

2.27 2.90 4.56 7.57

2.21 2.79 4.32 7.09

2.16 2.71 4.14 6.74

2.12 2.64 4.00 6.47

2.09 2.59 3.89 6.26

16

.100 .050 .010 .001

3.05 4.49 8.53 16.12

2.67 3.63 6.23 10.97

2.46 3.24 5.29 9.01

2.33 3.01 4.77 7.94

2.24 2.85 4.44 7.27

2.18 2.74 4.20 6.80

2.13 2.66 4.03 6.46

2.09 2.59 3.89 6.19

2.06 2.54 3.78 5.98

17

.100 .050 .010 .001

3.03 4.45 8.40 15.72

2.64 3.59 6.11 10.66

2.44 3.20 5.19 8.73

2.31 2.96 4.67 7.68

2.22 2.81 4.34 7.02

2.15 2.70 4.10 6.56

2.10 2.61 3.93 6.22

2.06 2.55 3.79 5.96

2.03 2.49 3.68 5.75

18

.100 .050 .010 .001

3.01 4.41 8.29 15.38

2.62 3.55 6.01 10.39

2.42 3.16 5.09 8.49

2.29 2.93 4.58 7.46

2.20 2.77 4.25 6.81

2.13 2.66 4.01 6.35

2.08 2.58 3.84 6.02

2.04 2.51 3.71 5.76

2.00 2.46 3.60 5.56

19

.100 .050 .010 .001

2.99 4.38 8.18 15.08

2.61 3.52 5.93 10.16

2.40 3.13 5.01 8.28

2.27 2.90 4.50 7.27

2.18 2.74 4.17 6.62

2.11 2.63 3.94 6.18

2.06 2.54 3.77 5.85

2.02 2.48 3.63 5.59

1.98 2.42 3.52 5.39

20

.100 .050 .010 .001

2.97 4.35 8.10 14.82

2.59 3.49 5.85 9.95

2.38 3.10 4.94 8.10

2.25 2.87 4.43 7.10

2.16 2.71 4.10 6.46

2.09 2.60 3.87 6.02

2.04 2.51 3.70 5.69

2.00 2.45 3.56 5.44

1.96 2.39 3.46 5.24

21

.100 .050 .010 .001

2.96 4.32 8.02 14.59

2.57 3.47 5.78 9.77

2.36 3.07 4.87 7.94

2.23 2.84 4.37 6.95

2.14 2.68 4.04 6.32

2.08 2.57 3.81 5.88

2.02 2.49 3.64 5.56

1.98 2.42 3.51 5.31

1.95 2.37 3.40 5.11

22

.100 .050 .010 .001

2.95 4.30 7.95 14.38

2.56 3.44 5.72 9.61

2.35 3.05 4.82 7.80

2.22 2.82 4.31 6.81

2.13 2.66 3.99 6.19

2.06 2.55 3.76 5.76

2.01 2.46 3.59 5.44

1.97 2.40 3.45 5.19

1.93 2.34 3.35 4.99

23

.100 .050 .010 .001

2.94 4.28 7.88 14.20

2.55 3.42 5.66 9.47

2.34 3.03 4.76 7.67

2.21 2.80 4.26 6.70

2.11 2.64 3.94 6.08

2.05 2.53 3.71 5.65

1.99 2.44 3.54 5.33

1.95 2.37 3.41 5.09

1.92 2.32 3.30 4.89

24

.100 .050 .010 .001

2.93 4.26 7.82 14.03

2.54 3.40 5.61 9.34

2.33 3.01 4.72 7.55

2.19 2.78 4.22 6.59

2.10 2.62 3.90 5.98

2.04 2.51 3.67 5.55

1.98 2.42 3.50 5.23

1.94 2.36 3.36 4.99

1.91 2.30 3.26 4.80 (continued )

