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Statistical tables for binomial & distribution analysis - b code môn Xác suất thống kê| Trường Đại học Ngoại Thương

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Statistical tables for binomial & distribution analysis - b code mônXác suất thống kê| Trường Đại học Ngoại Thương. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời đọc đón xem!

Môn: Xác suất thống kê (FTU) 355 tài liệu

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B-1
Appendix B
TABLES
TABLE 1Binomial Probabilities
Tabulated values are . (Values are rounded to four decimal places.)
n
5
p
k
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 0.9510 0.7738 0.5905 0.3277 0.2373 0.1681 0.0778 0.0313 0.0102 0.0024 0.0010 0.0003 0.0000 0.0000 0.0000
1 0.9990 0.9774 0.9185 0.7373 0.6328 0.5282 0.3370 0.1875 0.0870 0.0308 0.0156 0.0067 0.0005 0.0000 0.0000
2 1.0000 0.9988 0.9914 0.9421 0.8965 0.8369 0.6826 0.5000 0.3174 0.1631 0.1035 0.0579 0.0086 0.0012 0.0000
3 1.0000 1.0000 0.9995 0.9933 0.9844 0.9692 0.9130 0.8125 0.6630 0.4718 0.3672 0.2627 0.0815 0.0226 0.0010
4 1.0000 1.0000 1.0000 0.9997 0.9990 0.9976 0.9898 0.9688 0.9222 0.8319 0.7627 0.6723 0.4095 0.2262 0.0490
n
6
p
k
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 0.9415 0.7351 0.5314 0.2621 0.1780 0.1176 0.0467 0.0156 0.0041 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000
1 0.9985 0.9672 0.8857 0.6554 0.5339 0.4202 0.2333 0.1094 0.0410 0.0109 0.0046 0.0016 0.0001 0.0000 0.0000
2 1.0000 0.9978 0.9842 0.9011 0.8306 0.7443 0.5443 0.3438 0.1792 0.0705 0.0376 0.0170 0.0013 0.0001 0.0000
3 1.0000 0.9999 0.9987 0.9830 0.9624 0.9295 0.8208 0.6563 0.4557 0.2557 0.1694 0.0989 0.0159 0.0022 0.0000
4 1.0000 1.0000 0.9999 0.9984 0.9954 0.9891 0.9590 0.8906 0.7667 0.5798 0.4661 0.3446 0.1143 0.0328 0.0015
5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9959 0.9844 0.9533 0.8824 0.8220 0.7379 0.4686 0.2649 0.0585
n
7
p
k
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 0.9321 0.6983 0.4783 0.2097 0.1335 0.0824 0.0280 0.0078 0.0016 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000
1 0.9980 0.9556 0.8503 0.5767 0.4449 0.3294 0.1586 0.0625 0.0188 0.0038 0.0013 0.0004 0.0000 0.0000 0.0000
2 1.0000 0.9962 0.9743 0.8520 0.7564 0.6471 0.4199 0.2266 0.0963 0.0288 0.0129 0.0047 0.0002 0.0000 0.0000
3 1.0000 0.9998 0.9973 0.9667 0.9294 0.8740 0.7102 0.5000 0.2898 0.1260 0.0706 0.0333 0.0027 0.0002 0.0000
4 1.0000 1.0000 0.9998 0.9953 0.9871 0.9712 0.9037 0.7734 0.5801 0.3529 0.2436 0.1480 0.0257 0.0038 0.0000
5 1.0000 1.0000 1.0000 0.9996 0.9987 0.9962 0.9812 0.9375 0.8414 0.6706 0.5551 0.4233 0.1497 0.0444 0.0020
6 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9984 0.9922 0.9720 0.9176 0.8665 0.7903 0.5217 0.3017 0.0679
P(X…k)=a
k
x=0
p(xi)
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-2 APPENDIX B
n 8
p
k 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 0.9227 0.6634 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.9973 0.9428 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000
2 0.9999 0.9942 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113 0.0042 0.0012 0.0000 0.0000 0.0000
3 1.0000 0.9996 0.9950 0.9437 0.8862 0.8059 0.5941 0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 0.0000 0.0000
4 1.0000 1.0000 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 0.0004 0.0000
5 1.0000 1.0000 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 0.0058 0.0001
6 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9915 0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 0.0572 0.0027
7 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 0.8999 0.8322 0.5695 0.3366 0.0773
n 9
p
k 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 0.9135 0.6302 0.3874 0.1342 0.0751 0.0404 0. 0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000101
1 0.9966 0.9288 0.7748 0.4362 0.3003 0.1960 0.0705 0.0195 0.0038 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000
2 0.9999 0.9916 0.9470 0.7382 0.6007 0.4628 0.2318 0.0898 0.0250 0.0043 0.0013 0.0003 0.0000 0.0000 0.0000
3 1.0000 0.9994 0.9917 0.9144 0.8343 0.7297 0.4826 0.2539 0.0994 0.0253 0.0100 0.0031 0.0001 0.0000 0.0000
4 1.0000 1.0000 0.9991 0.9804 0.9511 0.9012 0.7334 0.5000 0.2666 0.0988 0.0489 0.0196 0.0009 0.0000 0.0000
5 1.0000 1.0000 0.9999 0.9969 0.9900 0.9747 0.9006 0.7461 0.5174 0.2703 0.1657 0.0856 0.0083 0.0006 0.0000
6 1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9750 0.9102 0.7682 0.5372 0.3993 0.2618 0.0530 0.0084 0.0001
7 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9962 0.9805 0.9295 0.8040 0.6997 0.5638 0.2252 0.0712 0.0034
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9899 0.9596 0.9249 0.8658 0.6126 0.3698 0.0865
TABLE 1 (Continued
)
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-3
APPENDIX B
TABLE 1 (Continued
)
n 10
p
k 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 0.9044 0.5987 0.3487 0.1074 0.0563 0.0282 0.0060 0.0010 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.9957 0.9139 0.7361 0.3758 0.2440 0.1493 0.0464 0.0107 0.0017 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.9999 0.9885 0.9298 0.6778 0.5256 0.3828 0.1673 0.0547 0.0123 0.0016 0.0004 0.0001 0.0000 0.0000 0.0000
3 1.0000 0.9990 0.9872 0.8791 0.7759 0.6496 0.3823 0.1719 0.0548 0.0106 0.0035 0.0009 0.0000 0.0000 0.0000
4 1.0000 0.9999 0.9984 0.9672 0.9219 0.8497 0.6331 0.3770 0.1662 0.0473 0.0197 0.0064 0.0001 0.0000 0.0000
5 1.0000 1.0000 0.9999 0.9936 0.9803 0.9527 0.8338 0.6230 0.3669 0.1503 0.0781 0.0328 0.0016 0.0001 0.0000
6 1.0000 1.0000 1.0000 0.9991 0.9965 0.9894 0.9452 0.8281 0.6177 0.3504 0.2241 0.1209 0.0128 0.0010 0.0000
7 1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9877 0.9453 0.8327 0.6172 0.4744 0.3222 0.0702 0.0115 0.0001
8 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9893 0.9536 0.8507 0.7560 0.6242 0.2639 0.0861 0.0043
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9990 0.9940 0.9718 0.9437 0.8926 0.6513 0.4013 0.0956
n 15
p
k 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 0.8601 0.4633 0.2059 0.0352 0.0134 0.0047 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.9904 0.8290 0.5490 0.1671 0.0802 0.0353 0.0052 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.9996 0.9638 0.8159 0.3980 0.2361 0.1268 0.0271 0.0037 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 1.0000 0.9945 0.9444 0.6482 0.4613 0.2969 0.0905 0.0176 0.0019 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
4 1.0000 0.9994 0.9873 0.8358 0.6865 0.5155 0.2173 0.0592 0.0093 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000
5 1.0000 0.9999 0.9978 0.9389 0.8516 0.7216 0.4032 0.1509 0.0338 0.0037 0.0008 0.0001 0.0000 0.0000 0.0000
6 1.0000 1.0000 0.9997 0.9819 0.9434 0.8689 0.6098 0.3036 0.0950 0.0152 0.0042 0.0008 0.0000 0.0000 0.0000
7 1.0000 1.0000 1.0000 0.9958 0.9827 0.9500 0.7869 0.5000 0.2131 0.0500 0.0173 0.0042 0.0000 0.0000 0.0000
8 1.0000 1.0000 1.0000 0.9992 0.9958 0.9848 0.9050 0.6964 0.3902 0.1311 0.0566 0.0181 0.0003 0.0000 0.0000
9 1.0000 1.0000 1.0000 0.9999 0.9992 0.9963 0.9662 0.8491 0.5968 0.2784 0.1484 0.0611 0.0022 0.0001 0.0000
10 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9907 0.9408 0.7827 0.4845 0.3135 0.1642 0.0127 0.0006 0.0000
11 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9981 0.9824 0.9095 0.7031 0.5387 0.3518 0.0556 0.0055 0.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9963 0.9729 0.8732 0.7639 0.6020 0.1841 0.0362 0.0004
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9948 0.9647 0.9198 0.8329 0.4510 0.1710 0.0096
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9953 0.9866 0.9648 0.7941 0.5367 0.1399
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-4 APPENDIX B
TABLE 1 (Continued
)
n 20
p
k 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 0.8179 0.3585 0.1216 0.0115 0.0032 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.9831 0.7358 0.3917 0.0692 0.0243 0.0076 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.9990 0.9245 0.6769 0.2061 0.0913 0.0355 0.0036 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 1.0000 0.9841 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 1.0000 0.9974 0.9568 0.6296 0.4148 0.2375 0.0510 0.0059 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
5 1.0000 0.9997 0.9887 0.8042 0.6172 0.4164 0.1256 0.0207 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
6 1.0000 1.0000 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000
7 1.0000 1.0000 0.9996 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.0002 0.0000 0.0000 0.0000 0.0000
8 1.0000 1.0000 0.9999 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0009 0.0001 0.0000 0.0000 0.0000
9 1.0000 1.0000 1.0000 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171 0.0039 0.0006 0.0000 0.0000 0.0000
10 1.0000 1.0000 1.0000 0.9994 0.9961 0.9829 0.8725 0.5881 0.2447 0.0480 0.0139 0.0026 0.0000 0.0000 0.0000
11 1.0000 1.0000 1.0000 0.9999 0.9991 0.9949 0.9435 0.7483 0.4044 0.1133 0.0409 0.0100 0.0001 0.0000 0.0000
12 1.0000 1.0000 1.0000 1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.1018 0.0321 0.0004 0.0000 0.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.2142 0.0867 0.0024 0.0000 0.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9984 0.9793 0.8744 0.5836 0.3828 0.1958 0.0113 0.0003 0.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9941 0.9490 0.7625 0.5852 0.3704 0.0432 0.0026 0.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9987 0.9840 0.8929 0.7748 0.5886 0.1330 0.0159 0.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9964 0.9645 0.9087 0.7939 0.3231 0.0755 0.0010
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9924 0.9757 0.9308 0.6083 0.2642 0.0169
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9968 0.9885 0.8784 0.6415 0.1821
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-5
APPENDIX B
TABLE 1 (Continued
)
n 25
p
k 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 0.7778 0.2774 0.0718 0.0038 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.9742 0.6424 0.2712 0.0274 0.0070 0.0016 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.9980 0.8729 0.5371 0.0982 0.0321 0.0090 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.9999 0.9659 0.7636 0.2340 0.0962 0.0332 0.0024 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 1.0000 0.9928 0.9020 0.4207 0.2137 0.0905 0.0095 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
5 1.0000 0.9988 0.9666 0.6167 0.3783 0.1935 0.0294 0.0020 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
6 1.0000 0.9998 0.9905 0.7800 0.5611 0.3407 0.0736 0.0073 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
7 1.0000 1.0000 0.9977 0.8909 0.7265 0.5118 0.1536 0.0216 0.0012 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8 1.0000 1.0000 0.9995 0.9532 0.8506 0.6769 0.2735 0.0539 0.0043 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
9 1.0000 1.0000 0.9999 0.9827 0.9287 0.8106 0.4246 0.1148 0.0132 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000
10 1.0000 1.0000 1.0000 0.9944 0.9703 0.9022 0.5858 0.2122 0.0344 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000
11 1.0000 1.0000 1.0000 0.9985 0.9893 0.9558 0.7323 0.3450 0.0778 0.0060 0.0009 0.0001 0.0000 0.0000 0.0000
12 1.0000 1.0000 1.0000 0.9996 0.9966 0.9825 0.8462 0.5000 0.1538 0.0175 0.0034 0.0004 0.0000 0.0000 0.0000
13 1.0000 1.0000 1.0000 0.9999 0.9991 0.9940 0.9222 0.6550 0.2677 0.0442 0.0107 0.0015 0.0000 0.0000 0.0000
14 1.0000 1.0000 1.0000 1.0000 0.9998 0.9982 0.9656 0.7878 0.4142 0.0978 0.0297 0.0056 0.0000 0.0000 0.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9868 0.8852 0.5754 0.1894 0.0713 0.0173 0.0001 0.0000 0.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9957 0.9461 0.7265 0.3231 0.1494 0.0468 0.0005 0.0000 0.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9988 0.9784 0.8464 0.4882 0.2735 0.1091 0.0023 0.0000 0.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9927 0.9264 0.6593 0.4389 0.2200 0.0095 0.0002 0.0000
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9980 0.9706 0.8065 0.6217 0.3833 0.0334 0.0012 0.0000
20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9905 0.9095 0.7863 0.5793 0.0980 0.0072 0.0000
21 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9976 0.9668 0.9038 0.7660 0.2364 0.0341 0.0001
22 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9910 0.9679 0.9018 0.4629 0.1271 0.0020
23 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9984 0.9930 0.9726 0.7288 0.3576 0.0258
24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9962 0.9282 0.7226 0.2222
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-6 APPENDIX B
TABLE 2 Poisson Probabilities
Tabulated values are . (Values are rounded to four decimal places.)
µ
k 0.10 0.20 0.30 0.40 0.50 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067 0.0041 0.0025
1 0.9953 0.9825 0.9631 0.9384 0.9098 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404 0.0266 0.0174
2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247 0.0884 0.0620
3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650 0.2017 0.1512
4 1.0000 1.0000 0.9999 0.9998 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405 0.3575 0.2851
5 1.0000 1.0000 0.9994 0.9955 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160 0.5289 0.4457
6 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622 0.6860 0.6063
7 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.8666 0.8095 0.7440
8 1.0000 0.9998 0.9989 0.9962 0.9901 0.9786 0.9597 0.9319 0.8944 0.8472
9 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.9682 0.9462 0.9161
10 0.9999 0.9997 0.9990 0.9972 0.9933 0.9863 0.9747 0.9574
11 1.0000 0.9999 0.9997 0.9991 0.9976 0.9945 0.9890 0.9799
12 1.0000 0.9999 0.9997 0.9992 0.9980 0.9955 0.9912
13 1.0000 0.9999 0.9997 0.9993 0.9983 0.9964
14 1.0000 0.9999 0.9998 0.9994 0.9986
15 1.0000 0.9999 0.9998 0.9995
16 1.0000 0.9999 0.9998
17 1.0000 0.9999
18 1.0000
19
20
P(X…k)=a
k
x=0p( )xi
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
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B-7
APPENDIX B
TABLE 2 ( Continued
)
µ
k
6.50 7.00 7.50 8.00 8.50 9.00 9.50 10 11 12 13 14 15
0 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0.0008 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000
2 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0.0042 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000
3 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.0149 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002
4 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0.0403 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009
5 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.0885 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028
6 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.1649 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076
7 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180
8 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374
9 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699
10 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185
11 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848
12 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676
13 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632
14 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657
15 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.9665 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681
16 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641
17 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489
18 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195
19 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752
20 1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170
21 1.0000 0.9999 0.9998 0.9996 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469
22 1.0000 0.9999 0.9999 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673
23 1.0000 0.9999 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805
24 1.0000 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888
25 0.9999 0.9997 0.9990 0.9974 0.9938
26 1.0000 0.9999 0.9995 0.9987 0.9967
27 0.9999 0.9998 0.9994 0.9983
28 1.0000 0.9999 0.9997 0.9991
29 1.0000 0.9999 0.9996
30 0.9999 0.9998
31 1.0000 0.9999
32 1.0000
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B-8 APPENDIX B
TABLE 3 Cumulative Standardized Normal Probabilities
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
P(-q6 6Z z)
0z
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B-9
APPENDIX B
.
