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

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B-1
A ppen di x B
TA B L E S
TA BL E Binomial Probabilities1
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 x( i)
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 eChapter(s).
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 restrictions require it.
B-2 A P P E N D I X 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 0.0101 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
TA B LE (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 eChapter(s).
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 restrictions require it.
B-3
A P P E N D I X B
TA BL E (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 eChapter(s).
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 restrictions require it.
B-4 A P P E N D I X B
TA B LE (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 eChapter(s).
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 restrictions require it.
B-5
A P P E N D I X B
TA BL E (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 eChapter(s).
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 restrictions require it.
B-6 A P P E N D I X B
TA B LE Poisson Probabilities2
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 eChapter(s).
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 restrictions require it.
B-7
A P P E N D I X B
TA BL E (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
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 eChapter(s).
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 restrictions require it.
B-8 A P P E N D I X B
TA B LE Cumulative Standardized Normal Probabilities3
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(-q6Z6z)
0z
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 eChapter(s).
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 restrictions require it.
B-9
A P P E N D I X 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(-q6Z6z)
0z
TA BL E (3
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 eChapter(s).
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 restrictions require it.
B-10 A P P E N D I X B
TA B LE 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
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 eChapter(s).
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 restrictions require it.
B-11
A P P E N D I X 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
TA BL E 5 Critical Values of the 2Distribution
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 eChapter(s).
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 restrictions require it.
B-12 A P P E N D I X B
TA B LE Critical Values of the 6(a)
F
-Distribution:
A
.05
f F( )
F
FA
A
0
NUMERATOR DEGREES OF FREEDOM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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 8.6847.71 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 5.856.61 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 3.9075.59 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 3.4785.32 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 2.9
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 2.811 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 2.7012 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 2.64 213 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 2.5514 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 2.4415 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.51 2.48 2.416 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.46 2.4217 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.41 2.3818 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.37 2.34 2.319 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.34 2.3120 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 2.2624 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.22 226 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.18 2.128 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.2430 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 235 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.1140 4.08 3.23 2.84 2.61 2.45 2.34 2.25 245 4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.150 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.1360 4.00 3.15 2.76 2.53 2.37 2.25 2.17 270 3.98 3.13 2.74 2.50 2.35 2.23 2.1480 3.96 3.11 2.72 2.49 2.33 2.21 2.1390 3.95 3.10 2.71 2.47 2.32
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 2.160 3.90 3.05 2.66 2.43 2.2180 3.89 3.05 2.65 2.42 2200 3.89 3.04 2.65 2.4
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 eChapter(s).
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 restrictions require it.
B-13
A P P E N D I X 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 5.65 554.54 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 3.69 373.43 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 3.283.13 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 2.9592.92 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
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 2.4412 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 2.3313 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 2.2414 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 2.1715 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 2.10 216 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 2.017 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 2.0018 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 1.97 119 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 1.920 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 1.9122 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 1.24 2.00 1.98 1.97 1.95 1.94 1.91 1.89 1.88 1.86 1.84 1.83 1.82 1.8126 1.97 1.95 1.93 1.91 1.90 1.87 1.85 1.84 1.82 1.80 1.79 1.78 128 1.93 1.91 1.90 1.88 1.87 1.84 1.82 1.80 1.79 1.77 1.730 1.91 1.89 1.87 1.85 1.84 1.81 1.79 1.77 1.76 1.74 1.72 1.71 1.70 1.7035 1.85 1.83 1.82 1.80 1.79 1.76 1.74 1.72 1.70 1.68 1.40 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 1.6050 1.76 1.74 1.72 1.70 1.69 1.66 1.63 1.61 1.6060 1.72 1.70 1.68 1.66 1.65 1.62 1.59 1.57 1.5670 1.70 1.67 1.65 1.64 1.62 1.59 1.57 1.55 1.53 1.50 180 1.68 1.65 1.63 1.62 1.60 1.57 1.54 1.5290 1.66 1.64 1.62 1.60 1.59 1.55 1.53 1.51
100 1.65 1.63 1.61 1.59 1.57 1.54 1.52 1120 1.63 1.61 1.59 1.57 1.55 1.52 1.50 1.4140 1.62 1.60 1.57 1.56 1.54 1.51 1.48160 1.61 1.59 1.57 1.55 1.53 1.50 1.47 1.45 1180 1.60 1.58 1.56 1.54 1.52 1.49 1.4200 1.60 1.57 1.55 1.53 1.52 1.48
1.54 1.52 1.50 1.48 1.46 1.42
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 eChapter(s).
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 restrictions require it.
B-14 A P P E N D I X B
TA B LE Values of the6(b)
F
-Distribution:
A
.025
NUMERATOR DEGREES OF FREEDOM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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 8.61510.0 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 4.5287.57 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 3.411 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 3.2812 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 3.2113 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 3.014 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 2.98 215 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 2.86 216 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 2.8217 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.87 2.82 2.79 218 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 2.719 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.76 2.72 2.6820 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.722 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.65 2.6024 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.59 226 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.528 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.5530 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.5735 5.48 4.11 3.52 3.18 2.96 2.80 2.68 2.58 2.50 2.4440 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.3945 5.38 4.01 3.42 3.09 2.86 2.70 2.58 2.450 5.34 3.97 3.39 3.05 2.83 2.67 2.5560 5.29 3.93 3.34 3.01 2.79 2.63 2.5170 5.25 3.89 3.31 2.97 2.75 2.5980 5.22 3.86 3.28 2.95 2.73 2.57 2.45 290 5.20 3.84 3.26 2.93 2.71 2.55 2.
100 5.18 3.83 3.25 2.92 2.70 2.5120 5.15 3.80 3.23 2.89 2.67140 5.13 3.79 3.21 2.88 2.160 5.12 3.78 3.20 2.87 2.6180 5.11 3.77 3.19 2200 5.10 3.76 3.18 2.8
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 eChapter(s).
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 restrictions require it.
B-15
A P P E N D I X 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 8.29 856.30 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 4.8874.44 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 4.1883.97 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 3.793.64 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
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 3.13 311 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 2.9212 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 2.7613 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 2.4016 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 2.17 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 2.3218 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 2.2619 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 2.2220 2.43 2.41 2.39 2.37 2.35 2.31 2.29 2.27 2.25 2.22 2.20 2.19 222 2.36 2.33 2.31 2.29 2.27 2.24 2.21 2.19 2.17 2.14 2.13 2.11 2.1024 2.30 2.27 2.25 2.23 2.21 2.17 2.15 2.12 2.11 2.08 2.06 2.05 2.0326 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 1.97 128 2.20 2.17 2.15 2.13 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.930 2.16 2.14 2.11 2.09 2.07 2.04 2.01 1.99 1.97 1.94 1.92 1.9035 2.09 2.06 2.04 2.02 2.00 1.96 1.93 1.91 1.89 1.86 1.84 1.82 140 2.03 2.01 1.98 1.96 1.94 1.90 1.88 1.85 1.8345 1.99 1.96 1.94 1.92 1.90 1.86 1.83 1.81 1.79 1.76 1.7450 1.96 1.93 1.91 1.89 1.87 1.83 1.80 1.77 1.75 1.72 1.70 1.6860 1.91 1.88 1.86 1.83 1.82 1.78 1.74 1.72 1.7070 1.88 1.85 1.82 1.80 1.78 1.74 1.71 1.68 1.6680 1.85 1.82 1.79 1.77 1.75 1.71 1.68 1.6590 1.83 1.80 1.77 1.75 1.73 1.69 1.66 1.63
100 1.81 1.78 1.76 1.74 1.71 1.67 1.64 1.61 1.59120 1.79 1.76 1.73 1.71 1.69 1.65 1.61140 1.77 1.74 1.72 1.69 1.67 1.63 1.60160 1.76 1.73 1.70 1.68 1.66 1.62 1.58180 1.75 1.72 1.69 1.67 1.65 1.61 1.5200 1.74 1.71 1.68 1.66 1.64
1.67 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 eChapter(s).