38217_App_p662-690.qxd

Table A.9

12/20/06

09:48

Page 679

Appendix Tables

679


10

12

15

20

25

30

40

50

60

120

1000

2.14 2.67 4.10 6.80

2.10 2.60 3.96 6.52

2.05 2.53 3.82 6.23

2.01 2.46 3.66 5.93

1.98 2.41 3.57 5.75

1.96 2.38 3.51 5.63

1.93 2.34 3.43 5.47

1.92 2.31 3.38 5.37

1.90 2.30 3.34 5.30

1.88 2.25 3.25 5.14

1.85 2.21 3.18 4.99

2.10 2.60 3.94 6.40

2.05 2.53 3.80 6.13

2.01 2.46 3.66 5.85

1.96 2.39 3.51 5.56

1.93 2.34 3.41 5.38

1.91 2.31 3.35 5.25

1.89 2.27 3.27 5.10

1.87 2.24 3.22 5.00

1.86 2.22 3.18 4.94

1.83 2.18 3.09 4.77

1.80 2.14 3.02 4.62

2.06 2.54 3.80 6.08

2.02 2.48 3.67 5.81

1.97 2.40 3.52 5.54

1.92 2.33 3.37 5.25

1.89 2.28 3.28 5.07

1.87 2.25 3.21 4.95

1.85 2.20 3.13 4.80

1.83 2.18 3.08 4.70

1.82 2.16 3.05 4.64

1.79 2.11 2.96 4.47

1.76 2.07 2.88 4.33

2.03 2.49 3.69 5.81

1.99 2.42 3.55 5.55

1.94 2.35 3.41 5.27

1.89 2.28 3.26 4.99

1.86 2.23 3.16 4.82

1.84 2.19 3.10 4.70

1.81 2.15 3.02 4.54

1.79 2.12 2.97 4.45

1.78 2.11 2.93 4.39

1.75 2.06 2.84 4.23

1.72 2.02 2.76 4.08

2.00 2.45 3.59 5.58

1.96 2.38 3.46 5.32

1.91 2.31 3.31 5.05

1.86 2.23 3.16 4.78

1.83 2.18 3.07 4.60

1.81 2.15 3.00 4.48

1.78 2.10 2.92 4.33

1.76 2.08 2.87 4.24

1.75 2.06 2.83 4.18

1.72 2.01 2.75 4.02

1.69 1.97 2.66 3.87

1.98 2.41 3.51 5.39

1.93 2.34 3.37 5.13

1.89 2.27 3.23 4.87

1.84 2.19 3.08 4.59

1.80 2.14 2.98 4.42

1.78 2.11 2.92 4.30

1.75 2.06 2.84 4.15

1.74 2.04 2.78 4.06

1.72 2.02 2.75 4.00

1.69 1.97 2.66 3.84

1.66 1.92 2.58 3.69

1.96 2.38 3.43 5.22

1.91 2.31 3.30 4.97

1.86 2.23 3.15 4.70

1.81 2.16 3.00 4.43

1.78 2.11 2.91 4.26

1.76 2.07 2.84 4.14

1.73 2.03 2.76 3.99

1.71 2.00 2.71 3.90

1.70 1.98 2.67 3.84

1.67 1.93 2.58 3.68

1.64 1.88 2.50 3.53

1.94 2.35 3.37 5.08

1.89 2.28 3.23 4.82

1.84 2.20 3.09 4.56

1.79 2.12 2.94 4.29

1.76 2.07 2.84 4.12

1.74 2.04 2.78 4.00

1.71 1.99 2.69 3.86

1.69 1.97 2.64 3.77

1.68 1.95 2.61 3.70

1.64 1.90 2.52 3.54

1.61 1.85 2.43 3.40

1.92 2.32 3.31 4.95

1.87 2.25 3.17 4.70

1.83 2.18 3.03 4.44

1.78 2.10 2.88 4.17

1.74 2.05 2.79 4.00

1.72 2.01 2.72 3.88

1.69 1.96 2.64 3.74

1.67 1.94 2.58 3.64

1.66 1.92 2.55 3.58

1.62 1.87 2.46 3.42

1.59 1.82 2.37 3.28

1.90 2.30 3.26 4.83

1.86 2.23 3.12 4.58

1.81 2.15 2.98 4.33

1.76 2.07 2.83 4.06

1.73 2.02 2.73 3.89

1.70 1.98 2.67 3.78

1.67 1.94 2.58 3.63

1.65 1.91 2.53 3.54

1.64 1.89 2.50 3.48

1.60 1.84 2.40 3.32

1.57 1.79 2.32 3.17

1.89 2.27 3.21 4.73

1.84 2.20 3.07 4.48

1.80 2.13 2.93 4.23

1.74 2.05 2.78 3.96

1.71 2.00 2.69 3.79

1.69 1.96 2.62 3.68

1.66 1.91 2.54 3.53

1.64 1.88 2.48 3.44

1.62 1.86 2.45 3.38

1.59 1.81 2.35 3.22

1.55 1.76 2.27 3.08

1.88 2.25 3.17 4.64

1.83 2.18 3.03 4.39

1.78 2.11 2.89 4.14

1.73 2.03 2.74 3.87

1.70 1.97 2.64 3.71

1.67 1.94 2.58 3.59

1.64 1.89 2.49 3.45

1.62 1.86 2.44 3.36

1.61 1.84 2.40 3.29

1.57 1.79 2.31 3.14

1.54 1.74 2.22 2.99 (continued )

38217_App_p662-690.qxd

680

12/20/06

09:48

Page 680

Appendix Tables

Table A.9

Critical Values for F Distributions (cont.)