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
P(-q6 6Z z)
0z
TABLE 3 ( Continued
)
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-10 APPENDIX B
TABLE 4
Critical Values of the
Student
t
Distribution
Degrees of
Freedom t
.100
t
.050
t
.025
t
.010
t
.005
1 3.078 6.314 12.706 31.821 63.657
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.533 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763
29 1.311 1.699 2.045 2.462 2.756
30 1.310 1.697 2.042 2.457 2.750
35 1.306 1.690 2.030 2.438 2.724
40 1.303 1.684 2.021 2.423 2.704
45 1.301 1.679 2.014 2.412 2.690
50 1.299 1.676 2.009 2.403 2.678
55 1.297 1.673 2.004 2.396 2.668
60 1.296 1.671 2.000 2.390 2.660
65 1.295 1.669 1.997 2.385 2.654
70 1.294 1.667 1.994 2.381 2.648
75 1.293 1.665 1.992 2.377 2.643
80 1.292 1.664 1.990 2.374 2.639
85 1.292 1.663 1.988 2.371 2.635
90 1.291 1.662 1.987 2.368 2.632
95 1.291 1.661 1.985 2.366 2.629
100 1.290 1.660 1.984 2.364 2.626
110 1.289 1.659 1.982 2.361 2.621
120 1.289 1.658 1.980 2.358 2.617
130 1.288 1.657 1.978 2.355 2.614
140 1.288 1.656 1.977 2.353 2.611
150 1.287 1.655 1.976 2.351 2.609
160 1.287 1.654 1.975 2.350 2.607
170 1.287 1.654 1.974 2.348 2.605
180 1.286 1.653 1.973 2.347 2.603
190 1.286 1.653 1.973 2.346 2.602
200 1.286 1.653 1.972 2.345 2.601
q1.282 1.645 1.960 2.326 2.576
tA
A
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B-11
APPENDIX B
Degrees of
Freedom 2 .995 2 .990 2 .975 2 .950 2 .900 2 .100 2 .050 2 .025 2 .010 2
.005
1 0.000039 0.000157 0.000982 0.00393 0.0158 2.71 3.84 5.02 6.63 7.88
2 0.0100 0.0201 0.0506 0.103 0.211 4.61 5.99 7.38 9.21 10.6
3 0.072 0.115 0.216 0.352 0.584 6.25 7.81 9.35 11.3 12.8
4 0.207 0.297 0.484 0.711 1.06 7.78 9.49 11.1 13.3 14.9
5 0.412 0.554 0.831 1.15 1.61 9.24 11.1 12.8 15.1 16.7
6 0.676 0.872 1.24 1.64 2.20 10.6 12.6 14.4 16.8 18.5
7 0.989 1.24 1.69 2.17 2.83 12.0 14.1 16.0 18.5 20.3
8 1.34 1.65 2.18 2.73 3.49 13.4 15.5 17.5 20.1 22.0
9 1.73 2.09 2.70 3.33 4.17 14.7 16.9 19.0 21.7 23.6
10 2.16 2.56 3.25 3.94 4.87 16.0 18.3 20.5 23.2 25.2
11 2.60 3.05 3.82 4.57 5.58 17.3 19.7 21.9 24.7 26.8
12 3.07 3.57 4.40 5.23 6.30 18.5 21.0 23.3 26.2 28.3
13 3.57 4.11 5.01 5.89 7.04 19.8 22.4 24.7 27.7 29.8
14 4.07 4.66 5.63 6.57 7.79 21.1 23.7 26.1 29.1 31.3
15 4.60 5.23 6.26 7.26 8.55 22.3 25.0 27.5 30.6 32.8
16 5.14 5.81 6.91 7.96 9.31 23.5 26.3 28.8 32.0 34.3
17 5.70 6.41 7.56 8.67 10.1 24.8 27.6 30.2 33.4 35.7
18 6.26 7.01 8.23 9.39 10.9 26.0 28.9 31.5 34.8 37.2
19 6.84 7.63 8.91 10.1 11.7 27.2 30.1 32.9 36.2 38.6
20 7.43 8.26 9.59 10.9 12.4 28.4 31.4 34.2 37.6 40.0
21 8.03 8.90 10.3 11.6 13.2 29.6 32.7 35.5 38.9 41.4
22 8.64 9.54 11.0 12.3 14.0 30.8 33.9 36.8 40.3 42.8
23 9.26 10.2 11.7 13.1 14.8 32.0 35.2 38.1 41.6 44.2
24 9.89 10.9 12.4 13.8 15.7 33.2 36.4 39.4 43.0 45.6
25 10.5 11.5 13.1 14.6 16.5 34.4 37.7 40.6 44.3 46.9
26 11.2 12.2 13.8 15.4 17.3 35.6 38.9 41.9 45.6 48.3
27 11.8 12.9 14.6 16.2 18.1 36.7 40.1 43.2 47.0 49.6
28 12.5 13.6 15.3 16.9 18.9 37.9 41.3 44.5 48.3 51.0
29 13.1 14.3 16.0 17.7 19.8 39.1 42.6 45.7 49.6 52.3
30 13.8 15.0 16.8 18.5 20.6 40.3 43.8 47.0 50.9 53.7
40 20.7 22.2 24.4 26.5 29.1 51.8 55.8 59.3 63.7 66.8
50 28.0 29.7 32.4 34.8 37.7 63.2 67.5 71.4 76.2 79.5
60 35.5 37.5 40.5 43.2 46.5 74.4 79.1 83.3 88.4 92.0
70 43.3 45.4 48.8 51.7 55.3 85.5 90.5 95.0 100 104
80 51.2 53.5 57.2 60.4 64.3 96.6 102 107 112 116
90 59.2 61.8 65.6 69.1 73.3 108 113 118 124 128
100 67.3 70.1 74.2 77.9 82.4 118 124 130 136 140
f( )x2
x2
A
0A
2
x
TABLE 5 Critical Values of the Distribution2
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B-12 APPENDIX B
TABLE 6(a)Critical Values of the
F
-Distribution:
A
.05
f F( )
F
FA
A
0
NUMERATOR DEGREES OF FREEDOM
12345678910111213141516171
1161 199 216 225 230 234 237 239 241 242 243 244 245 245 246 246 247 247 248 248218.5 19.0 19.2 19.2 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4310.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.76 8.74 8.73 8.71 8.70 8.69 8.68 8.67 8.67 8.6647.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.94 5.91 5.89 5.87 5.86 5.84 5.83 5.82 5.81 5.8056.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.70 4.68 4.66 4.64 4.62 4.60 4.59 4.58 4.57 4.5665.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.03 4.00 3.98 3.96 3.94 3.92 3.91 3.90 3.88 3.8775.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.60 3.57 3.55 3.53 3.51 3.49 3.48 3.47 3.46 3.4485.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.31 3.28 3.26 3.24 3.22 3.20 3.19 3.17 3.16 3.1595.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.95 2.94
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.94 2.91 2.89 2.86 2.85 2.83 2.81 2.80 211 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.67 2.612 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.72 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.5613 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.63 2.60 2.58 2.55 2.53 2.51 2.514 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.57 2.53 2.51 2.48 2.46 2.44 2.43 2.415 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.51 2.48 2.45 2.42 2.40 2.38 216 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.46 2.42 2.40 2.37 2.35 2.33 2.317 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.41 2.38 2.35 2.33 2.3118 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.37 2.34 2.31 2.29 2.19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.34 2.31 2.28 2.26 2.2320 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.31 2.28 2.25 222 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.26 2.23 2.20 2.17 2.24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.22 2.1826 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.18 2.15 2.12 228 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.15 2.1230 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.13 235 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11 2.040 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.0845 4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.0760 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 270 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.0780 3.96 3.11 2.72 2.49 2.33 2.21 2.1390 3.95 3.10 2.71 2.47 2.32 2.
100 3.94 3.09 2.70 2.46 2.31120 3.92 3.07 2.68 2.45 2.29140 3.91 3.06 2.67 2.44 2160 3.90 3.05 2.66 2.43 2.2180 3.89 3.05 2.65 2.42200 3.89 3.04 2.65 2.
3.84 3.00 2.61
DENOMINATOR DEGREES OF FREEDOM
N1
N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-13
APPENDIX B
NUMERATOR DEGREES OF FREEDOM
22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200
1249 249 249 250 250 251 251 251 252 252 252 253 253 253 253 253 254 254 254 254
219.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.538.65 8.64 8.63 8.62 8.62 8.60 8.59 8.59 8.58 8.57 8.57 8.56 8.56 8.55 8.55 8.55 8.54 8.54 8.54 8.5345.79 5.77 5.76 5.75 5.75 5.73 5.72 5.71 5.70 5.69 5.68 5.67 5.67 5.66 5.66 5.65 5.65 5.65 5.65 5.6354.54 4.53 4.52 4.50 4.50 4.48 4.46 4.45 4.44 4.43 4.42 4.41 4.41 4.41 4.40 4.39 4.39 4.39 4.39 4.3763.86 3.84 3.83 3.82 3.81 3.79 3.77 3.76 3.75 3.74 3.73 3.72 3.72 3.71 3.70 3.70 3.70 3.69 3.69 3.6773.43 3.41 3.40 3.39 3.38 3.36 3.34 3.33 3.32 3.30 3.29 3.29 3.28 3.27 3.27 3.26 3.26 3.25 3.25 3.2383.13 3.12 3.10 3.09 3.08 3.06 3.04 3.03 3.02 3.01 2.99 2.99 2.98 2.97 2.97 2.96 2.96 2.95 2.95 2.9392.92 2.90 2.89 2.87 2.86 2.84 2.83 2.81 2.80 2.79 2.78 2.77 2.76 2.76 2.75 2.74 2.74 2.73 2.73 2.71
10 2.75 2.74 2.72 2.71 2.70 2.68 2.66 2.65 2.64 2.62 2.61 2.60 2.59 2.59 2.58 2.57 2.57 2.57 2.56 2.5411 2.63 2.61 2.59 2.58 2.57 2.55 2.53 2.52 2.51 2.49 2.48 2.47 2.46 2.46 2.45 2.44 2.44 2.43 2.43 2.4112 2.52 2.51 2.49 2.48 2.47 2.44 2.43 2.41 2.40 2.38 2.37 2.36 2.36 2.35 2.34 2.33 2.33 2.33 2.32 2.3013 2.44 2.42 2.41 2.39 2.38 2.36 2.34 2.33 2.31 2.30 2.28 2.27 2.27 2.26 2.25 2.25 2.24 2.24 2.23 2.2114 2.37 2.35 2.33 2.32 2.31 2.28 2.27 2.25 2.24 2.22 2.21 2.20 2.19 2.19 2.18 2.17 2.17 2.16 2.16 2.1315 2.31 2.29 2.27 2.26 2.25 2.22 2.20 2.19 2.18 2.16 2.15 2.14 2.13 2.12 2.11 2.11 2.10 2.10 2.1016 2.25 2.24 2.22 2.21 2.19 2.17 2.15 2.14 2.12 2.11 2.09 2.08 2.07 2.07 2.06 2.05 2.05 217 2.21 2.19 2.17 2.16 2.15 2.12 2.10 2.09 2.08 2.06 2.05 2.03 2.03 2.02 2.01 2.00 2.00 1.99 1.918 2.17 2.15 2.13 2.12 2.11 2.08 2.06 2.05 2.04 2.02 2.00 1.99 1.98 1.98 1.97 1.96 1.96 1.95 1.9519 2.13 2.11 2.10 2.08 2.07 2.05 2.03 2.01 2.00 1.98 1.97 1.96 1.95 1.94 1.93 1.92 1.92 120 2.10 2.08 2.07 2.05 2.04 2.01 1.99 1.98 1.97 1.95 1.93 1.92 1.91 1.91 1.90 1.89 1.822 2.05 2.03 2.01 2.00 1.98 1.96 1.94 1.92 1.91 1.89 1.88 1.86 1.86 1.85 1.84 1.8324 2.00 1.98 1.97 1.95 1.94 1.91 1.89 1.88 1.86 1.84 1.83 1.82 1.81 1.80 1.79 1.726 1.97 1.95 1.93 1.91 1.90 1.87 1.85 1.84 1.82 1.80 1.79 1.78 1.77 1.76 1.75 1.7428 1.93 1.91 1.90 1.88 1.87 1.84 1.82 1.80 1.79 1.77 1.75 1.74 1.73 1.73 1.7130 1.91 1.89 1.87 1.85 1.84 1.81 1.79 1.77 1.76 1.74 1.72 1.71 1.7035 1.85 1.83 1.82 1.80 1.79 1.76 1.74 1.72 1.70 1.68 1.66 1.65 1.64 1.6340 1.81 1.79 1.77 1.76 1.74 1.72 1.69 1.67 1.66 1.64 1.62 1.61 1.645 1.78 1.76 1.74 1.73 1.71 1.68 1.66 1.64 1.63 1.60 1.59 1.57 1.5650 1.76 1.74 1.72 1.70 1.69 1.66 1.63 1.61 1.60 1.58 1.56 160 1.72 1.70 1.68 1.66 1.65 1.62 1.59 1.57 1.56 1.53 1.52 1.570 1.70 1.67 1.65 1.64 1.62 1.59 1.57 1.55 1.53 1.50 1.4980 1.68 1.65 1.63 1.62 1.60 1.57 1.54 1.52 1.51 1.48 1.90 1.66 1.64 1.62 1.60 1.59 1.55 1.53 1.51 1.49 1.46
100 1.65 1.63 1.61 1.59 1.57 1.54 1.52 1.49 1.48120 1.63 1.61 1.59 1.57 1.55 1.52 1.50 1.47 1.140 1.62 1.60 1.57 1.56 1.54 1.51 1.48 1.46160 1.61 1.59 1.57 1.55 1.53 1.50 1.47 1180 1.60 1.58 1.56 1.54 1.52 1.49 1.46 1.4200 1.60 1.57 1.55 1.53 1.52 1.48 1.46
1.54 1.52 1.50 1.48 1.46 1.42 1.40
DENOMINATOR DEGREES OF FREEDOM
N1
N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-14 APPENDIX B
TABLE 6(b)Values of the
F
-Distribution:
A
.025
NUMERATOR DEGREES OF FREEDOM
123456789101112131415161718
1648 799 864 900 922 937 948 957 963 969 973 977 980 983 985 987 989 990 992 993238.5 39.0 39.2 39.2 39.3 39.3 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4317.4 16.0 15.4 15.1 14.9 14.7 14.6 14.5 14.5 14.4 14.4 14.3 14.3 14.3 14.3 14.2 14.2 14.2 14.2 14.2412.2 10.6 10.0 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.79 8.75 8.71 8.68 8.66 8.63 8.61 8.59 8.58 8.56510.0 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.57 6.52 6.49 6.46 6.43 6.40 6.38 6.36 6.34 6.3368.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.41 5.37 5.33 5.30 5.27 5.24 5.22 5.20 5.18 5.1778.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.71 4.67 4.63 4.60 4.57 4.54 4.52 4.50 4.48 4.4787.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.24 4.20 4.16 4.13 4.10 4.08 4.05 4.03 4.02 4.0097.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.91 3.87 3.83 3.80 3.77 3.74 3.72 3.70 3.68 3.67
10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.66 3.62 3.58 3.55 3.52 3.50 3.47 3.45 3.44 3.4211 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.47 3.43 3.39 3.36 3.33 3.30 3.28 3.26 3.24 3.2312 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.32 3.28 3.24 3.21 3.18 3.15 3.13 3.1113 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.20 3.15 3.12 3.08 3.05 3.03 3.00 2.14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.09 3.05 3.01 2.98 2.95 2.92 2.9015 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 3.01 2.96 2.92 2.89 2.86 2.84 216 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.93 2.89 2.85 2.82 2.79 2.76 2.74 2.717 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.87 2.82 2.79 2.75 2.72 2.7018 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.81 2.77 2.73 2.70 2.19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.76 2.72 2.68 2.65 2.6220 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.72 2.68 2.64 222 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.65 2.60 2.56 2.524 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.59 2.54 2.5026 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.54 2.49 228 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.4930 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.46 235 5.48 4.11 3.52 3.18 2.96 2.80 2.68 2.58 2.50 2.44 2.340 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.3345 5.38 4.01 3.42 3.09 2.86 2.70 2.58 2.49 2.50 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.38 2.360 5.29 3.93 3.34 3.01 2.79 2.63 2.51 270 5.25 3.89 3.31 2.97 2.75 2.59 2.47 2.380 5.22 3.86 3.28 2.95 2.73 2.57 2.45 2.3590 5.20 3.84 3.26 2.93 2.71 2.55 2
100 5.18 3.83 3.25 2.92 2.70 2.120 5.15 3.80 3.23 2.89 2.67 2.52140 5.13 3.79 3.21 2.88 2160 5.12 3.78 3.20 2.87 2.6180 5.11 3.77 3.19 2200 5.10 3.76 3.