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 restrictions require it.
B-16 A P P E N D I X B
TA B LE Values of the 6(c)
F
-Distribution:
A
.01
NUMERATOR DEGREES OF FREEDOM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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 6.21811.3 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 5.48910.6 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 4.1512 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 3.913 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 3.7814 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 3.59 3.5615 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 3.416 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 3.4517 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 3.3118 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 3.27 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 3.15 3.1220 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 3.122 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 2.93 226 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.96 2.928 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 2.98 2.935 7.42 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.88 2.8040 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 245 7.23 5.11 4.25 3.77 3.45 3.23 3.07 2.9450 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 2.9570 7.01 4.92 4.07 3.60 3.29 3.07 2.9180 6.96 4.88 4.04 3.56 3.26 3.04 2.87 290 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 3.17140 6.82 4.76 3.92 3.46 3.1160 6.80 4.74 3.91 3.44180 6.78 4.73 3.89 3.43 3200 6.76 4.71
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 eChapter(s).
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 restrictions require it.
B-17
A P P E N D I X 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 5.685.32 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 3.612 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 3.4113 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 3.2314 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 3.015 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 2.9416 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 2.8217 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 2.63 2.6219 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 2.6020 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 2.38 224 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 2.2228 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 2.17 230 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 2.13 2.1135 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 2.02 240 2.33 2.29 2.26 2.23 2.20 2.15 2.11 2.08 2.06 2.02 1.9945 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 1.9160 2.15 2.12 2.08 2.05 2.03 1.98 1.94 1.90 1.88 1.8470 2.11 2.07 2.03 2.01 1.98 1.93 1.89 1.85 1.83 180 2.07 2.03 2.00 1.97 1.94 1.89 1.85 1.82 1.790 2.04 2.00 1.97 1.94 1.92 1.86 1.82 1.79 1.76 1.72
100 2.02 1.98 1.95 1.92 1.89 1.84 1.80 1.76 1.74 1.69120 1.99 1.95 1.92 1.89 1.86 1.81 1.76 1.73140 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 1.75200 1.93 1.89 1.85 1.82 1.79 1.74
1.83 1.79 1.76 1.73 1.70
ˆ
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 eChapter(s).
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 restrictions require it.
B-18 A P P E N D I X B
TA B LE Values of the 6(d)
F
-Distribution:
A
.005
NUMERATOR DEGREES OF FREEDOM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
116211 19999 21615 22500 23056 23437 23715 23925 24091 24224 24334 24426 24505 24572 24630 24681 24727 22199 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 9.6716.2 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 6.64 6.61913.6 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 5.9
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 5.311 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 5.0012 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 4.13 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 4.4614 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 4.2015 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 4.16 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 3.9217 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 3.719 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 3.522 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.70 3.61 3.5424 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.50 3.42 3.3526 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 3.35 8.98 6.19 5.09 4.48 4.09 3.81 3.61 3.45 3.32 3.21 3.12 3.0540 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.345 8.71 5.97 4.89 4.29 3.91 3.64 3.43 3.2850 8.63 5.90 4.83 4.23 3.85 3.58 3.38 3.22 3.0960 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.70 8.40 5.72 4.66 4.08 3.70 3.43 3.2380 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 3.1
100 8.24 5.59 4.54 3.96 3.59120 8.18 5.54 4.50 3.92 3.55 3.28140 8.14 5.50 4.47 3.89 3.52 3.2160 8.10 5.48 4.44 3.87 3.50180 8.08 5.46 4.42 3.85 3200 8.06 5.44 4.41 3.8
7.88 5.30 4.28 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 eChapter(s).
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 restrictions require it.
B-19
A P P E N D I X 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 3.17 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 3.0718 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 2.97 219 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 2.9120 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 2.77 2.7622 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 2.63 224 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 2.526 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 2.30 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 2.3235 2.64 2.60 2.56 2.53 2.50 2.44 2.39 2.36 2.33 2.28 2.25 2.22 2.20 240 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 2.045 2.47 2.43 2.39 2.36 2.33 2.27 2.22 2.19 2.16 2.11 2.08 2.0550 2.42 2.37 2.33 2.30 2.27 2.21 2.16 2.13 2.10 2.05 2.02 1.99 1.97 160 2.33 2.29 2.25 2.22 2.19 2.13 2.08 2.04 2.01 1.96 1.93 1.9070 2.28 2.23 2.19 2.16 2.13 2.07 2.02 1.98 1.95 1.90 180 2.23 2.19 2.15 2.11 2.08 2.02 1.97 1.94 1.90 1.890 2.20 2.15 2.12 2.08 2.05 1.99 1.94 1.90 1.87 1.82
100 2.17 2.13 2.09 2.05 2.02 1.96 1.91 1120 2.13 2.09 2.05 2.01 1.98 1.92 1.87 1.83 1.80 1.140 2.11 2.06 2.02 1.99 1.96 1.89 1.84160 2.09 2.04 2.00 1.97 1.93 1.87 1.82 1.78 1180 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 eChapter(s).
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 restrictions require it.
B-20 A P P E N D I X 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 eChapter(s).
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 restrictions require it.

Tài liệu khác của Trường Đại học Ngoại Thương

Preview text:

A ppen di x B TABLES
TA BL E 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 eChapter(s).
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 restrictions require it. B-2 AP PE ND I X B TA B LE 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 eChapter(s).
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 restrictions require it. A P P E N D I X B B-3 TA BL E 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 eChapter(s).
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 restrictions require it. B-4 AP PE ND I X B TA B LE 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 eChapter(s).
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 restrictions require it. A P P E N D I X B B-5 TA BL E 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 eChapter(s).
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 restrictions require it. B-6 AP PE ND I X B
TA B LE 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 eChapter(s).
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 restrictions require it. A P P E N D I X B B-7 TA BL E 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
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 eChapter(s).
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 restrictions require it. B-8 AP PE ND I X B
TA B LE 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
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 eChapter(s).
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 restrictions require it. A P P E N D I X B B-9 TA BL E 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
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 eChapter(s).