2 denominator df

1 numerator df

1

2

3

4

5

6

7

8

9

25

.100 .050 .010 .001

2.92 4.24 7.77 13.88

2.53 3.39 5.57 9.22

2.32 2.99 4.68 7.45

2.18 2.76 4.18 6.49

2.09 2.60 3.85 5.89

2.02 2.49 3.63 5.46

1.97 2.40 3.46 5.15

1.93 2.34 3.32 4.91

1.89 2.28 3.22 4.71

26

.100 .050 .010 .001

2.91 4.23 7.72 13.74

2.52 3.37 5.53 9.12

2.31 2.98 4.64 7.36

2.17 2.74 4.14 6.41

2.08 2.59 3.82 5.80

2.01 2.47 3.59 5.38

1.96 2.39 3.42 5.07

1.92 2.32 3.29 4.83

1.88 2.27 3.18 4.64

27

.100 .050 .010 .001

2.90 4.21 7.68 13.61

2.51 3.35 5.49 9.02

2.30 2.96 4.60 7.27

2.17 2.73 4.11 6.33

2.07 2.57 3.78 5.73

2.00 2.46 3.56 5.31

1.95 2.37 3.39 5.00

1.91 2.31 3.26 4.76

1.87 2.25 3.15 4.57

28

.100 .050 .010 .001

2.89 4.20 7.64 13.50

2.50 3.34 5.45 8.93

2.29 2.95 4.57 7.19

2.16 2.71 4.07 6.25

2.06 2.56 3.75 5.66

2.00 2.45 3.53 5.24

1.94 2.36 3.36 4.93

1.90 2.29 3.23 4.69

1.87 2.24 3.12 4.50

29

.100 .050 .010 .001

2.89 4.18 7.60 13.39

2.50 3.33 5.42 8.85

2.28 2.93 4.54 7.12

2.15 2.70 4.04 6.19

2.06 2.55 3.73 5.59

1.99 2.43 3.50 5.18

1.93 2.35 3.33 4.87

1.89 2.28 3.20 4.64

1.86 2.22 3.09 4.45

30

.100 .050 .010 .001

2.88 4.17 7.56 13.29

2.49 3.32 5.39 8.77

2.28 2.92 4.51 7.05

2.14 2.69 4.02 6.12

2.05 2.53 3.70 5.53

1.98 2.42 3.47 5.12

1.93 2.33 3.30 4.82

1.88 2.27 3.17 4.58

1.85 2.21 3.07 4.39

40

.100 .050 .010 .001

2.84 4.08 7.31 12.61

2.44 3.23 5.18 8.25

2.23 2.84 4.31 6.59

2.09 2.61 3.83 5.70

2.00 2.45 3.51 5.13

1.93 2.34 3.29 4.73

1.87 2.25 3.12 4.44

1.83 2.18 2.99 4.21

1.79 2.12 2.89 4.02

50

.100 .050 .010 .001

2.81 4.03 7.17 12.22

2.41 3.18 5.06 7.96

2.20 2.79 4.20 6.34

2.06 2.56 3.72 5.46

1.97 2.40 3.41 4.90

1.90 2.29 3.19 4.51

1.84 2.20 3.02 4.22

1.80 2.13 2.89 4.00

1.76 2.07 2.78 3.82

60

.100 .050 .010 .001

2.79 4.00 7.08 11.97

2.39 3.15 4.98 7.77

2.18 2.76 4.13 6.17

2.04 2.53 3.65 5.31

1.95 2.37 3.34 4.76

1.87 2.25 3.12 4.37

1.82 2.17 2.95 4.09

1.77 2.10 2.82 3.86

1.74 2.04 2.72 3.69

100

.100 .050 .010 .001

2.76 3.94 6.90 11.50

2.36 3.09 4.82 7.41

2.14 2.70 3.98 5.86

2.00 2.46 3.51 5.02

1.91 2.31 3.21 4.48

1.83 2.19 2.99 4.11

1.78 2.10 2.82 3.83

1.73 2.03 2.69 3.61

1.69 1.97 2.59 3.44

200

.100 .050 .010 .001

2.73 3.89 6.76 11.15

2.33 3.04 4.71 7.15

2.11 2.65 3.88 5.63

1.97 2.42 3.41 4.81

1.88 2.26 3.11 4.29

1.80 2.14 2.89 3.92

1.75 2.06 2.73 3.65

1.70 1.98 2.60 3.43

1.66 1.93 2.50 3.26

1000

.100 .050 .010 .001

2.71 3.85 6.66 10.89

2.31 3.00 4.63 6.96

2.09 2.61 3.80 5.46

1.95 2.38 3.34 4.65

1.85 2.22 3.04 4.14

1.78 2.11 2.82 3.78

1.72 2.02 2.66 3.51

1.68 1.95 2.53 3.30

1.64 1.89 2.43 3.13 (continued )