5.03 3.69 3.12 2
f F( )
F
FA
A
0
N1
N2
DENOMINATOR DEGREES OF FREEDOM
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-15
APPENDIX B
NUMERATOR DEGREES OF FREEDOM
22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200
1995 997 999 1000 1001 1004 1006 1007 1008 1010 1011 1012 1013 1013 1014 1015 1015 1015 1016 1018239.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5 39.5314.1 14.1 14.1 14.1 14.1 14.1 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 13.9 13.9 13.9 13.9 13.9 13.948.53 8.51 8.49 8.48 8.46 8.43 8.41 8.39 8.38 8.36 8.35 8.33 8.33 8.32 8.31 8.30 8.30 8.29 8.29 8.2656.30 6.28 6.26 6.24 6.23 6.20 6.18 6.16 6.14 6.12 6.11 6.10 6.09 6.08 6.07 6.06 6.06 6.05 6.05 6.0265.14 5.12 5.10 5.08 5.07 5.04 5.01 4.99 4.98 4.96 4.94 4.93 4.92 4.92 4.90 4.90 4.89 4.89 4.88 4.8574.44 4.41 4.39 4.38 4.36 4.33 4.31 4.29 4.28 4.25 4.24 4.23 4.22 4.21 4.20 4.19 4.18 4.18 4.18 4.1483.97 3.95 3.93 3.91 3.89 3.86 3.84 3.82 3.81 3.78 3.77 3.76 3.75 3.74 3.73 3.72 3.71 3.71 3.70 3.6793.64 3.61 3.59 3.58 3.56 3.53 3.51 3.49 3.47 3.45 3.43 3.42 3.41 3.40 3.39 3.38 3.38 3.37 3.37 3.33
10 3.39 3.37 3.34 3.33 3.31 3.28 3.26 3.24 3.22 3.20 3.18 3.17 3.16 3.15 3.14 3.13 3.13 3.12 3.12 3.0811 3.20 3.17 3.15 3.13 3.12 3.09 3.06 3.04 3.03 3.00 2.99 2.97 2.96 2.96 2.94 2.94 2.93 2.92 2.92 2.8812 3.04 3.02 3.00 2.98 2.96 2.93 2.91 2.89 2.87 2.85 2.83 2.82 2.81 2.80 2.79 2.78 2.77 2.77 2.76 2.7313 2.92 2.89 2.87 2.85 2.84 2.80 2.78 2.76 2.74 2.72 2.70 2.69 2.68 2.67 2.66 2.65 2.64 2.64 2.63 2.6014 2.81 2.79 2.77 2.75 2.73 2.70 2.67 2.65 2.64 2.61 2.60 2.58 2.57 2.56 2.55 2.54 2.54 2.53 2.53 2.4915 2.73 2.70 2.68 2.66 2.64 2.61 2.59 2.56 2.55 2.52 2.51 2.49 2.48 2.47 2.46 2.45 2.44 2.44 2.44 2.416 2.65 2.63 2.60 2.58 2.57 2.53 2.51 2.49 2.47 2.45 2.43 2.42 2.40 2.40 2.38 2.37 2.37 2.36 2.36 2.3217 2.59 2.56 2.54 2.52 2.50 2.47 2.44 2.42 2.41 2.38 2.36 2.35 2.34 2.33 2.32 2.31 2.30 2.29 2.218 2.53 2.50 2.48 2.46 2.44 2.41 2.38 2.36 2.35 2.32 2.30 2.29 2.28 2.27 2.26 2.25 2.24 2.23 2.2319 2.48 2.45 2.43 2.41 2.39 2.36 2.33 2.31 2.30 2.27 2.25 2.24 2.23 2.22 2.20 2.19 2.19 220 2.43 2.41 2.39 2.37 2.35 2.31 2.29 2.27 2.25 2.22 2.20 2.19 2.18 2.17 2.16 2.15 2.1422 2.36 2.33 2.31 2.29 2.27 2.24 2.21 2.19 2.17 2.14 2.13 2.11 2.10 2.09 2.08 224 2.30 2.27 2.25 2.23 2.21 2.17 2.15 2.12 2.11 2.08 2.06 2.05 2.03 2.02 2.01 2.026 2.24 2.22 2.19 2.17 2.16 2.12 2.09 2.07 2.05 2.03 2.01 1.99 1.98 1.97 1.9528 2.20 2.17 2.15 2.13 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.94 1.93 1.92 1.91 130 2.16 2.14 2.11 2.09 2.07 2.04 2.01 1.99 1.97 1.94 1.92 1.90 1.89 1.835 2.09 2.06 2.04 2.02 2.00 1.96 1.93 1.91 1.89 1.86 1.84 1.82 1.8140 2.03 2.01 1.98 1.96 1.94 1.90 1.88 1.85 1.83 1.80 1.78 1.76 1.75 1.45 1.99 1.96 1.94 1.92 1.90 1.86 1.83 1.81 1.79 1.76 1.74 1.72 1.7050 1.96 1.93 1.91 1.89 1.87 1.83 1.80 1.77 1.75 1.72 1.70 160 1.91 1.88 1.86 1.83 1.82 1.78 1.74 1.72 1.70 1.67 1.6470 1.88 1.85 1.82 1.80 1.78 1.74 1.71 1.68 1.66 1.63 1.6080 1.85 1.82 1.79 1.77 1.75 1.71 1.68 1.65 1.63 1.60 1.90 1.83 1.80 1.77 1.75 1.73 1.69 1.66 1.63 1.61 1.58
100 1.81 1.78 1.76 1.74 1.71 1.67 1.64 1.61120 1.79 1.76 1.73 1.71 1.69 1.65 1.61 1.140 1.77 1.74 1.72 1.69 1.67 1.63 1.60 1.57 1.5160 1.76 1.73 1.70 1.68 1.66 1.62 1.58 1180 1.75 1.72 1.69 1.67 1.65 1.61 1.5200 1.74 1.71 1.68 1.66 1.64 1.60
1.67 1.64 1.61 1.59 1.57 1.52
DENOMINATOR DEGREES OF FREEDOM
N1
N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-16 APPENDIX B
TABLE 6(c)Values of the
F
-Distribution:
A
.01
NUMERATOR DEGREES OF FREEDOM
12345678910111213141516171
14052 4999 5403 5625 5764 5859 5928 5981 6022 6056 6083 6106 6126 6143 6157 6170 6181 6192 6201 6209298.5 99.0 99.2 99.2 99.3 99.3 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.4334.1 30.8 29.5 28.7 28.2 27.9 27.7 27.5 27.3 27.2 27.1 27.1 27.0 26.9 26.9 26.8 26.8 26.8 26.7 26.7421.2 18.0 16.7 16.0 15.5 15.2 15.0 14.8 14.7 14.5 14.5 14.4 14.3 14.2 14.2 14.2 14.1 14.1 14.0 14.0516.3 13.3 12.1 11.4 11.0 10.7 10.5 10.3 10.2 10.1 9.96 9.89 9.82 9.77 9.72 9.68 9.64613.7 10.9 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.79 7.72 7.66 7.60 7.56 7.52 7.48 7.45 7.42 7.40712.2 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.54 6.47 6.41 6.36 6.31 6.28 6.24 6.21 6.18 6.811.3 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.73 5.67 5.61 5.56 5.52 5.48 5.44 5.41910.6 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.18 5.11 5.05 5.01 4.96 4.92 4.89 4.86 4.83 4
10 10.0 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.77 4.71 4.65 4.60 4.56 4.52 4.49 4.46 4.43 411 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.46 4.40 4.34 4.29 4.25 4.21 4.18 4.15 4.1212 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.22 4.16 4.10 4.05 4.01 3.97 3.94 3.91 313 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 4.02 3.96 3.91 3.86 3.82 3.78 3.714 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.86 3.80 3.75 3.70 3.66 3.62 3.5915 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.73 3.67 3.61 3.56 3.52 3.49 3.45 316 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.62 3.55 3.50 3.45 3.41 3.37 3.317 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.52 3.46 3.40 3.35 3.31 3.2718 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.43 3.37 3.32 3.219 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.36 3.30 3.24 3.19 3.1520 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 3.18 3.22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.18 3.12 3.0724 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.09 3.03 2.98 226 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.96 2.90 2.28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.96 2.9030 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.35 7.42 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.8840 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 245 7.23 5.11 4.25 3.77 3.45 3.23 3.07 2.94 2.850 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.7860 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 270 7.01 4.92 4.07 3.60 3.29 3.0780 6.96 4.88 4.04 3.56 3.26 3.04 2.87 2.7490 6.93 4.85 4.01 3.53 3.23 3.01
100 6.90 4.82 3.98 3.51 3.21120 6.85 4.79 3.95 3.48 3.17 2.96140 6.82 4.76 3.92 3.46 3.15 2.160 6.80 4.74 3.91 3.44180 6.78 4.73 3.89 3.43 3200 6.76 4.71 3.8
6.64 4.61 3.7
f F( )
F
FA
A
0
N1
N2
DENOMINATOR DEGREES OF FREEDOM
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-17
APPENDIX B
NUMERATOR DEGREES OF FREEDOM
22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200
16223 6235 6245 6253 6261 6276 6287 6296 6303 6313 6321 6326 6331 6334 6339 6343 6346 6348 6350 6366299.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5 99.5326.6 26.6 26.6 26.5 26.5 26.5 26.4 26.4 26.4 26.3 26.3 26.3 26.3 26.2 26.2 26.2 26.2 26.2 26.2 26.1414.0 13.9 13.9 13.9 13.8 13.8 13.7 13.7 13.7 13.7 13.6 13.6 13.6 13.6 13.6 13.5 13.5 13.5 13.5 13.559.51 9.47 9.43 9.40 9.38 9.33 9.29 9.26 9.24 9.20 9.18 9.16 9.14 9.13 9.11 9.10 9.09 9.08 9.08 9.0267.35 7.31 7.28 7.25 7.23 7.18 7.14 7.11 7.09 7.06 7.03 7.01 7.00 6.99 6.97 6.96 6.95 6.94 6.93 6.8876.11 6.07 6.04 6.02 5.99 5.94 5.91 5.88 5.86 5.82 5.80 5.78 5.77 5.75 5.74 5.72 5.72 5.71 5.70 5.6585.32 5.28 5.25 5.22 5.20 5.15 5.12 5.09 5.07 5.03 5.01 4.99 4.97 4.96 4.95 4.93 4.92 4.92 4.91 4.8694.77 4.73 4.70 4.67 4.65 4.60 4.57 4.54 4.52 4.48 4.46 4.44 4.43 4.41 4.40 4.39 4.38 4.37 4.36 4.31
10 4.36 4.33 4.30 4.27 4.25 4.20 4.17 4.14 4.12 4.08 4.06 4.04 4.03 4.01 4.00 3.98 3.97 3.97 3.96 3.9111 4.06 4.02 3.99 3.96 3.94 3.89 3.86 3.83 3.81 3.78 3.75 3.73 3.72 3.71 3.69 3.68 3.67 3.66 3.66 3.6012 3.82 3.78 3.75 3.72 3.70 3.65 3.62 3.59 3.57 3.54 3.51 3.49 3.48 3.47 3.45 3.44 3.43 3.42 3.41 3.3613 3.62 3.59 3.56 3.53 3.51 3.46 3.43 3.40 3.38 3.34 3.32 3.30 3.28 3.27 3.25 3.24 3.23 3.23 3.22 3.1714 3.46 3.43 3.40 3.37 3.35 3.30 3.27 3.24 3.22 3.18 3.16 3.14 3.12 3.11 3.09 3.08 3.07 3.06 3.06 3.0115 3.33 3.29 3.26 3.24 3.21 3.17 3.13 3.10 3.08 3.05 3.02 3.00 2.99 2.98 2.96 2.95 2.94 2.93 2.92 2.816 3.22 3.18 3.15 3.12 3.10 3.05 3.02 2.99 2.97 2.93 2.91 2.89 2.87 2.86 2.84 2.83 2.82 2.81 2.81 217 3.12 3.08 3.05 3.03 3.00 2.96 2.92 2.89 2.87 2.83 2.81 2.79 2.78 2.76 2.75 2.73 2.72 2.72 2.7118 3.03 3.00 2.97 2.94 2.92 2.87 2.84 2.81 2.78 2.75 2.72 2.70 2.69 2.68 2.66 2.65 2.64 2.6319 2.96 2.92 2.89 2.87 2.84 2.80 2.76 2.73 2.71 2.67 2.65 2.63 2.61 2.60 2.58 2.57 2.56 220 2.90 2.86 2.83 2.80 2.78 2.73 2.69 2.67 2.64 2.61 2.58 2.56 2.55 2.54 2.52 2.50 2.49 2.422 2.78 2.75 2.72 2.69 2.67 2.62 2.58 2.55 2.53 2.50 2.47 2.45 2.43 2.42 2.40 2.39 2.38 2.3724 2.70 2.66 2.63 2.60 2.58 2.53 2.49 2.46 2.44 2.40 2.38 2.36 2.34 2.33 2.31 2.326 2.62 2.58 2.55 2.53 2.50 2.45 2.42 2.39 2.36 2.33 2.30 2.28 2.26 2.25 2.23 2.22 2.2128 2.56 2.52 2.49 2.46 2.44 2.39 2.35 2.32 2.30 2.26 2.24 2.22 2.20 2.19 2.17 2.15 230 2.51 2.47 2.44 2.41 2.39 2.34 2.30 2.27 2.25 2.21 2.18 2.16 2.14 2.135 2.40 2.36 2.33 2.30 2.28 2.23 2.19 2.16 2.14 2.10 2.07 2.05 2.03 240 2.33 2.29 2.26 2.23 2.20 2.15 2.11 2.08 2.06 2.02 1.99 1.97 1.95 1.45 2.27 2.23 2.20 2.17 2.14 2.09 2.05 2.02 2.00 1.96 1.93 1.91 1.8950 2.22 2.18 2.15 2.12 2.10 2.05 2.01 1.97 1.95 1.91 1.88 160 2.15 2.12 2.08 2.05 2.03 1.98 1.94 1.90 1.88 1.84 1.81 1.770 2.11 2.07 2.03 2.01 1.98 1.93 1.89 1.85 1.83 1.7880 2.07 2.03 2.00 1.97 1.94 1.89 1.85 1.82 1.79 1.75 1.90 2.04 2.00 1.97 1.94 1.92 1.86 1.82 1.79 1.76 1.72 1.68
100 2.02 1.98 1.95 1.92 1.89 1.84 1.80 1.76 1.74120 1.99 1.95 1.92 1.89 1.86 1.81 1.76 1.73 1.140 1.97 1.93 1.89 1.86 1.84 1.78 1.74 1.70160 1.95 1.91 1.88 1.85 1.82 1.76 1.72 1180 1.94 1.90 1.86 1.83 1.81 1.75 1.7200 1.93 1.89 1.85 1.82 1.79 1.74 1.69
1.83 1.79 1.76 1.73 1.70 1.64
ˆ
DENOMINATOR DEGREES OF FREEDOM
N1
N2
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-18 APPENDIX B
TABLE 6(d)Values of the
F
-Distribution:
A
.005
NUMERATOR DEGREES OF FREEDOM
12345678910111213141516171
116211 19999 21615 22500 23056 23437 23715 23925 24091 24224 24334 24426 24505 24572 24630 24681 24727 24767 2482199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199355.6 49.8 47.5 46.2 45.4 44.8 44.4 44.1 43.9 43.7 43.5 43.4 43.3 43.2 43.1 43.0 42.9 42.9 42.8 42.8431.3 26.3 24.3 23.2 22.5 22.0 21.6 21.4 21.1 21.0 20.8 20.7 20.6 20.5 20.4 20.4 20.3 20.3 20.2 20.2522.8 18.3 16.5 15.6 14.9 14.5 14.2 14.0 13.8 13.6 13.5 13.4 13.3 13.2 13.1 13.1 13.0 13.0 12.9 12.9618.6 14.5 12.9 12.0 11.5 11.1 10.8 10.6 10.4 10.3 10.1 10.0 9.95 9.88 9.81 9.76 9.71 9.66 9716.2 12.4 10.9 10.1 9.52 9.16 8.89 8.68 8.51 8.38 8.27 8.18 8.10 8.03 7.97 7.91 7.87 7.83 7.79 7.75814.7 11.0 9.60 8.81 8.30 7.95 7.69 7.50 7.34 7.21 7.10 7.01 6.94 6.87 6.81 6.76 6.72 6.68 6.64913.6 10.1 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.42 6.31 6.23 6.15 6.09 6.03 5.98 5.94 5.90 5.86 5.83
10 12.8 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.85 5.75 5.66 5.59 5.53 5.47 5.42 5.38 5.34 5.31 5.2711 12.2 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54 5.42 5.32 5.24 5.16 5.10 5.05 5.00 4.96 4.92 4.89 4.812 11.8 8.51 7.23 6.52 6.07 5.76 5.52 5.35 5.20 5.09 4.99 4.91 4.84 4.77 4.72 4.67 4.63 4.59 4.5613 11.4 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.82 4.72 4.64 4.57 4.51 4.46 4.41 4.37 4.33 414 11.1 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.60 4.51 4.43 4.36 4.30 4.25 4.20 4.16 4.1215 10.8 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54 4.42 4.33 4.25 4.18 4.12 4.0716 10.6 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38 4.27 4.18 4.10 4.03 3.97 3.917 10.4 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.14 4.05 3.97 3.90 3.84 3.7918 10.2 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.03 3.94 3.86 3.79 3.73 319 10.1 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.93 3.84 3.76 3.70 3.6420 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96 3.85 3.76 3.68 3.61 3.55 322 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.70 3.61 3.54 3.4724 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.50 3.42 3.35 3.3026 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60 3.49 3.40 3.33 3.228 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52 3.41 3.32 3.2530 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.34 3.25 3.18 335 8.98 6.19 5.09 4.48 4.09 3.81 3.61 3.45 3.32 3.21 3.1240 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 345 8.71 5.97 4.89 4.29 3.91 3.64 3.43 3.28 3.15 3.050 8.63 5.90 4.83 4.23 3.85 3.58 3.38 3.22 3.09 2.9960 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.0170 8.40 5.72 4.66 4.08 3.70 3.43 3.23 3.080 8.33 5.67 4.61 4.03 3.65 3.39 3.19 390 8.28 5.62 4.57 3.99 3.62 3.35 3.15 3.