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 restrictions require it. B-10 AP PE ND I X B TA B LE 4 Critical Values of the Degrees of Freedom t t t t t Student t Distribution .100 .050 .025 .010 .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 A 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 tA 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
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 eChapter(s).
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 restrictions require it. A P P E N D I X B B -11
TA BL E 5 Critical Values of the 2Distribution 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
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 eChapter(s).
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 restrictions require it. B-12 AP PE ND I X B NUMERATOR DEGREES OF FREEDOM .05 A F -Distribution: F A FA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1161 2 1 1 9 8. 3 9 5 10.1 47.7 5 1 16.29 61. 56 0.9572 1.952 9 56.. 7 5 .2 59 95 8. 5 1 91.. 45 9 264 4 39 . 25 2 85 14..1 2 95. 974 2 3 16 6. 0 2.3 94 7 .42 9 5 . 3 1.4.4 9. 6 045 3 2 39 2.5 42 3 1. 6 434 0 7 9 0..1 6 9 73 2 31 54. 38 3 62 . 9 18 8 . 43 43 .6 1 8.. 439 8. 6 .4 692 40 84.734 92.1 1.39 8. 53 2. 8 4 48 7 21 .488. 3.2 9 673. 974 0 7 4.9 3 3 8..4 17.3 5 2 87 5.03 4 57. 4 8 .3. 2 .4 19 2 186 .0 3 4 .4 9.1 76 43 5 4 00 8 3. 2 2 1 4.3 3 4 9.. 693 54 46.8 8.31 2. 4 08 4 175. 6 3 6 9.99 653 2 48 31 . 6 4 17 4. 3 4 6 9 5. .4 1 2 48 94.03 4. 40. 7 19 75. 323.4 68 4 4 8 92.3 1 1. 14 03 0 9 75 .02 .3 65 2 4 8 0.7 4 9 7 1 39 5 .83. 52 .9 3 5 .3 04 48 85..9 7 8 17 74.6 2 2 9 4. 1534 8.3 8 .1 4 93.29 5. 45 2 3... 5 48 7 30. 3 . 517 64 93. 2 90 5. 25 3... 5 4 8 104 63.1 3 9 3. 8 3. 0 . 3 6 93. 1 .9 5 1 .47893 3. .4 16 2. 8 3. 9 . 36 93. 9 8 5 0.1 . 2 8 4.7 59 N1 10 41.9 1 6 4. 1 4 8 2 .1 41.0 3 3 . 7 9 5 41.83 6 4 3 .8 74 1.53 .9 36 . 5.0 417 93 8.613 .13 5.1. 4 3 9 7. 63 4 3.9 41.3 .64 8 3. 23 8354 1 .2 6. 40 36.3 9 8 3.1 325 1 4. 2 3 11 3 9.9 0 .423 32.5 8423 43. 0.2 5343 .3. 1 60 5 54 . 0132 93 120. 30 4 2 . 10 89.9 3. 43 2 6 3 0 3. 06 3 9142 . 41 02 2. 1 34 3 8 4 3 3.7 621.9 28 3 4 3 06 9.1 2 0 . 9 032 . 8030 120 4 . 5 9379 25.32 1 1 2.4. 827 4 9 5.2 73.0 . 4 83 1 2 2.4.7 8.27 0 35 3 9 21.70. 7.0 231 . 67 98 45 0 52 876.. 42 39 5 20 2 3267 0 . 78. 82 964 9 57 62 1..2 0 0 02 1.73 0.2 .6 52 77 14. 3 . 62 657 4603 0 2 24.. 6.89 0 3 . 6 51.09 2 7 58 4 . 62 548 3 9 8 2 7.6 783 9 . 862108 06 52. 52 . 26.5 39 5 02 5.5 327 3 . 246 1. 25 5.6 256 1. 24 8 93 9 .2 155 91 3 2 29.4 7.5. 1 . 5 426139 2 75.2 8 245 74 2 1. 6 21 . 72 408 5. 42 2.2 4 23 2 5 9.4 23 .4 2 4 552 .37 56 .3 0.9 5298 00 2. 2 .24 3.9 237 . 75623.9 2 614 3.6 2 1 232 .36 7.4 729 . 24 3.512 .9 2 3..5 234 . 7 42 3058 62 8.93 49 9 22 .26 35.9 31 73 .2. 2 .6 2.1 27 23 . 7 42 5 8 42 6. 39 2 6 .242 .0428 .2 . 427 2 .4 2 1 .4 1 23 8 . 7 25 8 2 563 4.11 1 5 .132 824 6 . 2432 85 2 .2. 48 23 5 1 . 7 2.2 218 0 2 5 4.4 3 5 4 23 16 21 13 2 10013 2.9 01 4 3.3 9 01 .0 2 36. 9 3 01 .82 0 13. . 27 7 3. 900 0 3.63 8 0 .20 93.3.2 .5 38. 8.6926 72 0 4 ..534 86. 3. 62 6 20. 0.4 24 2 6 0 ..253 5.4 2. 124 3 26. 6.52 41 9 2 . . 224 DENOMINATOR DEGREES OF FREEDOM N2 TAfB (F L ) E 6(a)C 0 ritical 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 eChapter(s).