38217_App_p662-690.qxd

Table A.9

12/20/06

09:48

Page 681

Appendix Tables

681


10

12

15

20

25

30

40

50

60

120

1000

1.87 2.24 3.13 4.56

1.82 2.16 2.99 4.31

1.77 2.09 2.85 4.06

1.72 2.01 2.70 3.79

1.68 1.96 2.60 3.63

1.66 1.92 2.54 3.52

1.63 1.87 2.45 3.37

1.61 1.84 2.40 3.28

1.59 1.82 2.36 3.22

1.56 1.77 2.27 3.06

1.52 1.72 2.18 2.91

1.86 2.22 3.09 4.48

1.81 2.15 2.96 4.24

1.76 2.07 2.81 3.99

1.71 1.99 2.66 3.72

1.67 1.94 2.57 3.56

1.65 1.90 2.50 3.44

1.61 1.85 2.42 3.30

1.59 1.82 2.36 3.21

1.58 1.80 2.33 3.15

1.54 1.75 2.23 2.99

1.51 1.70 2.14 2.84

1.85 2.20 3.06 4.41

1.80 2.13 2.93 4.17

1.75 2.06 2.78 3.92

1.70 1.97 2.63 3.66

1.66 1.92 2.54 3.49

1.64 1.88 2.47 3.38

1.60 1.84 2.38 3.23

1.58 1.81 2.33 3.14

1.57 1.79 2.29 3.08

1.53 1.73 2.20 2.92

1.50 1.68 2.11 2.78

1.84 2.19 3.03 4.35

1.79 2.12 2.90 4.11

1.74 2.04 2.75 3.86

1.69 1.96 2.60 3.60

1.65 1.91 2.51 3.43

1.63 1.87 2.44 3.32

1.59 1.82 2.35 3.18

1.57 1.79 2.30 3.09

1.56 1.77 2.26 3.02

1.52 1.71 2.17 2.86

1.48 1.66 2.08 2.72

1.83 2.18 3.00 4.29

1.78 2.10 2.87 4.05

1.73 2.03 2.73 3.80

1.68 1.94 2.57 3.54

1.64 1.89 2.48 3.38

1.62 1.85 2.41 3.27

1.58 1.81 2.33 3.12

1.56 1.77 2.27 3.03

1.55 1.75 2.23 2.97

1.51 1.70 2.14 2.81

1.47 1.65 2.05 2.66

1.82 2.16 2.98 4.24

1.77 2.09 2.84 4.00

1.72 2.01 2.70 3.75

1.67 1.93 2.55 3.49

1.63 1.88 2.45 3.33

1.61 1.84 2.39 3.22

1.57 1.79 2.30 3.07

1.55 1.76 2.25 2.98

1.54 1.74 2.21 2.92

1.50 1.68 2.11 2.76

1.46 1.63 2.02 2.61

1.76 2.08 2.80 3.87

1.71 2.00 2.66 3.64

1.66 1.92 2.52 3.40

1.61 1.84 2.37 3.14

1.57 1.78 2.27 2.98

1.54 1.74 2.20 2.87

1.51 1.69 2.11 2.73

1.48 1.66 2.06 2.64

1.47 1.64 2.02 2.57

1.42 1.58 1.92 2.41

1.38 1.52 1.82 2.25

1.73 2.03 2.70 3.67

1.68 1.95 2.56 3.44

1.63 1.87 2.42 3.20

1.57 1.78 2.27 2.95

1.53 1.73 2.17 2.79

1.50 1.69 2.10 2.68

1.46 1.63 2.01 2.53

1.44 1.60 1.95 2.44

1.42 1.58 1.91 2.38

1.38 1.51 1.80 2.21

1.33 1.45 1.70 2.05

1.71 1.99 2.63 3.54

1.66 1.92 2.50 3.32

1.60 1.84 2.35 3.08

1.54 1.75 2.20 2.83

1.50 1.69 2.10 2.67

1.48 1.65 2.03 2.55

1.44 1.59 1.94 2.41

1.41 1.56 1.88 2.32

1.40 1.53 1.84 2.25

1.35 1.47 1.73 2.08

1.30 1.40 1.62 1.92

1.66 1.93 2.50 3.30

1.61 1.85 2.37 3.07

1.56 1.77 2.22 2.84

1.49 1.68 2.07 2.59

1.45 1.62 1.97 2.43

1.42 1.57 1.89 2.32

1.38 1.52 1.80 2.17

1.35 1.48 1.74 2.08

1.34 1.45 1.69 2.01

1.28 1.38 1.57 1.83

1.22 1.30 1.45 1.64

1.63 1.88 2.41 3.12

1.58 1.80 2.27 2.90

1.52 1.72 2.13 2.67

1.46 1.62 1.97 2.42

1.41 1.56 1.87 2.26

1.38 1.52 1.79 2.15

1.34 1.46 1.69 2.00

1.31 1.41 1.63 1.90

1.29 1.39 1.58 1.83

1.23 1.30 1.45 1.64

1.16 1.21 1.30 1.43

1.61 1.84 2.34 2.99

1.55 1.76 2.20 2.77

1.49 1.68 2.06 2.54

1.43 1.58 1.90 2.30

1.38 1.52 1.79 2.14

1.35 1.47 1.72 2.02

1.30 1.41 1.61 1.87