100 8.24 5.59 4.54 3.96 3.59 3.33 3.1120 8.18 5.54 4.50 3.92 3.55 3.28140 8.14 5.50 4.47 3.89 3.52 3.160 8.10 5.48 4.44 3.87180 8.08 5.46 4.42 3.85 3200 8.06 5.44 4.41
7.88 5.30 4.28 3.
f F( )
F
FA
A
0
N1
N2
DENOMINATOR DEGREES OF FREEDOM
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-19
APPENDIX B
NUMERATOR DEGREES OF FREEDOM
22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200
124892 24940 24980 25014 25044 25103 25148 25183 25211 25253 25283 25306 25323 25337 25359 25374 25385 25394 25401 254642199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199 199342.7 42.6 42.6 42.5 42.5 42.4 42.3 42.3 42.2 42.1 42.1 42.1 42.0 42.0 42.0 42.0 41.9 41.9 41.9 41.8420.1 20.0 20.0 19.9 19.9 19.8 19.8 19.7 19.7 19.6 19.6 19.5 19.5 19.5 19.5 19.4 19.4 19.4 19.4 19.3512.8 12.8 12.7 12.7 12.7 12.6 12.5 12.5 12.5 12.4 12.4 12.3 12.3 12.3 12.3 12.3 12.2 12.2 12.2 12.169.53 9.47 9.43 9.39 9.36 9.29 9.24 9.20 9.17 9.12 9.09 9.06 9.04 9.03 9.00 8.98 8.97 8.96 8.95 8.8877.69 7.64 7.60 7.57 7.53 7.47 7.42 7.38 7.35 7.31 7.28 7.25 7.23 7.22 7.19 7.18 7.16 7.15 7.15 7.0886.55 6.50 6.46 6.43 6.40 6.33 6.29 6.25 6.22 6.18 6.15 6.12 6.10 6.09 6.06 6.05 6.04 6.03 6.02 5.9595.78 5.73 5.69 5.65 5.62 5.56 5.52 5.48 5.45 5.41 5.38 5.36 5.34 5.32 5.30 5.28 5.27 5.26 5.26 5.19
10 5.22 5.17 5.13 5.10 5.07 5.01 4.97 4.93 4.90 4.86 4.83 4.80 4.79 4.77 4.75 4.73 4.72 4.71 4.71 4.6411 4.80 4.76 4.72 4.68 4.65 4.60 4.55 4.52 4.49 4.45 4.41 4.39 4.37 4.36 4.34 4.32 4.31 4.30 4.29 4.2312 4.48 4.43 4.39 4.36 4.33 4.27 4.23 4.19 4.17 4.12 4.09 4.07 4.05 4.04 4.01 4.00 3.99 3.98 3.97 3.9113 4.22 4.17 4.13 4.10 4.07 4.01 3.97 3.94 3.91 3.87 3.84 3.81 3.79 3.78 3.76 3.74 3.73 3.72 3.71 314 4.01 3.96 3.92 3.89 3.86 3.80 3.76 3.73 3.70 3.66 3.62 3.60 3.58 3.57 3.55 3.53 3.52 3.51 3.50 3.4415 3.83 3.79 3.75 3.72 3.69 3.63 3.58 3.55 3.52 3.48 3.45 3.43 3.41 3.39 3.37 3.36 3.34 3.34 3.33 3.2616 3.68 3.64 3.60 3.57 3.54 3.48 3.44 3.40 3.37 3.33 3.30 3.28 3.26 3.25 3.22 3.21 3.20 3.19 3.18 3.1117 3.56 3.51 3.47 3.44 3.41 3.35 3.31 3.28 3.25 3.21 3.18 3.15 3.13 3.12 3.10 3.08 3.07 3.06 3.018 3.45 3.40 3.36 3.33 3.30 3.25 3.20 3.17 3.14 3.10 3.07 3.04 3.02 3.01 2.99 2.97 2.9619 3.35 3.31 3.27 3.24 3.21 3.15 3.11 3.07 3.04 3.00 2.97 2.95 2.93 2.91 2.89 2.87 2.20 3.27 3.22 3.18 3.15 3.12 3.07 3.02 2.99 2.96 2.92 2.88 2.86 2.84 2.83 2.81 2.79 2.78 2.722 3.12 3.08 3.04 3.01 2.98 2.92 2.88 2.84 2.82 2.77 2.74 2.72 2.70 2.69 2.66 2.65 2.6324 3.01 2.97 2.93 2.90 2.87 2.81 2.77 2.73 2.70 2.66 2.63 2.60 2.58 2.57 2.55 2.53 2.26 2.92 2.87 2.84 2.80 2.77 2.72 2.67 2.64 2.61 2.56 2.53 2.51 2.49 2.47 2.45 2.4328 2.84 2.79 2.76 2.72 2.69 2.64 2.59 2.56 2.53 2.48 2.45 2.43 2.41 2.39 2.37 230 2.77 2.73 2.69 2.66 2.63 2.57 2.52 2.49 2.46 2.42 2.38 2.36 2.34 2.32 2.30 2.235 2.64 2.60 2.56 2.53 2.50 2.44 2.39 2.36 2.33 2.28 2.25 2.22 2.20 2.19 2.1640 2.55 2.50 2.46 2.43 2.40 2.34 2.30 2.26 2.23 2.18 2.15 2.12 2.10 2.45 2.47 2.43 2.39 2.36 2.33 2.27 2.22 2.19 2.16 2.11 2.08 2.05 2.0350 2.42 2.37 2.33 2.30 2.27 2.21 2.16 2.13 2.10 2.05 2.02 1.99 160 2.33 2.29 2.25 2.22 2.19 2.13 2.08 2.04 2.01 1.96 1.93 1.970 2.28 2.23 2.19 2.16 2.13 2.07 2.02 1.98 1.95 1.90 1.8680 2.23 2.19 2.15 2.11 2.08 2.02 1.97 1.94 1.90 1.85 1.90 2.20 2.15 2.12 2.08 2.05 1.99 1.94 1.90 1.87 1.82 1.78
100 2.17 2.13 2.09 2.05 2.02 1.96 1.91 1.87 1.84 1.79120 2.13 2.09 2.05 2.01 1.98 1.92 1.87 1.83 1.140 2.11 2.06 2.02 1.99 1.96 1.89 1.84 1.80160 2.09 2.04 2.00 1.97 1.93 1.87 1.82 1.78180 2.07 2.02 1.98 1.95 1.92 1.85 1.8200 2.06 2.01 1.97 1.94 1.91 1.84
1.95 1.90 1.86 1.82 1.79 1.72 1.67
DENOMINATOR DEGREES OF FREEDOM
N1
N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r
B-20 APPENDIX B
TABLE 7(a) Critical Values of the Studentized Range, .05A
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r

Tài liệu khác của Trường Đại học Ngoại Thương

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Appendix B TABLES TABLE 1Binomial Probabilities P(X…k)=a Tabulated values are
k p(xi). (Values are rounded to four decimal places.) x=0 n 5 p k 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 0.9510
0.7738 0.5905 0.3277 0.2373 0.1681 0.0778 0.0313 0.0102 0.0024 0.0010 0.0003 0.0000 0.0000 0.0000 1 0.9990 0.9774 0.9185 0.7373 0.6328 0.5282 0.3370 0.1875 0.0870 0.0308 0.0156 0.0067 0.0005 0.0000 0.0000 2 1.0000 0.9988 0.9914 0.9421
0.8965 0.8369 0.6826 0.5000 0.3174 0.1631
0.1035 0.0579 0.0086 0.0012 0.0000 3
1.0000 1.0000 0.9995 0.9933 0.9844 0.9692 0.9130 0.8125 0.6630 0.4718 0.3672 0.2627 0.0815 0.0226 0.0010 4
1.0000 1.0000 1.0000 0.9997 0.9990 0.9976 0.9898 0.9688 0.9222 0.8319
0.7627 0.6723 0.4095 0.2262 0.0490 n 6 p k 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 0.9415 0.7351 0.5314 0.2621 0.1780 0.1176 0.0467 0.0156 0.0041 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000 1
0.9985 0.9672 0.8857 0.6554 0.5339 0.4202 0.2333 0.1094 0.0410 0.0109 0.0046 0.0016 0.0001 0.0000 0.0000 2 1.0000 0.9978 0.9842 0.9011
0.8306 0.7443 0.5443 0.3438 0.1792 0.0705 0.0376 0.0170 0.0013 0.0001 0.0000 3
1.0000 0.9999 0.9987 0.9830 0.9624 0.9295 0.8208 0.6563 0.4557 0.2557 0.1694 0.0989 0.0159 0.0022 0.0000 4
1.0000 1.0000 0.9999 0.9984 0.9954 0.9891
0.9590 0.8906 0.7667 0.5798 0.4661 0.3446 0.1143 0.0328 0.0015 5
1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9959 0.9844 0.9533 0.8824 0.8220 0.7379 0.4686 0.2649 0.0585 n 7 p k 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 0.9321
0.6983 0.4783 0.2097 0.1335 0.0824 0.0280 0.0078 0.0016 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 1
0.9980 0.9556 0.8503 0.5767 0.4449 0.3294 0.1586 0.0625 0.0188 0.0038 0.0013 0.0004 0.0000 0.0000 0.0000 2
1.0000 0.9962 0.9743 0.8520 0.7564 0.6471 0.4199 0.2266 0.0963 0.0288 0.0129 0.0047 0.0002 0.0000 0.0000 3
1.0000 0.9998 0.9973 0.9667 0.9294 0.8740 0.7102 0.5000 0.2898 0.1260 0.0706 0.0333 0.0027 0.0002 0.0000 4
1.0000 1.0000 0.9998 0.9953 0.9871 0.9712 0.9037 0.7734 0.5801
0.3529 0.2436 0.1480 0.0257 0.0038 0.0000 5
1.0000 1.0000 1.0000 0.9996 0.9987 0.9962 0.9812 0.9375 0.8414 0.6706 0.5551 0.4233 0.1497 0.0444 0.0020 6
1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9984 0.9922 0.9720 0.9176 0.8665 0.7903 0.5217 0.3017 0.0679 B-1
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-2 APPENDIX B TABLE 1 (Continued) n 8 p k 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
0.9227 0.6634 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9973 0.9428 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 2 0.9999 0.9942 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113 0.0042 0.0012 0.0000 0.0000 0.0000 3
1.0000 0.9996 0.9950 0.9437 0.8862 0.8059 0.5941
0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 0.0000 0.0000 4
1.0000 1.0000 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 0.0004 0.0000 5
1.0000 1.0000 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 0.0058 0.0001 6
1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9915
0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 0.0572 0.0027 7
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961
0.9832 0.9424 0.8999 0.8322 0.5695 0.3366 0.0773 n 9 p k 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 0.9135 0.6302 0.3874 0.1342 0.0751
0.0404 0.0101 0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1
0.9966 0.9288 0.7748 0.4362 0.3003 0.1960 0.0705 0.0195 0.0038 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 2 0.9999 0.9916 0.9470 0.7382 0.6007 0.4628 0.2318 0.0898 0.0250 0.0043 0.0013 0.0003 0.0000 0.0000 0.0000 3 1.0000 0.9994 0.9917 0.9144
0.8343 0.7297 0.4826 0.2539 0.0994 0.0253 0.0100 0.0031 0.0001 0.0000 0.0000 4 1.0000 1.0000 0.9991 0.9804 0.9511 0.9012
0.7334 0.5000 0.2666 0.0988 0.0489 0.0196 0.0009 0.0000 0.0000 5
1.0000 1.0000 0.9999 0.9969 0.9900 0.9747 0.9006 0.7461 0.5174 0.2703
0.1657 0.0856 0.0083 0.0006 0.0000 6
1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9750 0.9102 0.7682 0.5372 0.3993 0.2618 0.0530 0.0084 0.0001 7
1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9962 0.9805 0.9295 0.8040 0.6997 0.5638 0.2252 0.0712 0.0034 8
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9899 0.9596 0.9249 0.8658 0.6126 0.3698 0.0865
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-3 TABLE 1 (Continued) n 10 p k 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 0.9044 0.5987 0.3487 0.1074 0.0563 0.0282 0.0060 0.0010 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9957 0.9139 0.7361
0.3758 0.2440 0.1493 0.0464 0.0107
0.0017 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 2
0.9999 0.9885 0.9298 0.6778 0.5256 0.3828 0.1673 0.0547 0.0123 0.0016 0.0004 0.0001 0.0000 0.0000 0.0000 3 1.0000 0.9990 0.9872 0.8791 0.7759 0.6496 0.3823 0.1719 0.0548 0.0106
0.0035 0.0009 0.0000 0.0000 0.0000 4
1.0000 0.9999 0.9984 0.9672 0.9219 0.8497 0.6331 0.3770 0.1662 0.0473 0.0197 0.0064 0.0001 0.0000 0.0000 5
1.0000 1.0000 0.9999 0.9936 0.9803 0.9527 0.8338 0.6230 0.3669 0.1503 0.0781 0.0328 0.0016 0.0001 0.0000 6 1.0000 1.0000 1.0000 0.9991 0.9965 0.9894 0.9452 0.8281 0.6177 0.3504 0.2241 0.1209 0.0128 0.0010 0.0000 7
1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9877 0.9453 0.8327 0.6172 0.4744 0.3222 0.0702 0.0115 0.0001 8
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9893 0.9536 0.8507 0.7560 0.6242 0.2639 0.0861 0.0043 9
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9990 0.9940 0.9718 0.9437 0.8926 0.6513 0.4013 0.0956 n 15 p k 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
0.8601 0.4633 0.2059 0.0352 0.0134 0.0047 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9904 0.8290 0.5490 0.1671
0.0802 0.0353 0.0052 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2
0.9996 0.9638 0.8159 0.3980 0.2361 0.1268 0.0271
0.0037 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3
1.0000 0.9945 0.9444 0.6482 0.4613 0.2969 0.0905 0.0176 0.0019 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 4
1.0000 0.9994 0.9873 0.8358 0.6865 0.5155 0.2173 0.0592 0.0093 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 5