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 restrictions require it. A P P E N D I X 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 212 94 .3 9 58. 2 16 4 4 95.9 58 7. 2 16 94. 5 94 6 0 .358 7 4. 2 .74 87 5 16. 3. 0 9 5. 33 48 2 58 73.8 3 5 16 6 4.4391 95 . . 234 2 58 7 2.13 95 .4 821 1.39 62 5 1 2 .0 3..5 578 3 9.1 5 4.2 30 2 53 402.5 8 0.0 21 .6 4 8 .1 39 2 90 5. 435 .7 892 534 383 .72 .0 5 43 92.2 8 6..7 838 2 15 4.90 6 5 95. 948 3 57 2 1 243. 5 9 .0 3 . 436 25 8.. 46 25 7 8 59 4. 73 4 3 .8 7 43 2. 1 34 5 15403 98..4 3 2 2 57 856 33 19 5..32 .5 8 7.35 .07 4 1 54 9 7. 0322. 4 5 5 138.415 31. 0 2 9.. 43 2 5 8 6.. 1284 97 1 54 0 29 7. 5. 8 4 4 5. 13 1 55 3.0 9 6.31 2 .65 8 0.87 1 55 43 9.9 6.43. 65 80.7 231 54. 29 9 5.3 29..695 8927.7381 5 4. 29 9 5.3 29..695 8 927.75 641 37.95 5..286 38.6 927. 1 4 36.9 9 .32 7 . 3 5 8 7. 97 2 1 55 4 036.99 4.27.6 3 5 8 7. 72 5 5. 43 9 . 62 7 . 5 03. 4 .28 6 . 2 5 5. 4 5 9 .6 3. 62 5 703 2. 7 . 42 9 8 6 52. .5 3 7 3 5. 3 .6 3. 2 5 6 5 9 2.952.7 5 3 3 . 32 N1 10 2 1.7 1 5 2. 1 6 2 321 2 .5 3 2 .1 . 647 124 42 .5 2 1. 2 .1 3 . 57 217 94.62 2 3.122 .37 . 527 8 24.211 .5 2 4 2.. 8 . 92 5 93.12.7 2 3 29 . 4 21 4 2.. 7 2 2 83 11 0 . 2 9 7 23 2.1 2.0 22 .4 9 21.7 2 5 2 .731 0 2. . 52 4 6 53 1.2 12 0.28 2. 1562 1 3 0. 2 .7 8 2 01. 2 0 6 21 .09 8 62 .13.1 3. 421 7 25 42. 90. 26 19. 1 20 8 6 3 82 9 .03 1. 5 62 10 1. 5 .52 17 1 9 2 2. 91 4 . 219. 1 70 6 2 78. 37 21 4 2 4 2194. 5 . 42 13 85 2 5 3.0 91 85. 2180 5 6 2.5 2 8.02 20 193 7 .0 1851 18 6.2 291 7. 2097 0 . 5 2179 4 6 2. 3.4 2 08178 6 1 2 3 10 97 . 4924 0 86 1 7.2 5 12 78. 208 17 2 .1 4 2.2 0 6 21. 3.2 81701 4 0 4 1 20.8 0 71 9 0 82 0 6.19 1.5 7 4 1 70 2 .9 01 8 10 6.7 . 1 598 21 1 2. 76. 68 2 .6 0 97 9 71 71 2 4 2 9187 3 . 28 0.16 .9231 67.55 21. 32 04 16 9 2 01.86. 3520 591 741 6 2 4 8.6 81 8 1. 816 .8 201 6.5 .92 0 118 471 3 . 6 9 2 1.86.42 0 4918 57 6 41 2 4 27. 25 08 4 6 . 2 1095 7. 28 2 11 1 2 ..8 2 3 81.917 6 .73 0189 6 1 2 4 25. 23 2 1.11 856 .2 09 615 6. 22 0 121 8 76 6 7 2 3 71.94 7 46 25.62 0 2 4 2.3 79. 130 9 1 .2 9 0 5 6. 2721 15 7 3 721. 9 6 .108 76..2 2. 6. 14 82576.2 91 8075. 201 9 8 12 3 5 7 2 60.91 675. 32 7926 45 2 4 521. 108 76 1 .5 8 2915 2. 2.79 151 6 2 5 19.5 1 . 3109 7582 162 4 21.5. 171 8 34 6 1 .4 715 2919 8 15 .1. 06 4 52 8.03. 7 1 9 187 6 3 2 2 0.6.62 87 71 2 .1 965.9 1 . 320 87 1 5 4 321 0.0 9 18675 4 . 162 7 0.5 1860 1 2 1 4 5296 7 1. 82 .7 1 9 65. 87 5 . 01 20 1 9.7061 100112.6 0151 4.16 0 .6 3 1 6.3 6 01 1 2 18. . 026 1 6.01 1 . 60 1 6 0 1. 6 . 0 5 151.6.9 1 9 . 50 5 1 5 7 1. 54 . 8 5 91 51..7 1 7 . 57 5 56 12 7 .11 5 6.1 1 .5. . 5 5 154 1. 50 . 1 5 5 4.1 4 1 3 5. . 345 18 2 .1 5 1. . 1 5 05.41 26.5 1 4 2 1. 7.458 140 .4 9 1.11 5 4. .41 .84 2 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 eChapter(s).
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 restrictions require it. B-14 AP PE ND I X B NUMERATOR DEGREES OF FREEDOM .025 A F -Distribution: F A FA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1648 23789. 3 9 5 17 8 3. 4 6 9 41.40 1 2. 5193 6. 2009. 6 0. 82 1 0. 9 5 87 2 3.1 18.2 9 4.0 78 .9 2 16 2 7. 3 5. 8659 79 1 . . 46 93 1.2 4 66 1 8 3. 709 1.59. 0764 6 5 3 10 62. 717 4. 5 036 9 738 6 9 5. 37 4. 5 91 5 .25. 6 .15 509 44 69 2.8. 06996. 5547 9. 95.2 3 89 729 362.7 9.985 4 7 4 1.2 5. 4.4 9 3 4.05 8 8 9 5. 240 .914 1.2 . . 3 9 4 06 2 8 .7 64.53 57 4 . 949 66 9. 2 8 360 5 5 9. 3.865 4 9 4 1.8. 1 8 4 95 .4 0 7 3829 4.3.85 9 4 4 1.9 .0. 0 3 4.0 6 9 4 .6. 65 3 94 1 2. 8 4. 9 9 3. 613 .8 0 9. 85329 4 18 73 9 03 4. 47 1 9 9 3. 5 3 94 1. 4.82 33 4 6. 27 9 3857 4 9. 2 5643 4 17.8 3 496.0 23 9 38 47 0 . 5 4 17 9. 12 4.8 3 45 6.7 10 9 28 4 63. 5 4 17 6.2 4.7 3 4 16. 4 17 9 2 4 6 33. 574 1 3.4 4 6 2. 7 . 2 14 2 86 0 . 436 0 5. 32 4.7 3 864.0 2 9 836.5 3 4 16 8. 01 4.7 3 46.8 0 9 2835.54 16 6. 74 436 1. . 0 23 754 3. . 688 0 . 236 . 16 4. 6 . 4735 0 32 0 N1 10 61.9 1 4 6. 1 7 2 26 1 5 .3 5 .61 . 2 4 65 4 64 .1 16.54 .03 . 618 39 0.634 74 2.06 1 4 .87 . 2414 8 4 6 . 3.2 61 74 54 7..7 0 8 4 .725 1 . 04692 4 4.. 09 4 41 03 1.8 52 2 .38 54 6.9 0 3 .7 9 30 2 .8 4 2523 .8 7 8..0 85 24 .96 03.1 4 7 . 870 8 6 37. 5 427 3 93 5 6 4..46 .3 4 7 7 3 856... 25 6 3 5 13.8. 63 98 47 03 0.5. 46 85 3 3 5 16 9 3.. 0 . 246 9 4 03 7. .3 6 1 5 5 33 8. 13 825 . 24 57 3 .9 37.4 51 3.7 4 . 6230 8 6 3 8 64..3 2 4 56 4. 4 36852 3..73 15 3 13 3.8 3. 48 .. 8362 5 7 3 2..3 3 20 8 3 92 2.8 2 3 . 2358 6 5 32 0 11 9 1. 4 . 90 9 3. 6532. 1 4 .3 2 709.4 5 7 51 32. 140 . 303213 12 3.0 9 059 8 . 920 5. 7 3 15..3 1 96 2 2 3 1 2.0 29 35 . 40 21.43 9 3 5 43 23.69 38 42 .. 725 6 3 6 32 06..29 3 6 3 5 58 34. 2 . 2023 0 3 4 13 2..8.4.5 3 9106 7 3..2 0885 3 2 3 0.1 42 03. 98 .62 9 27 804 3 4 73. 98.. 8 271 . 392 7028 6 5 32.9 2863 3 8 3 03 7281. 032 9 2 .12 36 3 30 72. 27 . 3 9278 4 5 9.126 9. 86 20 5 3 35 27. 972.26 703 3 3025. 9 .9 2.026 9 . 35265 6.13 29 7. 8682 7 2 3 2 385. 98 125 7 .82 45 1 3 3072..8 76.2 . 3 12 75 5 3.09 271. 820 3 288 726.2 6 2 .4 26 3 3 9.2 54 . 264.50 3 8 26.5 72 .0 25 27 8.2 . 5 2.093 2 5 2.8 7.252 7 3 25 925.. 5 3 .13 96925 721 4 . 2.86 95 4 80 42 27.7 0 25 5. 10015 2.1 0 8 5 4.3 1 0 .8 5 6. 3 1 0 3 35 8. . 022 31.05 3 2 5 . 70 2 8 93 1.15.059 37.1.2 3 80. 032 2 13.3.337 23. 0 2 0.6. 68 2 79 92 .73.3. 8.28 7 3. 11.1 8 2 6 82 2 .9. 2 5 72.2. 628. DENOMINATOR DEGREES OF FREEDOM N2 TAfB (F L ) E 6(b)V 0 alues 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 eChapter(s).