1.27 1.36 1.54 1.77

1.25 1.33 1.50 1.69

1.18 1.24 1.35 1.49

1.08 1.11 1.16 1.22

38217_App_p662-690.qxd

682

12/20/06

09:48

Page 682

Appendix Tables

Table A.10

Critical Values for Studentized Range Distributions m

2

3

4

5

6

7

8

9

10

11

12

5

.05 .01

3.64 5.70

4.60 6.98

5.22 7.80

5.67 8.42

6.03 8.91

6.33 9.32

6.58 9.67

6.80 9.97

6.99 10.24

7.17 10.48

7.32 10.70

6

.05 .01

3.46 5.24

4.34 6.33

4.90 7.03

5.30 7.56

5.63 7.97

5.90 8.32

6.12 8.61

6.32 8.87

6.49 9.10

6.65 9.30

6.79 9.48

7

.05 .01

3.34 4.95

4.16 5.92

4.68 6.54

5.06 7.01

5.36 7.37

5.61 7.68

5.82 7.94

6.00 8.17

6.16 8.37

6.30 8.55

6.43 8.71

8

.05 .01

3.26 4.75

4.04 5.64

4.53 6.20

4.89 6.62

5.17 6.96

5.40 7.24

5.60 7.47

5.77 7.68

5.92 7.86

6.05 8.03

6.18 8.18

9

.05 .01

3.20 4.60

3.95 5.43

4.41 5.96

4.76 6.35

5.02 6.66

5.24 6.91

5.43 7.13

5.59 7.33

5.74 7.49

5.87 7.65

5.98 7.78

10

.05 .01

3.15 4.48

3.88 5.27

4.33 5.77

4.65 6.14

4.91 6.43

5.12 6.67

5.30 6.87

5.46 7.05

5.60 7.21

5.72 7.36

5.83 7.49

11

.05 .01

3.11 4.39

3.82 5.15

4.26 5.62

4.57 5.97

4.82 6.25

5.03 6.48

5.20 6.67

5.35 6.84

5.49 6.99

5.61 7.13

5.71 7.25

12

.05 .01

3.08 4.32

3.77 5.05

4.20 5.50

4.51 5.84

4.75 6.10

4.95 6.32

5.12 6.51

5.27 6.67

5.39 6.81

5.51 6.94

5.61 7.06

13

.05 .01

3.06 4.26

3.73 4.96

4.15 5.40

4.45 5.73

4.69 5.98

4.88 6.19

5.05 6.37

5.19 6.53

5.32 6.67

5.43 6.79

5.53 6.90

14

.05 .01

3.03 4.21

3.70 4.89

4.11 5.32

4.41 5.63

4.64 5.88

4.83 6.08

4.99 6.26

5.13 6.41

5.25 6.54

5.36 6.66

5.46 6.77

15

.05 .01

3.01 4.17

3.67 4.84

4.08 5.25

4.37 5.56

4.59 5.80

4.78 5.99

4.94 6.16

5.08 6.31

5.20 6.44

5.31 6.55

5.40 6.66

16

.05 .01

3.00 4.13

3.65 4.79

4.05 5.19

4.33 5.49

4.56 5.72

4.74 5.92

4.90 6.08

5.03 6.22

5.15 6.35

5.26 6.46

5.35 6.56

17

.05 .01

2.98 4.10

3.63 4.74

4.02 5.14

4.30 5.43

4.52 5.66

4.70 5.85

4.86 6.01

4.99 6.15

5.11 6.27

5.21 6.38

5.31 6.48

18

.05 .01

2.97 4.07

3.61 4.70

4.00 5.09

4.28 5.38

4.49 5.60

4.67 5.79

4.82 5.94

4.96 6.08

5.07 6.20

5.17 6.31

5.27 6.41

19

.05 .01

2.96 4.05

3.59 4.67

3.98 5.05

4.25 5.33

4.47 5.55

4.65 5.73

4.79 5.89

4.92 6.02

5.04 6.14

5.14 6.25

5.23 6.34

20

.05 .01

2.95 4.02

3.58 4.64

3.96 5.02

4.23 5.29

4.45 5.51

4.62 5.69

4.77 5.84

4.90 5.97

5.01 6.09

5.11 6.19

5.20 6.28

24

.05 .01

2.92 3.96

3.53 4.55

3.90 4.91

4.17 5.17

4.37 5.37

4.54 5.54

4.68 5.69

4.81 5.81

4.92 5.92

5.01 6.02

5.10 6.11

30

.05 .01

2.89 3.89

3.49 4.45

3.85 4.80

4.10 5.05

4.30 5.24

4.46 5.40

4.60 5.54

4.72 5.65

4.82 5.76

4.92 5.85

5.00 5.93

40

.05 .01

2.86 3.82

3.44 4.37

3.79 4.70

4.04 4.93

4.23 5.11

4.39 5.26

4.52 5.39

4.63 5.50

4.73 5.60

4.82 5.69

4.90 5.76

60

.05 .01