1.0000 0.9999 0.9978 0.9389 0.8516 0.7216 0.4032 0.1509 0.0338 0.0037 0.0008 0.0001 0.0000 0.0000 0.0000 6
1.0000 1.0000 0.9997 0.9819 0.9434 0.8689 0.6098 0.3036 0.0950 0.0152 0.0042 0.0008 0.0000 0.0000 0.0000 7
1.0000 1.0000 1.0000 0.9958 0.9827 0.9500 0.7869 0.5000 0.2131
0.0500 0.0173 0.0042 0.0000 0.0000 0.0000 8
1.0000 1.0000 1.0000 0.9992 0.9958 0.9848 0.9050 0.6964 0.3902 0.1311 0.0566 0.0181 0.0003 0.0000 0.0000 9
1.0000 1.0000 1.0000 0.9999 0.9992 0.9963 0.9662 0.8491 0.5968 0.2784 0.1484 0.0611 0.0022 0.0001 0.0000 10
1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9907 0.9408 0.7827 0.4845 0.3135 0.1642 0.0127 0.0006 0.0000 11
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9981 0.9824 0.9095 0.7031 0.5387 0.3518 0.0556 0.0055 0.0000 12
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9963 0.9729 0.8732 0.7639 0.6020 0.1841 0.0362 0.0004 13
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9948 0.9647 0.9198 0.8329 0.4510 0.1710 0.0096 14
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9953 0.9866 0.9648 0.7941 0.5367 0.1399
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-4 APPENDIX B TABLE 1 (Continued) n 20 p k 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 0.8179 0.3585 0.1216 0.0115
0.0032 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1
0.9831 0.7358 0.3917 0.0692 0.0243 0.0076 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2
0.9990 0.9245 0.6769 0.2061 0.0913 0.0355 0.0036 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 1.0000 0.9841 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4
1.0000 0.9974 0.9568 0.6296 0.4148 0.2375 0.0510
0.0059 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5
1.0000 0.9997 0.9887 0.8042 0.6172 0.4164 0.1256 0.0207
0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6
1.0000 1.0000 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 7
1.0000 1.0000 0.9996 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210
0.0013 0.0002 0.0000 0.0000 0.0000 0.0000 8
1.0000 1.0000 0.9999 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0009 0.0001 0.0000 0.0000 0.0000 9
1.0000 1.0000 1.0000 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171
0.0039 0.0006 0.0000 0.0000 0.0000 10
1.0000 1.0000 1.0000 0.9994 0.9961 0.9829 0.8725 0.5881 0.2447 0.0480 0.0139 0.0026 0.0000 0.0000 0.0000 11
1.0000 1.0000 1.0000 0.9999 0.9991
0.9949 0.9435 0.7483 0.4044 0.1133 0.0409 0.0100 0.0001 0.0000 0.0000 12
1.0000 1.0000 1.0000 1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.1018 0.0321 0.0004 0.0000 0.0000 13
1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.2142 0.0867 0.0024 0.0000 0.0000 14
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9984 0.9793 0.8744 0.5836 0.3828 0.1958 0.0113 0.0003 0.0000 15
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9941 0.9490 0.7625 0.5852 0.3704 0.0432 0.0026 0.0000 16
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9987 0.9840 0.8929 0.7748 0.5886 0.1330 0.0159 0.0000 17
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9964 0.9645 0.9087 0.7939 0.3231 0.0755 0.0010 18
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9924 0.9757 0.9308 0.6083 0.2642 0.0169 19
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9968 0.9885 0.8784 0.6415 0.1821
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-5 TABLE 1 (Continued) n 25 p k 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 0.7778 0.2774 0.0718
0.0038 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9742 0.6424 0.2712 0.0274 0.0070
0.0016 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.9980 0.8729 0.5371
0.0982 0.0321 0.0090 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3
0.9999 0.9659 0.7636 0.2340 0.0962 0.0332 0.0024 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4
1.0000 0.9928 0.9020 0.4207 0.2137 0.0905 0.0095 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5
1.0000 0.9988 0.9666 0.6167 0.3783 0.1935 0.0294 0.0020 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6
1.0000 0.9998 0.9905 0.7800 0.5611
0.3407 0.0736 0.0073 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7
1.0000 1.0000 0.9977 0.8909 0.7265 0.5118
0.1536 0.0216 0.0012 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 8
1.0000 1.0000 0.9995 0.9532 0.8506 0.6769 0.2735 0.0539 0.0043 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 9
1.0000 1.0000 0.9999 0.9827 0.9287 0.8106 0.4246 0.1148
0.0132 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 10
1.0000 1.0000 1.0000 0.9944 0.9703 0.9022 0.5858 0.2122 0.0344 0.0018 0.0002 0.0000 0.0000 0.0000 0.0000 11
1.0000 1.0000 1.0000 0.9985 0.9893 0.9558 0.7323 0.3450 0.0778 0.0060 0.0009 0.0001 0.0000 0.0000 0.0000 12
1.0000 1.0000 1.0000 0.9996 0.9966 0.9825 0.8462 0.5000 0.1538 0.0175 0.0034 0.0004 0.0000 0.0000 0.0000 13
1.0000 1.0000 1.0000 0.9999 0.9991 0.9940 0.9222 0.6550 0.2677 0.0442 0.0107 0.0015 0.0000 0.0000 0.0000 14
1.0000 1.0000 1.0000 1.0000 0.9998 0.9982 0.9656 0.7878 0.4142 0.0978 0.0297 0.0056 0.0000 0.0000 0.0000 15
1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9868 0.8852 0.5754 0.1894 0.0713 0.0173 0.0001 0.0000 0.0000 16
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9957 0.9461 0.7265 0.3231 0.1494 0.0468 0.0005 0.0000 0.0000 17
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9988 0.9784 0.8464 0.4882 0.2735 0.1091 0.0023 0.0000 0.0000 18
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9927 0.9264 0.6593 0.4389 0.2200 0.0095 0.0002 0.0000 19
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9980 0.9706 0.8065 0.6217 0.3833 0.0334 0.0012 0.0000 20
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9905 0.9095 0.7863 0.5793 0.0980 0.0072 0.0000 21
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9976 0.9668 0.9038 0.7660 0.2364 0.0341 0.0001 22
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9910 0.9679 0.9018 0.4629 0.1271 0.0020 23
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9984 0.9930 0.9726 0.7288 0.3576 0.0258 24
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9962 0.9282 0.7226 0.2222
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-6 APPENDIX B TABLE 2 Poisson Probabilities
Tabulated values are P(X…k)=a k
x=0p(xi) . (Values are rounded to four decimal places.) µ k 0.10 0.20 0.30 0.40 0.50 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067 0.0041 0.0025
1 0.9953 0.9825 0.9631 0.9384 0.9098 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404 0.0266 0.0174
2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247 0.0884 0.0620
3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650 0.2017 0.1512 4
1.0000 1.0000 0.9999 0.9998 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405 0.3575 0.2851 5 1.0000 1.0000 0.9994 0.9955 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160 0.5289 0.4457 6 0.9999 0.9991
0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622 0.6860 0.6063 7
1.0000 0.9998 0.9989 0.9958 0.9881
0.9733 0.9489 0.9134 0.8666 0.8095 0.7440 8
1.0000 0.9998 0.9989 0.9962 0.9901
0.9786 0.9597 0.9319 0.8944 0.8472 9
1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.9682 0.9462 0.9161 10
0.9999 0.9997 0.9990 0.9972 0.9933 0.9863 0.9747 0.9574 11 1.0000 0.9999 0.9997 0.9991 0.9976 0.9945 0.9890 0.9799 12 1.0000 0.9999 0.9997 0.9992 0.9980 0.9955 0.9912 13 1.0000 0.9999 0.9997 0.9993 0.9983 0.9964 14 1.0000 0.9999 0.9998 0.9994 0.9986 15 1.0000 0.9999 0.9998 0.9995 16 1.0000 0.9999 0.9998 17 1.0000 0.9999 18 1.0000 19 20
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-7 TABLE 2 ( Continued) µ k 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10 11 12 13 14 15
0 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0.0008 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000
2 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0.0042 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000
3 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.0149 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002
4 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0.0403 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009
5 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.0885 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028
6 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.1649 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076
7 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180
8 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374
9 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699
10 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185
11 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848
12 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676
13 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632
14 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657
15 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.9665 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681
16 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641
17 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489
18 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195
19 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752 20
1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170 21
1.0000 0.9999 0.9998 0.9996 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469 22
1.0000 0.9999 0.9999 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673 23
1.0000 0.9999 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 24
1.0000 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 25
0.9999 0.9997 0.9990 0.9974 0.9938 26
1.0000 0.9999 0.9995 0.9987 0.9967 27 0.9999 0.9998 0.9994 0.9983 28 1.0000 0.9999 0.9997 0.9991 29 1.0000 0.9999 0.9996 30 0.9999 0.9998 31 1.0000 0.9999 32 1.0000
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TABLE 3 Cumulative Standardized Normal Probabilities z 0 P(-q6Z6z) Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.0
0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9
0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8
0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7
0.0035 0.0034 0.0033 0.0032 0.0031