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 restrictions require it. A P P E N D I X 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. 3 5 14. 4 9 31 8 9 9. 7 5 1 563 4 3. 9 1 836.05 1 5 4 16 . . 1 7 9 3.2 4.9 9 1 .8495 1 56 .4 3.1 4. 190 31 8 4 . 27 30 9.4 650 5 14 96 .61 13. 1 3.80 9 0 9 1. 25 3.0 .1 4 1 54 86 3 6. .1 8 4. 9 . 2 4 35 3 6 .93 1 3 6.. 040 9 2 8. 93 0 .5 3 1 4 5 1.83 . 60.9 0 8.7 4 .1348 3 9. 3 6 5 1 3 68 09 8. 0. 15 3 6 5 14 641 .0 3 5. 1 3. 648 6 0 9 01.60 .1 4 3 7 54 3 . 60 8. 4 .33 15. 9 2.0 1 3 5.1 3 68 3 0 9 .4 3 0 .1 1 8 54 5 . 1 1 38 4.0 9 0. .421 5 3.9 30 89.3 4. 6989 012 3 .45 1 0. 4 3 46 9. 1 3.8 4. 8 0 9 0.2 1 1 .391 5 184 661 3. 0 9 04. 1 .83 4 2 59.73 4.8 647 9 0.2 8 . 3 5 1 75 13 3.8 0 9.4.1 9. 33 4 3 5 136 9.47 5 1 3. 8.7 0 93 04 2 1 .3 643.3 56 94.8 37 1 39. 02 6 3 0 9 4. 36 4 1 5 129 3.3 4 3 64.8 273 1 9. 04 2 5 0 35.23 4 1 19.2 5 3 6. 2 474 3.1 9 02. 440 5 1 53 1 36 9. 5 3. 807 9 .0 3 1. 32 4 0 5 109 3.1 34.0735 92.41 0 0 4 0 1 8. 6 34 1 .91 08 3. 0 89731 . 8 249. 3 89 4.1 3. 83 3 .887.24 1 9.88 4.1 3. 83 3 . 887 N1 10 3 1.3 1 9 3. 1 3 2 .3 031.7 3. 0 3 1 42 1.. 4 3 79 4 3 2. 1 .5 3 1 8 .3 2 3 5.2 6 3 0. 7 .27 3 2 1 3 1.96 7 .3 83 3.92 5 21 1 3 0. 8 . 2 5 1 02. 7.92 1 2 8 7 2. 69 .3 259 72..02 5 3 2 3 82. 7.62 4 . 5 2682 8.0 5 8 3 52 6.0 4 .. 8520 2 3 . 74 2. 9 235.. 8 52 9 42 6 8 24.. 6 .65 8 242 3 6 3 62 1 . 72 4.0.0232 25. 84 33 8 6 3 9 026 7.2. 6 24 0 326 45.2.2 0 6 2 .7 02 43 7 . 7 10 9 826 43 12. 5 . 4 2 1 3 126 12. 91 4 . 50 2 250. 7 2 4 36 5 3.2 2 49 . 82150 92 .43 7 2..4 0 4 62 . 7213 57 . 3 . 91 5 2.0 3 .8 42 5 41 92..92 6 3 .72 6 2. 210 . 06192 37 12 50 .1 3.62 .18 5. 3 77 690 5 4.26 9 24 3 52. 18 .2 6 11 0 183 7.0 2 .358 42 1. 91 .. 6 01 3 .2 2.19 408 . 02 6.8 9 2 0. 43 2 71.2 0 13 18 5 0 .98 6.95 . 124 312. 91 8 3 1 2.2 1729 381. 206 9 1 2 43 1.8 0 12 8 2 .720. 09.4 692 18 2 3 92 51 9210. 0. 167. 520 8 1 92. 1.6 83 15 2 19187 28 9 06 1... 82 57 01 3 9 22 5. 41 967 . 317. 42 8 1 7 2.6 7215 2 97176 2 84 .237.1 7372 081 3 92 5 83. 1 35 . 20 7 .2 01 8 1 6.6 62 1372 0 195 .5 2 84. 17. 62 599 17 9 05 7. 112 9 3.0 81 6 2 2. 4281 .6 523 801 7 2 75 29.81. 42 358 1 3 .92 5 62 1 .20 18 7 . 94711 46 2 1. 2 340 187 4 .2 0 2.9 6 . 42 30 17 3 .2 5 2 7 9 .2 81 14 . 92 451 7 1 4.6 2. 0 239 85 7 3 7.218 4 2 91. 44 2 3981.2 2962 2 54 4. 9578 1.. 320 11 8 1 2 7 6.34 .8 6.0 91 7 3 .74 2.261 1 6 .. 92 5171 3 2 3.. 329 180 16 3 82 7 6.08 19 2.. 043 2. 8619 742 .51 9 23 06.2 .16 5 . 9 2167 2. 21 0984 69.7 1 76 . 9 3 60 24. 0 321 9 1 100112.8 011 4.17 0 . 1 7 9 1. 6 81 7 0 .17 71 8 .. 0 7 6 1 2. 7 61 7 6 1. 0 . 0 17 41 7 .. 51 7 3 1. 1. 7. 41 7 3 1. 76 . 4 1 21 77 . 7.21 7 1. 1. 7.16 0 1. 769 6 14 1 91 1 .1... 6 6 167 11. 6 .7 1 6 96. 71 81 6 .. 8 16 1. 6 .5 1 6 51. 1. 6. 46 65 1 31 9 ..6 1 1. 6. 1 2 15. 6. 1 6 01 67 .. 1 5 156 1. 9 8 1.55 42 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 eChapter(s).