2.83 3.76

3.40 4.28

3.74 4.59

3.98 4.82

4.16 4.99

4.31 5.13

4.44 5.25

4.55 5.36

4.65 5.45

4.73 5.53

4.81 5.60

120

.05 .01

2.80 3.70

3.36 4.20

3.68 4.50

3.92 4.71

4.10 4.87

4.24 5.01

4.36 5.12

4.47 5.21

4.56 5.30

4.64 5.37

4.71 5.44

∞

.05 .01

2.77 3.64

3.31 4.12

3.63 4.40

3.86 4.60

4.03 4.76

4.17 4.88

4.29 4.99

4.39 5.08

4.47 5.16

4.55 5.23

4.62 5.29

38217_App_p662-690.qxd

12/20/06

09:48

Page 683

Appendix Tables

Table A.11

683

Chi-Squared Curve Tail Areas

Upper-tail Area

1

2

3

4

5

.100 .100 .095 .090 .085 .080 .075 .070 .065 .060 .055 .050 .045 .040 .035 .030 .025 .020 .015 .010 .005 .001 .001

2.70 2.70 2.78 2.87 2.96 3.06 3.17 3.28 3.40 3.53 3.68 3.84 4.01 4.21 4.44 4.70 5.02 5.41 5.91 6.63 7.87 10.82

10.82

4.60 4.60 4.70 4.81 4.93 5.05 5.18 5.31 5.46 5.62 5.80 5.99 6.20 6.43 6.70 7.01 7.37 7.82 8.39 9.21 10.59 13.81

13.81

6.25 6.25 6.36 6.49 6.62 6.75 6.90 7.06 7.22 7.40 7.60 7.81 8.04 8.31 8.60 8.94 9.34 9.83 10.46 11.34 12.83 16.26

16.26

7.77 7.77 7.90 8.04 8.18 8.33 8.49 8.66 8.84 9.04 9.25 9.48 9.74 10.02 10.34 10.71 11.14 11.66 12.33 13.27 14.86 18.46

18.46

9.23 9.23 9.37 9.52 9.67 9.83 10.00 10.19 10.38 10.59 10.82 11.07 11.34 11.64 11.98 12.37 12.83 13.38 14.09 15.08 16.74 20.51

20.51

Upper-tail Area

6

7

8

9

10

.100 .100 .095 .090 .085 .080 .075 .070 .065 .060 .055 .050 .045 .040 .035 .030 .025 .020 .015 .010 .005 .001 .001

10.64 10.64 10.79 10.94 11.11 11.28 11.46 11.65 11.86 12.08 12.33 12.59 12.87 13.19 13.55 13.96 14.44 15.03 15.77 16.81 18.54 22.45

22.45

12.01 12.01 12.17 12.33 12.50 12.69 12.88 13.08 13.30 13.53 13.79 14.06 14.36 14.70 15.07 15.50 16.01 16.62 17.39 18.47 20.27 24.32

24.32

13.36 13.36 13.52 13.69 13.87 14.06 14.26 14.48 14.71 14.95 15.22 15.50 15.82 16.17 16.56 17.01 17.53 18.16 18.97 20.09 21.95 26.12

26.12

14.68 14.68 14.85 15.03 15.22 15.42 15.63 15.85 16.09 16.34 16.62 16.91 17.24 17.60 18.01 18.47 19.02 19.67 20.51 21.66 23.58 27.87

27.87

15.98 15.98 16.16 16.35 16.54 16.75 16.97 17.20 17.44 17.71 17.99 18.30 18.64 19.02 19.44 19.92 20.48 21.16 22.02 23.20 25.18 29.58

29.58 (continued )

38217_App_p662-690.qxd

684

12/20/06

09:48

Page 684

Appendix Tables

Table A.11

Chi-Squared Curve Tail Areas (cont.)

Upper-tail Area

.100 .100 .095 .090 .085 .080 .075 .070 .065 .060 .055 .050 .045 .040 .035 .030 .025 .020 .015 .010 .005 .001 .001

Upper-tail Area

.100 .100 .095 .090 .085 .080 .075 .070 .065 .060 .055 .050 .045 .040 .035 .030 .025 .020 .015 .010 .005 .001 .001

11

12

13

14

15

17.27 17.27 17.45 17.65 17.85 18.06 18.29 18.53 18.78 19.06 19.35 19.67 20.02 20.41 20.84 21.34 21.92 22.61 23.50 24.72 26.75 31.26

31.26

18.54 18.54 18.74 18.93 19.14 19.36 19.60 19.84 20.11 20.39 20.69 21.02 21.38 21.78 22.23 22.74 23.33 24.05 24.96 26.21 28.29 32.90