0.0030 0.0029 0.0028 0.0027 0.0026 -2.6
0.0047 0.0045 0.0044 0.0043 0.0041
0.0040 0.0039 0.0038 0.0037 0.0036 -2.5
0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.2
0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170
0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207
0.0202 0.0197 0.0192 0.0188 0.0183 -1.9
0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351
0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516
0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.5
0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808
0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901
0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075
0.1056 0.1038 0.1020 0.1003 0.0985 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515
0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119
0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7
0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4
0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.3 0.3821 0.3783 0.3745 0.3707
0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129
0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1
0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.0
0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-9 TABLE 3 ( Continued) 0z P(-q6Z6z) . Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1
0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6
0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611
0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910
0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9
0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0
0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1
0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907
0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3
0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251
0.9265 0.9279 0.9292 0.9306 0.9319 1.5
0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6
0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7
0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8
0.9641 0.9649 0.9656 0.9664 0.9671
0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719
0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1
0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3
0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4
0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5
0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6
0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7
0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9
0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
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TABLE 5 Critical Values of the Distribution 2 f(x2) A x2 0A 2 x Degrees of Freedom 2 .995 2 .990 2 .975 2 .950 2 .900 2 .100 2 .050 2 .025 2 .010 2 .005 1 0.000039 0.000157 0.000982 0.00393 0.0158 2.71 3.84 5.02 6.63 7.88 2 0.0100 0.0201 0.0506 0.103 0.211 4.61 5.99 7.38 9.21 10.6 3 0.072 0.115 0.216 0.352 0.584 6.25 7.81 9.35 11.3 12.8 4 0.207 0.297 0.484 0.711 1.06 7.78 9.49 11.1 13.3 14.9 5 0.412 0.554 0.831 1.15 1.61 9.24 11.1 12.8 15.1 16.7 6 0.676 0.872 1.24 1.64 2.20 10.6 12.6 14.4 16.8 18.5 7 0.989 1.24 1.69 2.17 2.83 12.0 14.1 16.0 18.5 20.3 8 1.34 1.65 2.18 2.73 3.49 13.4 15.5 17.5 20.1 22.0 9 1.73 2.09 2.70 3.33 4.17 14.7 16.9 19.0 21.7 23.6 10 2.16 2.56 3.25 3.94 4.87 16.0 18.3 20.5 23.2 25.2 11 2.60 3.05 3.82 4.57 5.58 17.3 19.7 21.9 24.7 26.8 12 3.07 3.57 4.40 5.23 6.30 18.5 21.0 23.3 26.2 28.3 13 3.57 4.11 5.01 5.89 7.04 19.8 22.4 24.7 27.7 29.8 14 4.07 4.66 5.63 6.57 7.79 21.1 23.7 26.1 29.1 31.3 15 4.60 5.23 6.26 7.26 8.55 22.3 25.0 27.5 30.6 32.8 16 5.14 5.81 6.91 7.96 9.31 23.5 26.3 28.8 32.0 34.3 17 5.70 6.41 7.56 8.67 10.1 24.8 27.6 30.2 33.4 35.7 18 6.26 7.01 8.23 9.39 10.9 26.0 28.9 31.5 34.8 37.2 19 6.84 7.63 8.91 10.1 11.7 27.2 30.1 32.9 36.2 38.6 20 7.43 8.26 9.59 10.9 12.4 28.4 31.4 34.2 37.6 40.0 21 8.03 8.90 10.3 11.6 13.2 29.6 32.7 35.5 38.9 41.4 22 8.64 9.54 11.0 12.3 14.0 30.8 33.9 36.8 40.3 42.8 23 9.26 10.2 11.7 13.1 14.8 32.0 35.2 38.1 41.6 44.2 24 9.89 10.9 12.4 13.8 15.7 33.2 36.4 39.4 43.0 45.6 25 10.5 11.5 13.1 14.6 16.5 34.4 37.7 40.6 44.3 46.9 26 11.2 12.2 13.8 15.4 17.3 35.6 38.9 41.9 45.6 48.3 27 11.8 12.9 14.6 16.2 18.1 36.7 40.1 43.2 47.0 49.6 28 12.5 13.6 15.3 16.9 18.9 37.9 41.3 44.5 48.3 51.0 29 13.1 14.3 16.0 17.7 19.8 39.1 42.6 45.7 49.6 52.3 30 13.8 15.0 16.8 18.5 20.6 40.3 43.8 47.0 50.9 53.7 40 20.7 22.2 24.4 26.5 29.1 51.8 55.8 59.3 63.7 66.8 50 28.0 29.7 32.4 34.8 37.7 63.2 67.5 71.4 76.2 79.5 60 35.5 37.5 40.5 43.2 46.5 74.4 79.1 83.3 88.4 92.0 70 43.3 45.4 48.8 51.7 55.3 85.5 90.5 95.0 100 104 80 51.2 53.5 57.2 60.4 64.3 96.6 102 107 112 116 90 59.2 61.8 65.6 69.1 73.3 108 113 118 124 128 100 67.3 70.1 74.2 77.9 82.4 118 124 130 136 140
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-12 APPENDIX B NUMERATOR DEGREES OF FREEDOM .05 A F -Distribution: F A FA 7 1 6 1 5 1 4 1 3 1 2 1 1 123456789 01 1 1161 2 199 18.5 31 19.0 0.1 47.71 5 216 19.2 6.61 6 7225 19.2 9.55 5.995.59 8 230 9.28 6.945.79 5.14 5.32 9 234 19.39.12 6.595.4 4.76 4.74 5.12 1 4.46 237 19.39.0 6.39 4.53 4.354.0 4.26 7 239 19.4 1 6.26 4.12 19.4 3.866.16 5.19 4.39 4.28 3.97 3.84 3.63 241 19.4 8.94 6.09 5.054.2 3.87 1 3.48 242 19.4 8.89 6.04 4.95 3.79 3.693.37 243 19.4 8.85 6.00 4.88 3.73 3.58 244 19.4 8.8 4.15 3.29 1 4.82 3.68 3.50 245 5.96 4.77 4.10 3.44 3.23 245 19.4 8.79 5.94 4.74 3.64 3.39 3.18 246 19.4 8.76 5.914.70 4.06 3.60 3.35 3.14 246 19.4 4.03 3.57 3.3 3.10 1 247 19.4 8.74 5.89 4.684.00 3.55 247 19.4 8.73 5.87 4.663.98 3.53 3.07 248 19.4 8.71 5.86 4.64 3.5 3.28 1 248 19.4 5.84 4.62 3.96 3.263.05 19.4 8.70 3.94 3.24 8.69 5.83 4.603.92 3.49 3.22 3.03 8.68 5.82 4.593.91 3.48 3.20 3.01 8.67 5.81 4.583.90 3.47 3.19 2.99 8.67 5.80 4.573.88 3.46 3.17 2.97 8.66 4.563.87 3.44 3.16 2.96 3.15 2.95 2.94 N1 10 4.96 11 4.1 4.84 12 03.98 4.75 13 4.67 14 153.7 3.59 3.893.8 4.60 1613.36 3.49 13.74 4.544.49 17 18 3.48 3.20 3.26 3.68 4.45 3.1 3.4 3.34 191 3.63 4.4 3.33 3.09 1 3.1 3.29 20 1 3.24 3.59 4.38 22 3.22 3.0 3.06 3.20 4.35 24 1 3.18 3.0 3.55 3.52 4.30 26 3.14 3.00 3.03 2.96 2.90 2.96 3.49 4.26 2.8 3.16 3.133.1 3.44 4.23 28 3.0 2.95 2.91 2.85 2.79 2.85 1 2.90 0 3.40 4.20 30 7 3.05 352.90 2.85 2.92 2.7 2.932.83 2.76 1 2.74 3.0 3.37 1 4.17 402.7 2.77 2.74 2.82 2.98 3.34 4.12 45 3.02 2.85 2.80 2.77 2.70 2.66 02.66 2.63 2.87 3.32 2.7 2.66 2.74 2.95 3.27 4.084.06 50 2.98 2.82 2.75 2.7 2.65 2.641 2.78 2.7 2.92 3.23 60 1 2.59 2.58 2.54 2.55 2.59 1 2.87 3.20 4.03 70 2.94 2.79 2.72 2.60 2.592.54 2.612.5 2.48 2.62 2.69 2.84 3.18 4.00 80 1 2.60 2.46 2.5 2.47 2.64 2.8 3.98902.91 2.76 2.69 2.67 2.57 2.54 2.55 2.53 2.6 3.152.5 2.49 2.42 2.40 1 2.56 2.49 2.79 3.13 3.96 1 2.51 2.39 3.952.89 2.74 2.66 2.63 2.53 2.46 2.492.46 2.38 2.76 3.12.45 2.34 2.32 2.45 2.42 2.37 2.58 2.56 2.74 13.10 2.86 2.72 2.64 2.60 2.51 2.48 2.42 2.452.41 2.34 2.532.39 2.30 2.422.27 2.36 2.33 2.29 2.452.42 2.40 2.50 2.85 2.7 2.62 2.41 2.3 2.36 2.27 2.34 2.37 2.72 0 2.58 2.48 2.45 2.40 2.37 1 2.35 2.26 2.22 2.292.2 2.22 2.3 2.291 2.35 2.7 2.83 2.60 2.55 2.46 2.42 2.37 2.382.34 1 2.252.31 2.23 2.302.18 2.24 2.16 2.25 2.20 2.23 2.493.84 2.81 2.69 2.58 2.53 2.44 2.40 2.35 2.352.31 2.28 2.172.28 2.20 2.252.15 2.19 2.1 2.18 2.33 1 2.22 2.13 2.1 2.14 2.47 3.00 2.80 2.67 2.57 2.51 2.43 2.1602.38 2.33 2.332.29 2.26 2.25 2.17 2.222.12 2.15 2.12 2.15 2.0 2.217 2.07 2.32 2.61 2 2.6 2.56 2.5 2.4 2.13 2.3 2.312. 2.23 2.18 2.122 2.0 2.08 2. 2.13 100 3.94 120 3.09 3.92 140 3.9 160 2.7 3.0 1 7 180 0 3.90 3.05 3.89 200 3.89 2.46 2.68 3.062.66 3.053.04 2.3 2.45 2.67 2.65 12.29 2.44 2.43 2.65 2 2.2 2.422. DENOMINATOR DEGREES OF FREEDOM N2 TABLE f(F) 6(a)Critical 0 Values of the
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-13 NUMERATOR DEGREES OF FREEDOM 22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 1249 2 249 19.5 3 249 19.5 8.65 4 5 250 19.5 8.64 5.794.54 6 250 719.5 8.63 5.77 3.86 8.62 5.76 4.538 4.52 3.84 3.43 3.4 3.13 9 1251 19.58.62 5.754.50 3.83 3.12 2.92 251 19.58.60 5.75 3.82 3.1 2.90 0 251 19.5 5.73 4.50 3.8 3.40 1 2.89 252 19.5 8.59 5.72 4.48 3.39 2.87 252 19.5 8.59 5.7 4.46 3.38 3.09 1 3.79 2.86 252 19.5 8.58 4.45 3.36 3.08 253 19.5 8.57 5.7 4.44 3.77 3.34 3.06 2.84 253 8.57 04.43 3.76 3.33 3.04 2.83 253 19.58.56 4.42 3.75 3.03 2.81 253 19.58.56 5.69 3.324.4 3.74 3.02 253 19.5 5.68 1 3.73 3.303.0 2.80 1254 19.5 8.55 5.67 3.72 3.29 2.79 254 19.5 8.55 5.67 4.413.72 3.29 2.78 254 19.5 8.55 5.66 3.7 3.28 2.992.77254 19.5 8.54 5.66 4.41 13.27 2.99 19.5 8.54 5.65 4.40 3.27 2.98 2.76 19.5 8.54 4.39 3.70 2.97 2.76 8.53 5.65 3.26 5.65 4.39 3.703.26 2.97 2.75 5.65 4.39 3.703.25 2.96 2.74 5.63 4.39 3.69 2.96 2.74 4.37 3.69 3.25 2.73 3.67 3.23 2.95 2.95 2.73 2.93 2.71 N1 10 2.75 11 2.74 2.63 12 13 2.72 2.6 2.52 12.5 2.44 14 15 2.7 1 2.37 16 1 2.59 2.42 2.3 2.4 2.35 117 1 2.252.2 18 2.7 2.58 2.49 2.33 2.24 119 02.57 2.48 2.172.39 2.32 2.29 202.27 2.22 2.15 2.132.1 22 02.68 2.55 2.472.38 2.31 2.26 2.2 2.19 2.1 24 1 2.13 1 2.05 26 2.66 2.53 2.442.36 2.25 2.172.12 2.08 2.03 2.001.97 28 2.65 2.52 2.43 2.16 1.98 30 2.4 2.34 2.28 2.22 2.19 2.1 2.10 2.0 1.93 1 2.0 1 357 1.95 1.912.64 2.5 1 2.15 1.97 1.9 401 2.33 2.27 2.20 2.17 2.08 1.93 1.851.8 45 2.62 2.3 2.25 2.12 2.07 1.95 1501 2.19 2.152.1 2.08 2.05 2.00 1.9 1.89 1.83 1.78 2.61 2.49 2.40 2.24 602.18 2.14 02.06 2.04 1.98 1.94 1.901.9 1.87 1.82 1.76 1.7670 2.60 2.48 2.382.30 2.22 1.722.16 2.12 2.05 2.052.01 1.96 1 1.90 1.881.85 1.80 1.791.74 1.741.7 1.7 80 0 0 90 2.59 2.47 2.372.28 2.212.15 2.1 2.09 1.77 1.681 2.04 2.031.99 1.94 1.87 1.871.84 1.79 1.73 1.72 1.66 2.59 2.46 2.362.27 2.14 2.082.02 2.011.98 1.92 1.891.85 1.841.8 1.76 1.761.7 1.70 1.67 1.65 1 1 1.68 1.64 2.58 2.46 2.362.27 2.202.13 2.09 2.062.00 2.001.97 1.9 1.88 1.74 1.631 1.84 1.82 1.74 1.66 1.65 1.62 2.57 2.45 2.352.26 2.192.12 2.08 2.051.99 1.981.95 1.861.82 1.80 1.79 1.72 1.721.68 1.691.65 1.64 1.621.60 2.57 2.44 2.342.25 2.192.1 2.0 2.03 1.84 1.697 1.97 1.89 1.79 1.7 1.60 0 1.66 1.621 1.98 1.93 1.80 1.77 1.66 1.62 1.59 1.54 2.57 2.44 2.332.25 2.18 2.031.98 1.961.92 1.88 1.831.79 1.77 1.76 1.671.64 1.631.59 1.59 1.571.55 1.52 2.56 2.43 2.332.24 2.17 2.1 2.0 2.02 1.67 1.95 1.86 1.82 1.75 1.661 1.54 1 1.97 1.91 1.8 1.78 1.74 1.68 1.63 1.57 1.57 1.53 1.50 2.54 2.43 2.33 2.17 2.01 1.94 1.86 1 1.74 1.66 1.64 1.55 1.521.52.41 2.32 2.24 2.00 1.96 1.91 1.77 1.72 1.62 1.60 1.56 1.5 1 1.48 12.30 2.23 2.16 2.10 2.06 1.96 1.93 1.85 1.76 1.73 1.7 1.65 1.59 1.60 1.53 1.462.21 2.16 2.05 2.00 1.92 1.90 1.80 1.73 1 1.61 1.58 1.53 2.13 2.10 1.95 1.89 1.84 1.75 1.64 1.57 1.50 1.49 1.42 2.10 2.05 1.99 1.92 1.79 1.7 1.52 1 1.56 1.48 2 1.9 1.95 1 1.8 1.831.7 1.74 1.70 1.63 1.6 1.56 1.5 1.49 1. 