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 restrictions require it. B-16 AP PE ND I X B NUMERATOR DEGREES OF FREEDOM .01 A F -Distribution: F A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 FA 1405 2 2 98. 3 5 34.4 4 912 9 9.159 0 3.19 02.6. 65 9 83 14 .230 29 1. 7 3 9.3 719 5 1.2. 812 . 3 8 01 1. 2 .95 97 1 2.31 6 9. 610 2 3 27 . 59 8 6.1 5 9 26. 7 .2 9 5 6 37 01.5 8. 4 . 79 1.8 6 .5 58. 448 5 9.70 5 9 1.2 9 15.596 5 4 2.8 9 7 21.9.12 97 1. 70 9 8 9 5..2 5 016.8 5 47 0 8.4 9. 42 8 5 17 1 46.8669 80. 09 1. 276.2. 4 76352 4 2.7 8.. 686 .13 00 3175 4. 5 6 179 50. 6 91 .97. 0 .2 4 58158 47 .196 3. 542 0.3 867. 17 9 85.9 79. 63 6 9 1 76. 05 1 .4 98 3 0 4 2.14 5. 69 7. 40 7 .6 2 6 9 176. 2 14 2 4 2. 75 2 73 2 5..6 9. 19 1 98 6. 4 1 1 4 2.1 5.4 7. 20 713 99 01 6 6. .4 2 4 06.25 9 67.. 2 95 68.6 9 1. 1 14 2 4 65. 5 5 62 97 407 9.9 1 5 .4 2 4 62.5. 9 697. 16 0 . 7 6 9 81 43 1 .2 4 98 4 .57 49 7. 0 6. 1 814 6. 425 7 .15 9 097..6 9 6 9174. 6 1. 472 3 8 4 2.6 19 6. 0976 9 .26 9 84. 7314 2 05 4.9 6.82 .7 . 65 6 .9 68 242 85. 0 965 8 1 9 .2 6 . 626 4 25.2 6..807 64.39 2 8 1 4 N1 10 10 1 .0 9. 1 6 2 591 7 .3 . 339 1 7 21 .4 . 0 5 7 8 1 6 .8 5 6 .6 8. 1 . 765 69 0 5 .2 3 81.75 2 16. 5 .38 1 9 5 3.. 8 9 .6 5 64 . 50 81 5 7 65.. 9 .6 2 6 5 4. 2. 98 4 . 603 5 2. 1 . 01 6 5 2 54 2.82. 8 .. 3023 5 4 18. 15 9 . 5020 16 9.5 7 . 94 5 7 594 2 . 3 .. 95072 2 045.. 956 0 64 1.5 8 . 48 05 27 5 48 6. 7. 18 .. 458 2 7 0 4 63.. 845 27 68 24. 60 . 27 4516 4 946 87 .0 83... 429 5 9 4 2.5. 6453 47 4. 376 . 1420 4 4..7 35 4 . 40162 7 8 4 1.3. 4135 56 4 4. 1295 3 . 02 94517 4 3 4.. 30 47 2 . 4317 52 7 4 5 0.6. 347 75 09 0.910 3. 40 . 749 03851 4 4 3.. 438 719 7 4 . 380 41 7 4 389 30.2 5151 .4 94. 6 1378.3 8 6 4 83. 637 14 0 . 1637 9 0 4 3 98.1 83 593 0 16.. 37 94 0 4 04. 5 289.8 9530 764 0 43. 5 26 . 10 92 5 . 379 20 6 4 2 03 7.0 79 4 . 535 . 6303 24. 358 .7 8 3436 514 05 3. 45 78 . 863 0. . 35 49 7286 4 23 6. 02 41. 750 . 5372 3. 72.7 69 3344 9 4..0 3 49561. 345 2705 4 163. 16 9 3 . 53 16 . 6530 22 3 1.15.6 3.37 2914 5 4..920 3 6 . 36 10 5 4 10 13. 1 6 .3 78 2 . 473 15 4 6 3 0..2 3.9 1 4 1. 6 33 2 30 .0 3287 95 45 3 5.70 . 3 9.749 3 64.32 9 .6 50 3 01 3944 82 3. 539 .1902 0 . 6 3201 7 4 4 53.2 7 . 3.23 61 23.84 3. 2.5 3 918 2. 92 83 4 8.9 3025 06 8 . 02 37 984 4 3.7. 1 3.628531 9.832.5 4 9213 2907 4 5. 39 7 5.88 6.0 94 212 90 81 100 6 1 . 2 9 0106 4 4 .01. 8 8 5 6.28 01 2 6 8.8 02 4 0 6.03 .7 . 7869 4 6..837 4. 6 .649 6 4. 7 5 3 7.9 43.3 3.28.45 43 9. 4. 1 8.4 13 76 .13 3.6 34 1 ..2 13 4 3. 1 7.43 7 N DENOMINATOR DEGREES OF FREEDOM 2 TAfB (F L ) E 6(c)V 0 alues 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 eChapter(s).
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 restrictions require it. A P P E N D I X 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 9 6 9. 3 2 5 2 3 6. 4 5 99 6 1 6 .2 4.5 2 56 09 4 9. 5 9 6 15 .3 17 6 5 2.92 6 937. 5 96 1 4 56. 3 9.7 85 2 31.9 15.9 6 9.39 5 1 42.3 7 65 2.7 2 6 9 3.. 7 6 9.4 16. 2 1 9 5 18.3 0 7 6 5 2.9 2 75.2 6 8.87 5 1 34.6 3 8 7 .5 7 9 8 9 2.3. 6 9 3 5.24 .3 7 02 6 5 2.47 2 6 2.0. 9 8 94 12 32 7 9. 02 3. 9 6 579 1 5. 2 .8149 4 1205. 6 37. 6276 9 79 1. 5 3 92 4 .0 .2 4 7963 56 .5.5. 9 1 64 1. 1 3 2. 1 .05 6 39 75.0 9 .04. 1 9 5 2 746 8.5 . 05763 1 9.9 3 1 94. 2 .6 71519 705.49 9.6 0 . 8745 2 17.6 4. 85 6 9. 052.3 9 3 1.842 .3. 176 6 53.54 9 6. 05.8 9 3 1 9.1 0 . 834 5 2 3. 176 1. 25. 4 6 9. 05.0 6 3 9 3 10813 .3 4 .61 5 206 .9 4. 4 6 9..9 4 3 9 2 1 . 194 35 2 3.0 6 4 4 9 6.. 9 53 69 2 1.7 9 3. 3 06 8 74 3 5 2.94 9 6.. 9 51.6 .9 6 9 2 17 . 06 35 2 3.8 6 7 4 6 59 4. 3 .2 1 9.5 .7 94 6 3 05 5. 3 .84 4 9 5.0 6 9. 4 9 .03 4 6 5 26. 33 65 4.94 92 137 9 8 9. 42 32.6 4 6 55. 3 3 .8 5 2 18740 3. 24369 5.739 9 6. 24 6 5 254 3 .1 79 6 32 14.5 3.7 1 1 4.86 5.70 5.6 N1 10 4 1.3 1 6 4. 1 4 0 2 .3 631.38 3 4 23 1.. 4 3 36.0 4 31.7 254 08 4 .2 63 1 2 3.. 6 7 3.3 3 1.4 95. 42 7 .9 3 2 3 5.1. 2 57 93. 289 3 1.4 2 3. 41 23 1 . 03 9 2 3 5.0. 8 0 3.7 6326 3. 0 4 90 31 83 9.. 673 2 1 3. 0. 52 7 3.63 39204 02. 0 2 4 95. 31 52.7 4 . 453 2 1 3. 2 9.2 8 4 383. 2761 07. 9 6 2 4 . 31 32.27 0 . 503 28 1 3 3. 0 9.62 5 2 2 .838 63 1427 0.6. 