32.90

19.81 19.81 20.00 20.21 20.42 20.65 20.89 21.15 21.42 21.71 22.02 22.36 22.73 23.14 23.60 24.12 24.73 25.47 26.40 27.68 29.81 34.52

34.52

21.06 21.06 21.26 21.47 21.69 21.93 22.17 22.44 22.71 23.01 23.33 23.68 24.06 24.48 24.95 25.49 26.11 26.87 27.82 29.14 31.31 36.12

36.12

22.30 22.30 22.51 22.73 22.95 23.19 23.45 23.72 24.00 24.31 24.63 24.99 25.38 25.81 26.29 26.84 27.48 28.25 29.23 30.57 32.80 37.69

37.69

16

17

18

19

20

23.54 23.54 23.75 23.97 24.21 24.45 24.71 24.99 25.28 25.59 25.93 26.29 26.69 27.13 27.62 28.19 28.84 29.63 30.62 32.00 34.26 39.25

39.25

24.77 24.76 24.98 25.21 25.45 25.70 25.97 26.25 26.55 26.87 27.21 27.58 27.99 28.44 28.94 29.52 30.19 30.99 32.01 33.40 35.71 40.78

40.78

25.98 25.98 26.21 26.44 26.68 26.94 27.21 27.50 27.81 28.13 28.48 28.86 29.28 29.74 30.25 30.84 31.52 32.34 33.38 34.80 37.15 42.31

42.31

27.20 27.20 27.43 27.66 27.91 28.18 28.45 28.75 29.06 29.39 29.75 30.14 30.56 31.03 31.56 32.15 32.85 33.68 34.74 36.19 38.58 43.81

43.81

28.41 28.41 28.64 28.88 29.14 29.40 29.69 29.99 30.30 30.64 31.01 31.41 31.84 32.32 32.85 33.46 34.16 35.01 36.09 37.56 39.99 45.31

45.31

38217_App_p662-690.qxd

12/20/06

09:48

Page 685

Appendix Tables

Table A.12

Critical Values for the Ryan–Joiner Test of Normality

n

5 10 15 20 25 30 40 50 60 75

.10

.05

.01

.9033 .9347 .9506 .9600 .9662 .9707 .9767 .9807 .9835 .9865

.8804 .9180 .9383 .9503 .9582 .9639 .9715 .9764 .9799 .9835

.8320 .8804 .9110 .9290 .9408 .9490 .9597 .9664 .9710 .9757

685

38217_App_p662-690.qxd

686

12/20/06

09:48

Page 686

Appendix Tables

Table A.13 n

c1

P0(S c1)

3 4

6 9 10 13 14 15 17 19 20 21 22 24 26 28 28 30 32 34 35 36 34 37 39 42 44 41 44 47 50 52 48 52 55 59 61 56 60 61 64 68 71 64 65 69 70 74

.125 .125 .062 .094 .062 .031 .109 .047 .031 .016 .109 .055 .023 .008 .098 .055 .027 .012 .008 .004 .102 .049 .027 .010 .004 .097 .053 .024 .010 .005 .103 .051 .027 .009 .005 .102 .055 .046 .026 .010 .005 .108 .095 .055 .047 .024

5

6

7

8

9

10

11

12

13

P0(S c1) P(S c1 when H0 is true)

Critical Values for the Wilcoxon Signed-Rank Test n

14

15

16

17

18

19

20

c1

P0(S c1)

78 79 81 73 74 79 84 89 92 83 84 89 90 95 100 101 104 93 94 100 106 112 113 116 104 105 112 118 125 129 116 124 131 138 143 128 136 137 144 152 157 140 150 158 167 172

.011 .009 .005 .108 .097 .052 .025 .010 .005 .104 .094 .053 .047 .024 .011 .009 .005 .106 .096 .052 .025 .011 .009 .005 .103 .095 .049 .025 .010 .005 .098 .049 .024 .010 .005 .098 .052 .048 .025 .010 .005 .101 .049 .024 .010 .005

38217_App_p662-690.qxd

12/20/06

09:48

Page 687

Appendix Tables

Table A.14

n

c

P0(W c)

3

3 4

15 17 18 20 21 22 23 24 24 26 27 27 28 29 30 24 25 26 27 28 29 30 30 32 33 34 33 35 36 37 36 38 40 41 36 37 39

.05 .057 .029 .036 .018 .048 .024 .012 .058 .017 .008 .042 .024 .012 .006 .057 .029 .014 .056 .032 .016 .008 .057 .019 .010 .005 .055 .021 .012 .006 .055 .024 .008 .004 .048 .028 .008

5 6

7

8

4

4

5

6

7

8

5

P0(W c) P(W c when H0 is true)

Critical Values for the Wilcoxon Rank-Sum Test

m

5

687

m

n

6

7

8

6

6

7

8

7

7

8

8

8

c

P0(W c)