1.46 100 1.65 120 1.63 1.63 140160 1.6 1.6 1.62 1 1.6 180 1 1.60 11.60 200 1.60 1.59 1.59 1.57 1.59 1.58 1.57 1.57 1.57 1.56 1.57 1.56 1.55 1.54 1.55 1.54 1.5 1.55 1.54 1.53 1.52 1.52 1 1.53 1.52 1.49 1.50 1.50 1.49 1.48 1.48 1.47 1.48 1.46 1. 1.46 1.47 1 1.4 1.46 1.40 DENOMINATOR DEGREES OF FREEDOM N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-14 APPENDIX B NUMERATOR DEGREES OF FREEDOM .025 A F -Distribution: F A 8 7 1 6 1 5 1 4 1 3 1 FA 2 1 1 123456789 01 1 1648 2 799 38.5 3 864 39.0 17.4 4 5 900 39.2 16.0 12.210.0 6 922 15.4 8.87 1 18.08 937 39.2 15.1 0.6 77.57 9 948 39.3 14.9 8.43 7.2 1 7.26 6.06 1 957 39.3 0.0 7.76 6.60 6.54 963 39.4 14.7 7.39 6.23 5.89 5.42 5.71 969 39.4 14.69.60 7.15 5.52 5.05 973 39.4 14.5 6.98 5.995.29 4.82 5.08 977 39.4 14.5 9.366.85 5.825.12 4.65 980 14.4 9.20 5.70 4.53 4.72 983 39.4 14.4 9.07 6.76 4.994.43 4.48 985 39.4 14.3 6.68 5.60 4.904.36 4.32 987 39.4 8.98 6.62 5.52 4.82 4.20 989 39.4 14.3 8.90 6.57 5.46 4.76 4.30 4.10 990 39.4 14.3 8.84 6.52 5.41 4.7 4.241 4.03 992 39.4 14.3 8.79 6.49 4.20 3.96 993 39.4 14.2 8.75 6.46 5.374.67 4.16 3.91 39.4 14.2 8.7 5.33 4.13 1 6.43 4.63 3.87 39.4 14.2 6.40 5.304.60 4.10 3.83 39.4 14.2 5.27 14.2 8.68 6.38 4.57 3.80 8.66 6.36 5.244.54 4.08 3.77 8.63 6.34 5.224.52 4.05 3.74 8.61 6.33 5.204.50 4.03 3.72 8.59 5.184.48 4.02 3.70 8.58 5.174.47 4.00 3.68 8.56 3.67 N1 10 6.94 11 5.46 6.72 12 13 4.83 5.26 6.55 5.1 6.4 14 115 4.47 4.63 0 6.306.20 16 4.24 4.28 174.47 4.97 4.864.77 6.12 18 4.0 4.04 4.24 4.69 6.04 19 73.88 4.12 4.35 5.984.00 3.89 4.15 20 3.80 4.08 4.62 4.0 4.56 5.925.87 22 3.95 3.76 3.893.77 3.663.58 3.73 13.95 4.514.46 5.79 24 26 3.85 3.66 3.73 5.723.6 3.60 3.503.4 3.50 3.6 4.38 28 1 1 3.86 5.66 303.78 3.59 13.48 3.38 3.34 3.66 3.90 5.63.5 3.78 4.32135 1 4.27 5.573.72 3.53 3.443.51 3.39 3.29 3.29 3.22 3.38 3.56 3.44 3.723.67 4.18 5.48 40 45 3.66 3.47 3.2 3.283.44 3.3 1 3.33 3.38 4.22 4.1 5.42501 3.20 3.12 3.22 3.29 3.22 3.33 3.59 1 5.38 603.62 3.43 3.163.37 3.12 3.05 3.1 3.17 3.15 3.63 4.05 5.340 3.13 3.05 3.1 3.25 4.01 5.29 70 3.58 3.39 3.063.32 3.25 3.153.06 2.99 3.053.0 2.93 2.99 3.29 3.52 3.46 3.97 5.25 80 1 3.03 3.93 90 3.55 3.36 2.983.28 3.20 3.093.0 2.93 2.96 2.84 2.87 3.06 3.18 3.13 3.39 3.89 5.22 1 3.01 2.94 2.87 3.42 3.34 5.20 3.52 3.33 2.923.24 3.15 3.05 2.89 2.93 2.88 2.91 2.76 2.78 2.90 2.90 3.86 2.7 2.82 2.75 2.96 3.09 3.05 3.0 3.31 1 3.84 3.50 3.30 3.0 2.8703.21 3.12 1 2.96 2.85 2.87 2.82 2.84 2.7 2.74 3.28 0 2.73 2.782.65 2.80 2.86 2.83 3.26 3.47 3.28 2.823.18 3.08 2.92 2.82 2.81 2.76 2.77 2.65 2.692.57 2.68 2.62 2.7 2.67 2.95 0 2.79 2.97 2.93 3.45 3.26 2.79 2.64 2.6 3.15 3.05 2.982.89 2.79 2.77 2.72 2.72 2.65 2.59 12.5 2.58 2.53 2.55 2.75 2.732.7 1 2.63 1 5.03 3.44 3.24 2.75 2.593.13 3.03 2.952.86 2.76 2.73 2.68 2.68 2.60 2.54 2.50 2.45 2.58 2.46 2.5 2.59 2.57 1 3.69 3.42 3.23 2.72 2.543.1 3.00 2.92 2.74 2.70 2.65 2.56 2.49 2.55 2.44 2.39 2.38 2.47 2.45 1 3.122. 2.90 2.84 2.7 2.64 2.46 2.55 2 2.7 0 2. 2.62 2.5 2.502 2.49 2.3 2.33 2.35 100 5.18 120 3.83 5.15 140160 3.25 3.80 5.135.12 180 5.1 200 2.92 3.23 3.79 3.2 3.78 15.10 2.7 2.89 1 02.67 3.20 2.87 3.773.76 2. 2.52 2.88 2 2.6 3.193.2 2 N DENOMINATOR DEGREES OF FREEDOM 2 TABLE f(F) 6(b)Values of the 0
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-15 NUMERATOR DEGREES OF FREEDOM 22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 1995 239.5 3 4 9 14.1 97 39.5 5 39.5 14.1 8.53 8.5 6.30 6 17 99 14.1 6.28 5.14 8 9 39.5 4.44 39.5 14.1 8.49 6.26 5.124.4 3.97 9 1 10 14.1 5.10 3.95 3.64 00 39.5 8.48 6.24 3.61 10 14.1 6.23 3.93 01 39.5 8.46 4.39 39.5 14.0 8.43 6.20 5.08 3.9 5.0 4.38 1 3.59 10 14.0 6.18 7 04 39.5 8.41 4.36 3.58 100 39.5 14.0 6.16 4.33 3.893.566 5.04 3.8610 39.5 14.0 8.39 6.14 4.31 0 5.01 3.53 7 14.0 3.84 100 39.5 8.38 6.12 4.99 3.51 8 39.5 14.0 6.1 3.82 14.0 8.36 1 4.98 4.293.81 1010 39.5 8.35 4.28 3.49 39.5 14.0 6.10 4.96 13.9 8.336.09 4.94 4.25 3.78 3.47 101 39.5 8.33 4.93 4.24 3.45 1 13.9 6.08 3.77 1012 39.5 13.9 8.326.0 4.92 4.23 3.43 7 4.22 3.76 101 39.5 13.9 8.31 4.92 3.75 3.42 3 39.5 8.30 4.21 101 13.9 6.06 4.90 3.74 3.41 3 39.5 8.30 4.20 3.40 1014 13.9 8.29 6.06 4.90 4.89 4.19 3.733.39 101 8.29 6.05 4.18 3.723.38 5 4.89 3.71 1015 8.26 6.05 6.02 4.88 4.18 3.38 101 4.85 4.18 3.7 3.371 5 1016 4.14 3.37 101 3.70 3.33 8 3.67 N1 10 3.39 11 3.37 3.20 12 13 3.34 3.17 3.042.92 14 15 3.33 3.15 3.022.89 2.812.73 16 3.3 3.13 3.00 2.65 17 13.12 2.98 2.87 2.7 18 2.85 2.79 0 2.63 2.592.53 19 203.28 3.09 2.962.84 2.772.68 2.60 2.562.50 2.482.43 22 3.26 3.06 2.93 2.75 2.54 24 2.9 2.80 2.66 2.58 2.48 2.452.4 2.36 1 26 3.24 3.04 12.78 2.732.64 2.57 2.522.46 2.43 2.33 2.302.24 28 303.22 3.03 2.76 2.702.6 2.53 2.50 2.41 2.3 2.27 1 2.20 35 1 2.44 2.39 2.22 2.163.20 3.00 2.892.74 2.5 2.47 2.25 40 1 2.4 2.17 1 2.37 2.19 2.14 2.09 45 3.18 2.99 2.872.72 2.672.59 2.44 2.392.35 2.29 2.23 2.03 2.2 2.17 2.152.1 2.06 50 1 2.0 1.99 603.17 2.97 2.852.7 2.65 2.42 2.36 1 2.13 1.96 0 2.56 2.492.4 2.38 2.3 2.27 2.04 701 2.16 1.96 1.9 3.16 2.96 2.83 2.642.55 2.47 1 2.36 2.33 2.24 2.12 2.11 2.09 2.02 1.94 1.93 1.88 80 90 3.15 2.96 2.82 2.61 2.3 2.17 1.98 1.9 1.852.8 2.69 2.52 2.45 2.35 1 2.29 2.21 2.09 2.0 2.00 1 1.857 1.92 1.88 1.83 3.14 2.94 12.68 2.602.51 2.43 2.382.32 2.27 2.152.0 2.08 1.96 1.82 7 1.96 1.90 1.86 1.82 1.80 3.13 2.94 2.36 2.12 1.942.80 2.67 2.582.49 2.42 2.30 2.302.25 2.19 1.792.1 2.05 2.04 1.93 1.86 1.891.83 1.80 1.77 3.13 2.93 2.35 1 1.902.79 2.66 2.572.48 2.40 2.29 2.272.22 2.17 2.05 2.03 2.01 1.9 1.77 1 1.83 1.871.82 1.78 1.75 3.12 2.92 2.34 1.882.78 2.65 2.562.47 2.40 2.28 2.252.20 2.14 2.08 2.03 2.01 1.99 1.8 1.83 1.75 1 1.78 1.74 1.7 1.73 1.67 3.12 2.92 2.33 1.8512.77 2.64 2.552.46 2.38 2.27 2.242.19 2.13 2.06 2.0 1.98 1.80 1.7 1 1.97 1.89 1.74 1.69 1.64 3.08 2.88 2.32 1.832.77 2.64 2.542.45 2.37 2.23 2.12.3 2.26 1 1.96 1.86 1.79 1.77 1.66 1.61 1 2.18 2.05 1.94 1.80 1.72 1.682.76 2.63 2.542.44 2.37 2.25 2.222.17 2.03 1.99 1.94 1.92 1.841.78 1.76 1.751.7 1.68 0 1.65 1.63 2.73 2.60 2.53 2.20 2.10 1.93 1.722.53 2.44 2.36 2.30 2.24 2.19 2.16 2.09 2.02 1.981.92 1.90 1.82 1.66 1.6 1.8 1.76 1.741.7 1 1.59 0 1.63 2.49 2.44 2.36 2.23 2.15 1.97 1.89 1 1.72 1.67 1.63 1.57 2.4 2.32 2.29 2.01 1.75 1.602.2 2.23 2.19 2.08 1.912 2.14 1.72 2.0 1.951 1.8 1.0 1.64 1.60 1. 1.58 100 1.8 120 11.79 140160 1.78 1.76 1.77 1.76 1802001.76 1.73 1.74 1.73 1.751.741.74 1.7 1.72 1 1.7 1.72 0 1.71 1.7 1.69 1.69 11.69 1.67 1.68 1.67 1.681.67 1.65 1.63 1.66 1.65 1.661.64 1.6 1.6 1 1.60 1.62 1 1.641.61 1.57 1. 1.5 1.58 1 1.5 1.60 1.52 DENOMINATOR DEGREES OF FREEDOM N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-16 APPENDIX B NUMERATOR DEGREES OF FREEDOM .01 A F -Distribution: F A 7 1 6 1 5 1 4 1 3 1 F 2 1 A 1 123456789 01 1 14052 2 4999 98.5 334.1 42 5403 99.0 30.8 1.2 516.3 6 5625 99.2 29.5 18.013.3 13.7 712.2 815764 99.2 16.799.3 28.7 12.1 9 1 1.31 5859 16.0 0.699.3 28.2 15.5 0.9 1 9.55 5928 99.4 27.9 15.2 1.4 8.65 99.4 27.7 8.45 15.0 9.78 7.59 8.02 1 7.85598 27.5 1.0 9.15 7.0 6.99 1 1 99.4 14.8 7.46 6022 99.4 27.3 14.7 8.75 6.42 1 7.19 6.06 6056 99.4 27.2 14.5 0.7 8.47 8.26 6.99 6.635.80 6083 99.4 27.1 14.5 1 6.375.6 99.4 27.1 8.1 6.84 14.4 0.506.72 6.18 1 61 27.01 6.03 06 99.4 14.399.4 26.9 6.62 5.4714.2 0.3 7.986.54 5.915.35 6 7.87 126 99.4 26.9 14.2 1 99.4 26.8 6.47 5.2614.2 0.2 7.796.4 5.81 1 6143 99.4 26.8 5.1814.1 1 7.72 0.1 5.11 6157 99.4 26.8 14.1 7.666.36 5.73 99.4 26.7 14.0 7.606.3 5.67 1 5.6 5.05 6 9.96 7.561 170 26.7 14.0 9.89 7.526.28 5.01 4.966 7.48 5.56181 9.82 6.24 4.92 6192 9.77 7.45 5.52 7.42 6.21 5.48 4.89 6201 9.72 9.68 7.40 5.44 4.86 6209 9.64 6.18 6. 5.41 4.83 4 N1 10 10.0 11 9.65 12 9.33 13 7.56 7.216.93 9.0 14 715 6.55 5.95 8.86 6.5 8.68 16 17 5.99 6.225.4 6.7 1 0 8.53 18 1 6.36 8.40 5.64 5.67 5.42 6.23 6.1 8.29 19 1 20 5.39 5.32 5.56 6.0 8.18 225.0 5.06 5.74 4.89 5.291 8.1024 5.20 74.82 5.21 5.044.56 4.77 5.18 5.93 5.0 7.957.82 26 5.06 4.64 4.86 4.694.32 4.44 4.67 5.09 1 5.85 5.725.6 7.72 28 1 30 4.94 4.894.50 4.62 4.464.14 4.20 4.34 4.58 4.94 4.82 5.53 7.647.56 35 40 4.85 4.744.39 4.44 4.284.00 4.03 4.10 4.25 4.50 4.43 4.31 4.72 4.64 5.455.39 7.427.3 45 1 4.77 4.634.30 4.30 4.143.89 3.89 3.93 4.0 4.17 4.57 501 4.1 5.270 4.22 4.144.0 4.51 7.23 60 4.7 4.54 4.19 4.03 3.78 3.94 3.99 3.82 7 4.40 5.1 7.17 1 70 1 4.46 4.22 3.80 3.79 3.90 5.18 7.08 80 4.16 4.10 3.943.73 3.69 3.68 3.84 3.77 3.87 3.763.67 3.59 4.02 3.91 4.3 5.06 7.0901 4.98 6.964.65 4.404.1 4.02 3.86 3.62 3.7 3.63 3.751 3.70 3.59 3.42 3.7 4.25 4.20 6.93 0 3.67 3.59 3.50 0 4.13 4.884.60 4.34 3.96 3.803.6 3.55 3.52 3.45 3.53 3.59 3.72 4.92 1 3.52 3.56 3.36 3.29 3.83 3.773.4 3.65 4.04 4.85 4.56 4.294.05 3.9 3.75 3.43 3.36 4.0 1 1 3.7 3.50 3.46 3.60 3.46 3.353.26 3.18 3.47 3.37 3.51 3.45 3.34 73.56 4.01 4.52 4.254.01 03.56 3.45 3.40 3.51 3.36 3.37 3.263.17 3.09 3.23 3.30 3.20 3.29 3.23 3.12 3.264.49 4.213.97 3.86 3.52 3.4 3.30 3.12 3.0 3.191 3.35 3.43 3.29 3.183.09 3.02 3.17 7 3.12 3.07 2.95 3.603.04 3.53 6.64 4.46 4.183.94 3.82 3.663.49 3.31 3.37 3.24 3.23 3.123.03 2.96 3.03 3.0 3.02 3.29 4.67 2.99 2.82 3.0 2.87 3.231 4.43 4.153.91 3.78 3.623.45 3.37 3.27 3.32 3.19 3.18 3.072.98 2.90 2.96 2.962.89 2.94 2.892.72 2.74 3.01 4 4.123 3.7 3.593 3.3 3.2 3.15 3.2 2. 2.90 2.88 2.8 2.782 100 6.90 120 4.82 6.85 140160 3.98 4.79 6.826.80 180200 3.5 3.95 4.76 6.78 13.48 3.92 4.74 3.9 4.73 6.76 1 4.71 3.2 3.17 3.46 3.89 12.96 3.15 2. 3.44 3.43 3 3.8 3.7 N DENOMINATOR DEGREES OF FREEDOM 2 TABLE f(F) 6(c)Values of the 0