8 3 20 4 9 2.0 02 5.97 63. 426 0 3 3..6 5 29. 8 .8553 822 9 20 6.4. 1 4 6 9.7 2 5.6 30 . 432 0 3 .82 54. 90 6 . 1748 .7522 3. 5 . 8 637 4 30 76 245.3 32 . 32 90 0 3. 27 5. 6 4 . 1768 53 2 477 3 2 9..2 0 83 54 4 129. 46 8 243 92 .28 6 7 0 3 09.4 2 530 3 .17 .8 02 43 .192 8 52 4 83. 02 24 13 621 0 . 328 4 0 3. 8.26 40 19 1 .5 174 3.8 2 50. 89 22 05 .3 19 72.6 32 17 4 672 2.. 9 2.5 . 83 8 21. 0 3 36..8 87 2 4 .7 0 . 928 0 4 .13 2.5 9.02 13 . 342 0 0 3.2 74 2 . 25.31 0 0 .7 531 362..5 2 5.0874 2 40 . 415 0 3 3 19 2. 35 62 10 . 325 9 3. 2 0 . 7230 8 .7 439 3 32 69.9 2 0 .. 71 2 4033 2 11 3 9214.51 0 . 3219 3. 027 51. 092. 7 .428 3 2 056. 94.. 78 2 419 3 12 3 98 207.41 0 . 3120 9 .83 0 263 1 . 7 26 7 423. 0 295 .0 7 66 2 3. 5 3 29 86 70 .41. 39261 9 3.72 1.3 9 26.30548 6 4295 . 285010 9.72 3 09 6 . 14 3 98 2 85 9 4.4 6 291. 3.724 18 9 3.2.3 9 26.0 1 6 43.8 25 10 91 8 4.0 72 3. 86 0 3 27 834 19 .42 01. 56 23 4 9 26. 8. 2 7183 3 652. 6 251 2 .8 732.. 69134 2 31 8 .20 5 1 . 29763 39 2605..25 1 897. 5 4031 2 0.8 710 2 38..1 45 3 62 18 .29 01. 576 43 39 26 .24 1 186 2. 4 31 2 0.8 71 09 2.. 392 3 62 2. 287 01 1 . 2 3 6 4 3 68. 287 1 .90 242 3 2 19 94 1 72 10012.0 0121 4.19 0 . 1 9 9 1. 6 81 9 0 .19 71 8 .. 0 9 59 2 51 5 1. 0 . 0 19 9 .1 4 9 2. 1. 21 98 .318 1. 3 .18 9. 9191 8 1. . 918 91.0. 18 6 1. 81.41 8.9 7 .8918 61.6. 18 1 1. 81.0 8 5.8 5 761 41.3. 17 1. 88.6 1 7 27 . 231 7 81. .7 6 1. 71 4 1 7 6. . 8 9 1 7 41. 1 . 1 6 3 1. 71.79 7 27 01 745 0 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 eChapter(s).
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 restrictions require it. B-18 AP PE ND I X B NUMERATOR DEGREES OF FREEDOM .005 A F -Distribution: F A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 FA 11621193 1 95 91 5 9 .4 9 63 9 151 4.29 93.29 8. 6 24 8 1 1 17 8. 6 9.8 1 1 95 2.6 54 68. 3 1 6 31 42 1.. 4 2 6 51. 9 .7 12 4 2 . 532 143 4. 5 95 16.0 94 2 51.10 1 1 0 4 3. 629 1 2 94 21. 3 9.2 4 9 0 1 82 .0 5 9. 9 6 9 511 2 2 4.1 0 3 4 2.8. 5240 . 1973 .0271 42 6 94 1 07.94 18. 64 9 2 1. 98 6 3 1 2. 7 4. 5 1 3 128. 45 51 9 4.3.72 94 01 0. 3 9167 4 91 .3 7 29 7 21 .18 9.759 4. 815 1 .8 1 3 19.39 5 3.18 2 9 6 0..4 41 8 67 0 1 38..3 89 94 2. 18 6 1 9 1. 5 0. 96 1 06 57 9 12 3 . . 18 5 2 90..4 06 4 48 .3 2 3 7. 48 5 2 3 218 4 4 0.. 042 6 2 13 74 4 9.2 3 3 9 20 .18.13 4. 301 6 4 3 617. 8 2 1 2 3. 1 4 0. 2 4 1 45072 9 3 1. 6 90 2 3 0 .8.162 14. 11 4 92 410 6.5 9.2 3901 9.8.459 4.0 9 2 41 93 6.59 2 3.7 8.624 07..942 31 87 6 1 5. 3 85 71 8 2.7.6294 0 1..02 92 31 6 . 9418 2 2.769 0 9. 6 39 .800 217 6 1 2 .3 9 2.9 7.59 09 2..7 8 2 6 3 9 4 .8 6 9 7 6 .8 7 8 1 9 6. 2 7 654 . 7 79 2 5 6. 4 7 9. 61 5 2 69 N1 10 12 1 .8 12 1 . 2 211 1 . 3 81 9 1. 4 .4 41 3 8 15 .. 8 9 1 . 060 18. 8 75 81 .6 18 07.071 6 1 .862 9 70.17 .36 9409. 8.273 89.214 3 6. 707 0.6 6.1 92 . 858 6.17 9 2 7 65.49 2.36 4 264. 05 7 . 05 26 9.6 29 3 4 60 35 4.1795 6 . 861926 1 75.. 508 . 6 539.43 07.05 8 16.190 95 8 .5 52662 0 6 5.6. 20 6958 3 . 56.1 44 0 25. 5 2 5 83 46 . 76 750 578 4 5 8.7 5 240. 2469.6 2 4 9 14 3 77 4.3 8 7 57 1 .5 .0 47 4863 56 8 5 6.38 40 9385. 42 1.8 52 97 0 8 .50 14 9 47.9 2 9 6165 5 468.2 .48 745 747 5 0 5 5.6 5 690 4 68 7 .4 50 6137 .8 9 4.6 94 0 5 5 348 .54 .4289 5 4. 73409. 345.2 596 046 .4 82 410 87 08 9.6 5 2469 0 . 4.39 5 3 046.30 8.82 5 .0 4. 1.234 7 . 840 389255 0 24 64.49 9738 .9 742 .536 5 2 4.9. 54 13827 .4 1 386. 5 4. 784 29 3716 9 9 283 1.4.1 4. 68374 326 5 4.3.4 03 681 . 4 25 635 . 64 7 483 35619 5 3 59 4.039 7.1 24 .70 359 63 36 5 1 44 .93 5.3 0 .6 4 3129 4 .3 8 37 3845 1 9 7 58 4.937 4.4 3. 99 3568 316 5 1. 347 831 94.3. 045 61 3 4 .7 2 03 46 34 2 7 4.0374 .5 3283 . 3 90. 45 0 4. 7309. 0963 .2 368 5 .1 34 6 42 . 7 483 31459 5 0 2. 83 6731 24.5 49 313 5.7 805 3 52 .28 5 136. 21 .4 423 355 31 5 0.2 73.634 502 9 3 .0 49 32 3 .6 02 745 28 931 100 8 1 . 2 2 0148.1 0 8 6.1 0 5 5.4 8 .05 51 2 9 4.5 0 8.04 4.0 5 .5850 4. 7. 4. 03 8 5.6 8 .89 74.52 3 4 6. 5 .4..33 3 84.4 0 . 9 9 58 24. 4 6 5 3.7 34 . .23 3 51.8 8 . 2 5 25 3. 3.9 8 3.2 0 387 N DENOMINATOR DEGREES OF FREEDOM 2 TAfB (F L ) E 6(d)V 0 alues 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 eChapter(s).