40 40 41 43 44 43 45 47 48 47 49 51 52 50 52 54 55 54 56 58 60 58 61 63 65 66 68 71 72 71 73 76 78 84 87 90 92

.004 .041 .026 .009 .004 .053 .024 .009 .005 .047 .023 .009 .005 .047 .021 .008 .004 .051 .026 .011 .004 .054 .021 .01 .004 .049 .027 .009 .006 .047 .027 .01 .005 .052 .025 .01 .005

38217_App_p662-690.qxd

688

5 6

7

8

9

10

11

12

09:48

Page 688

Appendix Tables

Table A.15 n

12/20/06

Critical Values for the Wilcoxon Signed-Rank Interval

Confidence Level (%)

c

n

93.8 87.5 96.9 93.7 90.6 98.4 95.3 89.1 99.2 94.5 89.1 99.2 94.5 90.2 99.0 95.1 89.5 99.0 94.6 89.8 99.1 94.8 90.8

15 14 21 20 19 28 26 24 36 32 30 44 39 37 52 47 44 61 55 52 71 64 61

13

14

15

16

17

18

19

(x(n(n1)/2c1), x(c))


c

n

99.0 95.2 90.6 99.1 95.1 89.6 99.0 95.2 90.5 99.1 94.9 89.5 99.1 94.9 90.2 99.0 95.2 90.1 99.1 95.1 90.4

81 74 70 93 84 79 104 95 90 117 106 100 130 118 112 143 131 124 158 144 137

20

21

22

23

24

25

Confidence Level (%) 99.1 95.2 90.3 99.0 95.0 89.7 99.0 95.0 90.2 99.0 95.2 90.2 99.0 95.1 89.9 99.0 95.2 89.9

c 173 158 150 188 172 163 204 187 178 221 203 193 239 219 208 257 236 224

38217_App_p662-690.qxd

12/20/06

09:48

Page 689

Appendix Tables

Table A.16

Critical Values for the Wilcoxon Rank-Sum Interval

689

(dij(mnc1), dij(c))

Smaller Sample Size 5

6

7

8

Larger Sample Size


c


c


c


c

5

99.2 94.4 90.5 99.1 94.8 91.8 99.0 95.2 89.4 98.9 95.5 90.7 98.8 95.8 88.8 99.2 94.5 90.1 99.1 94.8 91.0 99.1 95.2 89.6

25 22 21 29 26 25 33 30 28 37 34 32 41 38 35 46 41 39 50 45 43 54 49 46

99.1 95.9 90.7 99.2 94.9 89.9 99.2 95.7 89.2 99.2 95.0 91.2 98.9 94.4 90.7 99.0 95.2 90.2 99.0 94.7 89.8

34 31 29 39 35 33 44 40 37 49 44 42 53 48 46 58 53 50 63 57 54

98.9 94.7 90.3 99.1 94.6 90.6 99.2 94.5 90.9 99.0 94.5 89.1 98.9 95.6 89.6 99.0 95.5 90.0

44 40 38 50 45 43 56 50 48 61 55 52 66 61 57 72 66 62

99.0 95.0 89.5 98.9 95.4 90.7 99.1 94.5 89.9 99.1 94.9 90.9 99.0 95.3 90.2

56 51 48 62 57 54 69 62 59 75 68 65 81 74 70

6

7

8

9

10

11

12

Smaller Sample Size 9

10

11

12

Larger Sample Size


c


c


c


c

9

98.9 95.0 90.6 99.0 94.7 90.5 99.0 95.4 90.5 99.1 95.1 90.5

69 63 60 76 69 66 83 76 72 90 82 78

99.1 94.8 89.5 99.0 94.9 90.1 99.1 95.0 90.7

84 76 72 91 83 79 99 90 86

98.9 95.3 89.9 99.1 94.9 89.6

99 91 86 108 98 93

99.0 94.8 89.9

116 106 101

10

11

12

0

.2

.4

.6

.8

1.0

0

.2

0.4

99

0.4

0.8

1.2

1.2

14 29 19

0.8

9

19 14 9 6

3

6

74

49

1.6

39

1.6

4

2.4

2.8

2.0

2.4

3

4 2.8

df 2

.01, one-tailed

2.0

df 2

3.2

3.2

d

d

0

.2

.4

.6

.8

1.0

0

.2

.4

.6

.8

74

74

49 0.4

99

0.4

99

0.8

0.8

19

1.2

1.2

14

14 1.6

39 29 19

1.6

9

9

2.4

3

2.8

2

2.0

6 2.4

4

2.8

3

d

3.2

df 2

.01, two-tailed

4

39 49

2.0

6

29

df 1

.05, two-tailed

d

09:48

.4

99 74 49 39 29

.05, one-tailed

1.0

12/20/06

.6

.8

1.0

Curves for t Tests

690

Table A.17

38217_App_p662-690.qxd Page 690

Appendix Tables

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS, 7TH EDITION

Recommend Documents