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-17 ˆ NUMERATOR DEGREES OF FREEDOM 22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 16223 2 6235 99.5 326.6 4 6245 99.526.6 14.0 59.51 6 6253 99.5 99.5 26.6 13.9 7.35 7 26.5 13.9 6.1 8 9.47 7.3 1 1 5.32 9 626 99.5 13.9 4.77 1 26.5 9.43 6.0 5.28 6276 99.5 7 99.5 26.5 13.8 9.40 7.28 5.25 4.73 4.76287 99.5 26.4 13.8 9.38 7.25 6.04 5.22 0 6296 99.5 26.4 13.7 13.7 9.33 7.23 6.02 5.20 4.67 6303 99.5 26.4 9.29 7.18 5.99 5.15 99.5 26.3 13.7 4.65 13.7 9.26 7.14 7.1 5.94 5.12 4.6063 26.3 1 5.0913 99.5 9.24 5.91 99.5 26.3 13.6 9.20 5.88 5.0 4.57 7 632 26.3 13.6 9.18 7.09 4.54 1 99.5 13.6 5.86 4.526326 99.5 26.2 9.16 7.065.82 5.03 99.5 26.2 13.6 9.14 7.035.80 5.0 4.48 1 6331 99.5 26.2 13.6 7.01 4.46 13.5 9.13 5.78 4.44 6334 99.5 26.2 7.0013.5 9.116.99 5.77 4.994.43 6339 99.5 26.2 13.5 6.97 5.75 4.97 4.96 4.41 6343 99.5 26.2 9.10 26.1 13.5 9.09 6.96 5.74 4.95 6346 13.5 9.08 6.95 5.72 4.93 4.40 6348 9.08 6.94 5.72 5.7 4.92 4.39 16350 9.02 6.93 4.92 4.38 6366 6.88 5.70 4.91 4.37 5.65 4.86 4.36 4.31 N1 10 4.36 11 4.33 4.06 12 13 4.30 4.02 3.823.62 14 15 4.27 3.99 3.783.59 3.463.33 16 4.25 3.96 3.753.56 3.433.29 3.22 17 18 4.20 3.94 3.72 3.12 3.7 3.53 3.403.26 3.18 3.03 19 20 4.17 3.89 03.5 3.37 3.08 2.96 1 3.24 3.15 3.00 2.90 22 4.14 3.86 3.05 243.65 3.353.2 3.12 2.92 2.78 1 2.97 2.86 2.7 26 4.12 3.83 3.03 0 3.62 3.46 3.30 3.10 2.94 2.892.83 2.75 2.62 28 30 4.08 3.8 3.00 1 3.59 3.43 3.27 3.17 2.92 2.872.80 2.72 2.66 2.58 2.562.5 35 1 4.06 2.96 403.57 3.40 3.24 3.13 3.05 2.87 2.842.78 2.69 2.63 2.55 2.52 2.40 45 4.04 3.78 2.92 2.333.54 3.38 3.22 3.1 3.02 2.80 2.67 2.49 2.36 50 0 2.84 2.73 2.60 2.53 2.47 2.27 60 4.03 3.75 2.89 2.293.5 3.34 3.18 2.99 2.8 2.76 2.46 2.22 1 2.62 2.50 2.33 2.23 70 1 2.69 2.58 2.44 2.15 4.0 3.73 3.16 2.97 2.87 2.73 2.58 2.44 2.4 2.30 2.26 2.18 2.1 80 1 1 3.72 3.32 3.08 2.7 2.67 2.53 2.45 2.20 2.12 2.0 90 73.49 3.30 3.14 3.05 2.93 2.83 2.23 2.8 2.78 12.64 2.55 2.42 2.39 2.28 2.17 2.152.08 2.04 4.00 3.7 1 2.49 2.201 3.48 3.28 3.12 3.02 2.9 2.75 2.6 2.53 2.35 2.23 2.12 2.07 1 2.39 2.14 2.05 2.00 3.98 3.1 2.46 2.1 2.033.47 3.27 1 3.00 2.72 2.67 2.50 2.36 2.32 2.34 2.19 2.15 2.1 2.09 02.03 1.97 3.97 3.69 2.79 2.441 2.003.45 3.25 2.99 2.89 2.7 2.65 2.300 2.58 2.47 2.33 2.30 2.16 2.05 1.98 2.03 1.94 3.97 3.68 2.78 2.40 1.973.44 3.24 3.09 2.98 2.87 2.632.56 2.45 2.30 2.26 2.27 2.14 2.02 2.051.94 2.01 1.92 1.83 3.96 3.67 2.76 2.6 2.38 2.08 2.0 1.943.43 3.23 3.08 2.96 2.86 2.69 12.55 2.43 2.28 2.24 2.25 2.10 2.00 1.90 1.98 1.86 1.79 3.9 3.66 3.07 2.84 2.75 2.42 2.36 2.22 2.06 1.93 1.89 1 3.66 3.42 3.23 2.95 2.83 2.73 2.682.60 2.54 2.34 2.262.20 2.212.0 2.02 1.96 1.88 1.85 1.82 1.76 7 1.97 1.89 3.60 3.41 3.22 2.94 2.72 2.66 2.52 2.40 2.33 2.25 2.18 1.99 1.93 1.84 1.82 1.79 1.73 3.36 3.17 3.06 2.58 1.95 3.06 2.93 2.822.72 2.652.57 2.50 2.39 2.3 2.23 2.19 1.9 1.85 1.71 1.8 1.76 0 1 2.16 1.97 1.91 1 1.79 3.01 2.92 2.812.7 2.64 2.49 2.38 2.22 2.17 2.14 2.05 1.83 1.72 2.8 2.81 1 2.56 2.2 2.15 2.03 1.95 1.88 1.78 1.75 2 2.632 2.4 2.37 2.3 1 2.1 1. 1.89 1 1.7 1. 1.68 100 2.0 120 21.99 140160 1.98 1.95 1.97 1.95 1802001.95 1.92 1.93 1.9 1.94 1 1.931.92 1.89 1.89 1.901.891.89 1.86 1.86 1.88 1.861.851.84 1.8 1.84 1 1.85 1.831.821.80 1.78 1.82 1.811.791.76 1.76 1.74 1.7 1.76 1.741.74 1.73 0 1.75 1. 1.72 1 1.7 1.69 1.64 DENOMINATOR DEGREES OF FREEDOM N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-18 APPENDIX B NUMERATOR DEGREES OF FREEDOM .005 A F -Distribution: F 7 1 6 1 5 1 4 1 3 1A 2 1 1 123456789 01 1 FA 1162 2 113 19999 199 199 55.6 43 199 49.8 1.3 5 6 2 22.8 1615 199 47.5 26.318.3 18.6 716.2 8 22500 199 24.3 14.5 9 199 46.2 23.2 16.512.9 12.4 14.713.6 23056 199 45.4 44.8 22.5 15.6 14.9 12.0 11.0 23437 199 22.0 10.9 10.1 199 44.4 44.1 14.5 1 10.1 2 1.5 9.60 237 199 1.6 14.28.8 8.72 15 199 43.9 14.0 1 9.5223925 199 43.7 2 1.1 7.96 199 43.5 1.4 13.8 13.6 9.16 8.30 7.47 24091 199 10.8 8.89 7.13 199 43.4 21.1 13.5 10.6 8.68 7.956.88 24224 199 43.3 7.69 43.2 21.0 13.4 10.4 8.51 7.50 6.69 24334 199 20.8 13.3 199 43.1 20.7 13.2 10.3 8.38 8.27 7.34 6.54 24426 199 43.0 20.6 13.1 10.1 6.4210.0 8.18 7.216.31 24505 199 42.9 42.9 20.5 13.1 13.0 8.10 7.10 6.23 24572 42.8 20.4 20.4 13.0 9.95 8.03 7.97 7.01 6.15 24630 42.8 20.3 12.9 9.88 6.09 9.8 6.94 1 7.91 6.87 6.03 24681 20.3 12.9 20.2 7.87 6.81 5.98 24727 20.2 9.76 7.83 5.94 9.7 6.76 1 7.79 5.90 24767 7.75 6.72 6.68 5.86 248 9.66 9 6.64 5.83 N1 10 12.8 11 12.2 12 11.8 13 1 9.43 1.4 14 1 15 8.08 8.91 1.110.8 16 1 17 7.34 7.60 8.51 8.19 0.6 10.4 18 1 6.87 6.88 7.23 6.93 7.927.7 0.2 19 1 0 20 6.54 6.42 6.52 6.23 6.68 7.5 0.1 1 9.94 22 24 6.30 6.10 6.07 5.79 6.00 6.48 7.35 7.2 9.73 1 6.99 9.55 26 6.12 5.86 5.76 5.48 5.56 5.80 6.30 6.16 7.09 5.82 6.816.66 9.4 28 130 5.97 5.68 5.52 5.25 5.26 5.37 5.64 5.50 9.28 5.0 6.03 5.92 5.17 5.52 9.18 35 40 5.85 5.54 5.35 5.08 5.03 5.0 5.2 7 6.441 5.27 5.65 6.54 8.98 7 5.37 4.76 4.89 6.35 8.83 45 5.75 5.42 5.20 4.94 4.864.78 4.96 4.85 4.47 5.024.49 5.41 5.32 50 4.7 5.24 6.196.0 8.71 7 60 5.66 5.32 5.09 4.82 4.72 4.85 4.91 04.56 4.66 4.56 4.26 4.614.20 4.79 4.62 5.09 8.638.49 70 80 5.59 5.24 4.99 4.72 4.60 4.67 4.694.39 4.44 4.34 4.09 4.32 4.48 5.90 8.404.1 3.99 4.38 4.23 4.98 5.97 5.79 8.33 90 5.53 5.16 4.91 4.64 4.51 4.54 4.52 4.30 4.25 4.28 4.18 3.96 13.83 4.10 3.95 4.09 4.37 4.89 4.834.73 5.725.67 8.28 5.47 5.10 4.84 4.57 4.43 4.42 4.38 4.02 3.84.14 4.14 4.04 3.85 3.69 3.89 3.74 1 3.99 4.29 4.234.14 4.664.6 5.62 1 5.42 5.05 4.77 4.51 4.36 4.33 4.27 3.81 4.05 4.03 3.93 3.76 3.943.59 3.73 3.58 3.7 3.91 3.85 4.08 4.571 3.76 5.38 5.00 4.72 4.46 4.30 4.25 4.18 3.65 3.73.97 3.94 3.84 3.68 3.813.50 3.60 3.45 3.61 3.64 3.583.49 0 4.03 3.99 5.34 4.96 4.67 4.41 4.25 4.18 4.10 3.52 3.90 3.86 3.76 3.6 3.70 3.45 3.38 1 3.42 3.49 3.34 3.5 3.43 3.29 3.65 3.62 7.88 5.31 4.92 4.63 4.37 4.20 4.12 4.03 3.7 3.41 3.84 3.79 0 3.613.35 3.40 3.25 3.32 3.28 3.223.13 3.433.39 3.35 5.30 5.27 4.89 4.59 4.16 4.0 3.97 3.54 3.33 3.32 3.21 3.15 3.093.0 3.23 3.15 4.28 4.8 4.56 4.337 3.73 3.55 3.18 3.3514 4.12 3.9 3.79 3 3.64 3.47 3.30 3.2 3.25 3.193 3.12 3.0 2.99 3.0 3. 100 8.24 120 5.59 8.18 140160 4.54 5.54 8.148.1 180 0 200 3.96 4.50 5.50 8.088.06 3.59 3.92 4.47 5.48 5.465.44 3.33 3.55 3.89 4.44 4.424.41 3.1 3.28 3.52 3. 3.87 3.85 3 3. N DENOMINATOR DEGREES OF FREEDOM 2 TABLE f(F) 6(d)Values of the 0
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r APPENDIX B B-19 NUMERATOR DEGREES OF FREEDOM 22 24 26 28 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 124892 2199 3 24940 199 42.7 420.1 5 24980 199 42.66 199 42.6 20.0 12.8 12.8 9.53 77.69 8 25014 199 20.0 9.47 9 199 42.5 19.9 12.79.43 7.64 6.555.78 25044 199 42.5 19.9 12.7 7.60 6.50 199 42.4 5.73 19.8 12.7 9.39 9.36 7.57 6.465.69 251 199 42.3 12.6 7.53 6.43 03 199 42.3 19.8 5.65 19.7 12.5 9.297.47 6.405.62 25148 199 42.2 9.24 6.33 199 42.1 19.7 12.59.20 7.42 6.29 5.56 25183 199 19.6 12.59.17 7.38 5.52 199 42.1 6.25 42.1 19.6 12.49.12 7.35 6.22 5.48 2521 199 19.5 12.49.09 7.31 5.45 1 42.0 12.3 6.18 25253 199 5.4 199 42.0 19.51 19.5 12.3 9.06 7.28 6.15 25283 199 42.0 12.3 9.04 6.12 199 42.0 19.5 9.03 7.256.1 5.38 0 25306 199 19.4 12.3 12.3 9.00 7.23 7.22 5.36 25323 41.9 19.4 5.34 19.4 12.2 8.98 6.098.97 7.19 5.32 25337 41.9 6.06 41.9 19.4 12.2 12.2 8.96 7.18 6.05 5.30 25359 41.8 19.312.1 8.95 7.16 7.15 6.04 5.28 5.27 25374 8.88 7.15 6.03 6.02 5.26 25385 7.08 5.95 5.26 25394 5.19 25401 25464 N1 10 5.22 11 5.17 4.80 12 13 5.13 4.76 4.484.22 14 15 5.1 4.72 4.43 4.0116 04.68 4.39 4.17 4.13 3.83 3.68 17 18 5.0 4.65 4.364.1 3.96 3.79 3.64 3.56 19 74.60 4.33 0 3.92 3.75 3.60 3.5 3.45 13.40 3.35 20 22 5.0 4.27 4.0 3.89 3.72 3.3 3.27 1 24 1 4.557 3.57 3.12 4.52 4.23 3.86 3.69 3.54 3.47 3.36 26 3.33 3.223.08 3.012.92 28 4.97 4.49 4.19 4.0 3.80 3.63 3.44 3.27 3.18 30 1 3.48 3.30 3.04 2.87 2.84 35 4.93 4.45 4.17 3.76 3.58 3.44 3.413.25 3.24 3.153.0 2.97 2.77 40 1 2.84 2.79 2.64 45 4.90 4.4 4.12 3.55 3.35 3.12 2.93 2.73 2.55 1 3.97 3.73 3.40 3.20 3.213.0 2.80 2.76 2.60 2.47 50 4.86 4.09 3.94 3.70 3.52 3.37 3.313.17 3.15 7 2.98 2.902.77 2.72 2.692.56 2.502.43 2.42 60 70 4.83 4.39 4.07 3.91 3.66 3.48 3.33 3.283.14 3.11 2.92 2.872.72 2.69 2.662.53 2.462.39 2.37 2.332.28 80 90 4.80 4.37 3.87 3.62 3.45 3.30 3.25 3.023.1 2.88 2.81 2.64 2.63 2.43 2.33 2.29 2.23 0 2.67 2.50 2.36 2.23 2.20 4.79 4.36 4.05 3.84 3.60 3.43 3.21 3.0 2.99 2.77 2.57 2.25 3.4 3.28 7 2.84 2.64 2.59 2.44 2.402.33 2.30 2.19 2.192.15 4.77 4.34 4.04 3.81 3.58 1 3.26 3.183.0 2.96 2.73 2.56 2.52 2.34 2.27 2.22 2.15 7 2.82 2.61 2.39 2.27 2.16 2.12 4.75 4.32 4.01 3.79 3.57 3.25 3.15 3.04 2.922.77 2.70 2.53 2.492.36 2.302.22 2.2 2.19 2.1 1 2.13 12.08 4.73 4.31 4.00 3.78 3.55 3.393.22 3.13 3.04 3.00 2.882.74 2.662.56 2.48 2.462.33 2.262.19 2.132.07 2.05 1.95 4.72 4.30 3.99 3.76 3.53 3.373.2 3.12 2.97 2.86 2.63 2.42 2.23 2.16 2.08 1 3.02 2.72 2.53 2.45 2.28 2.16 1.99 1.90 4.7 3.98 3.52 3.36 3.10 3.0 2.95 2.84 2.60 2.43 2.38 2.18 2.13 2.04 2.02 1 4.29 3.74 2.70 2.25 2.1 2.02 4.23 3.97 3.73 3.51 3.34 3.20 3.08 2.93 2.832.69 2.58 2.511 2.0 1.94 1.86 2.49 2.4 2.36 1 1.971 2.22 2.15 2.10 1.98 1.824.7 3.91 3.50 3.34 3.0 1.907 2.91 2.81 2.57 2.34 2.12 2.05 1.94 1 3.72 3.19 2.99 2.66 2.20 1.95 3.7 3.33 2.89 2.79 2.55 2.47 2.32 2.1 2.08 1.96 1.87 1.79 0 1.90 1 3.44 3.18 2.97 2.65 2.39 2.19 2.02 1.90 4.64 3.26 3.1 3.06 2.87 2.78 2.53 2.45 2.30 2.05 1.93 1.85 1.82 1.72 1 2.96 2.63 2.37 1.99 1.863 3.0 2. 2.7 2.432 2.2 2.16 2. 2.031 1.9 1. 1.78 100 2.17 120 2.13 2.13 140 2.1 160 2.09 2.09 1 2.09 180 2.0 200 2.05 2.05 2.04 72.06 2.0 2.0 2.06 1 2 2.00 2.01 1.96 2.021.97 2.02 1.91 1.98 1.991.93 1.981.97 1.87 1.92 1.961.87 1.951.94 1.84 1.87 1.891.82 1.921.91 1.79 1.83 1.84 1.85 1. 1.80 1.78 1.8 1.84 1.67 DENOMINATOR DEGREES OF FREEDOM N2
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r B-20 APPENDIX B
TABLE 7(a) Critical Values of the Studentized Range, A .05
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or e
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r

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