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 restrictions require it. A P P E N D I X 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 1248 2 9 1 2 93 2 94 4 1 2.9 7 2 4 90 0 51 4.22 9. 4 9 6 2. 9 4 08. 9 8 12 0157 0 99 .62 2. 37 2 0896 5 4.9 6.0 2 01. 491 5 2 5. 7 4 5 1 97.. 9672 9 14 4 6.85 9. 237 0 5 1. .4 1 976. 974 9 069 2 913..297 4 3 1 4 1.975 65.. 9 2 981 .7 6.5 92 37 4 9 1. 63 5 0 4 695. 3 2 .3 6 . 25 1 3 197 4 9 .4 0 5. 2 94.17 6 5 92 8. 2 1 3 2.47 4 95 .3. 8 4. 92 71. 6 5 . 261 2 2.0795 . 2 94. 93 5 92 71 86 5. 1 .2.7 2 8 9 15 . 3 9 4 9. 35 6 4 1 2 61.. 8 9 1 2.2 72 5 2 94 4.. 93 51 2 6. 1 4.2 . 01 5 1 91. 9 1 94 8 5 . 2 15 6 4.15 92. 71 2 939 5 5 4.83 2. 0672 0 1.5 5 4 9. 92. 2 150 6 3. 8 9.2 8 .4 7 1 3 9 0 19 .2 25. 2 4.1 3 6 5 2 5.2 .6 3 0 1. 0 93 05. 6 1 4. 9 2 510 63. 9 .01 27 4 . 3 32 9 2 1 9. 5 9410 6. 3 91 27. 0 219 3 6 5. 39 4 81 .4 .96 3 2 9.7 2 5 91. 80 3 921 5. . 8 34 1 .86 3 7 9.0 1 2. 70 2 149 5. 5 91. 86 2 3 9.4 1 68 5 91 2. 670 9 14281 3 5. .2 9 1 2.319 56 59 27 .7 3 1. 05 7 918 2. .4 98 5 2 .6 2 87. 9 5 40 5. 3 18 2 8 .6 5 8 2 . 5 1 3 9 94 25401 25464 N1 10 51.2 1 2 4. 1 5 8 2 .1 041.7 4 3 . 4 5 7 84 1.. 4 1 642.3 4 2 4. 1 . 4 7 34 0 5 2 .41 13.64 .3 7 3. 815 .94 37. 6 1 84 63.8 304 .3 3.. 75 8 5 .64 93 1 . 620 541 3 9.37 44 .0 3. 75 32 . 35. 6 34 8 5.1 0 0 .4 93 65 2.3.73 02 . 70 32 5 28 2 3 4.3 7 3 . 734 0 63 51 1 .34 36 7 3.2 2 3 . 6 5 48 9 3 40.3 2 3 5 . 41 240 3. 708.34 .16 4 393 8 2.24. 23 3 48 90 .5 3.13 2892 4.3 0 7 7 43.4 .3 8425.0 31724. 13 7 5 3 92 4 .4 93 2.709 63.. 13 09 2 6 3 432.84 .1 24. 512 754. 13 7 8 32 95 . 4 75.0 2759 5 3 4.. 3 962.00 43.4 . 2 81 1 3 824 . 5 302 674 .23 7 5 31 89 50 . 4.7 208 14 03 45..32 95.7 6 0.4 .2 70 7 3. 2640. 52 037 634 .93 6 2 381 2 84 . 3126.8 9 63 125 27 0 3 48.7 31 4 . 2738 9 . 4792 604. 07 6 8 3 29 273 2 4 .3 57628 74 23 8.1 24 5.3 0. 3823 0. 4956 205 3 5 32.0 2741. 613.2 75 8 03. 78 329 .1 24.04 4.13 00 42 672. 92 4 .03 93 25. 2731. 34 5 2 7 6 .83 2 09 4. 52 9 7. 30 274 4. 87 32 68 212 5 2.4 .01 3 17 2 . 08 261. 31 825. 9 7 4 3 2 42 7 6.6 21 7 4. 312 4. 3 679 20.38 212 4 .0359 106 2 18 . 69 2 . 30 52. 7 2 730 07 3. 11 2. 5 3. 35 6 4. 83 2 460.38 62 4 .9357 31292 5 . 6 20 . 392 4. 7 1 53 27082 610 81.3 5 02. 34 3. 6. 2 5179.3 249 0 4 .9356 3 8228 0 9 . 38247 0 33 2.5 2 312 2 .204 3. 43 02 581 . 3126 0 4 .935 3 822 91 1. 8 241 9 . 2758 4.17 9 230 6.2 07 1 . 1 24 54 3. 33 9 2192 5 2910 81 .. 72 4 2 91 30 2 56 1.19. 54943 7 16 7.2 504 1 2 31293. 26 4 2 . 2 951 4 .3 .302 9.2 975 71 069. 53827 0 296 5 23.2 290 1 1 739 13. 09 25 2 4 0 . 0 28 4 .230 89.7 2 975 51 7 . 46172 3 6 4 19 3 2.2 091 4 97 2 7. 1 .32 0718 3 3.2 59.2 7 326 2 50 18 10012.1 0 7 2 4.1 0 3 2 1 . 6 2 1 0 2 .18 . 01 90 2 32 9 2. 002 .0 . 070 5 2. 1 9 .2 049. 60 62 5 1 2.. 0 1 0 2..92 1.0 10. 120 91.15 8.997 1..82 1.96. 180 91. 112 2.993 1.. 981 17.6 92. 159 81. 116 7.887 1.. 971 14.99.8 129 .111 3819.1 2.7.88 15 2 0 1..8 7 11.. 8 1 14 6.487 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 eChapter(s).
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 restrictions require it. B-20 AP PE ND I X 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 eChapter(s).
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 restrictions require it.

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