28 trang 2 lượt tải

Bảng xác suất và Lý thuyết Nhỏ trong Thống kê môn Xác suất thống kê| Trường Đại học Ngoại Thương

Bảng xác suất và Lý thuyết Nhỏ trong Thống kê môn Xác suấtthống kê| Trường Đại học Ngoại Thương. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời đọc đón xem!

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

Trường: Trường Đại học Ngoại Thương 1.1 K tài liệu

Tác giả:

Lan Anh Trần

3 tuần trước

Tải xuống Báo cáo

Danh sách Quiz

B-1

A p p e n d i x B

TA B L E S

TABLE Binomial Probabilities1

Tabulated values are . (Values are rounded to four decimal places.)

n 5

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

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

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

x=0

p x( i)

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

B-2 A P P E N D I X B

n 8

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

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

TABL E (1

Continued

)

B-3

A P P E N D I X B

TABLE (1

Continued

)

10

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

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

B-4 A P P E N D I X B

TABL E (1

Continued

)

20

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

B-5

A P P E N D I X B

TABLE (1

Continued

)

n 25

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

B-6 A P P E N D I X B

TABL E Poisson Probabilities2

Tabulated values are . (Values are rounded to four decimal places.)

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

P(X…k)=a

x=0p( )xi

B-7

A P P E N D I X B

TABLE (2

Continued

)

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

B-8 A P P E N D I X B

TABL E Cumulative Standardized Normal Probabilities3

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)

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)

TABLE (3

Continued

)

B-10 A P P E N D I X B

TABL E 4

Critical Values of the

Student

Distribution

Degrees of

Freedom t

.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

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

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

TABLE Critical Values of the 5 2Distribution

B-12 A P P E N D I X B

TABL E Critical Values of the 6(a)

-Distribution:

.05

f F( )

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 8.68 8.67 8.67 8.6647.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.94 5.91 5.89 5.87 5.86 5.84 5.83 5.82 5.81 5.8056.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.70 4.68 4.66 4.64 4.62 4.60 4.59 4.58 4.57 4.5665.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.03 4.00 3.98 3.96 3.94 3.92 3.91 3.90 3.88 3.8775.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.60 3.57 3.55 3.53 3.51 3.49 3.48 3.47 3.46 3.4485.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.31 3.28 3.26 3.24 3.22 3.20 3.19 3.17 3.16 3.1595.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.94 2.91 2.89 2.86 2.85 2.83 2.81 2.80 2.11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.6712 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.72 2.69 2.66 2.64 2.62 2.60 213 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 2.55 2.53 2.51 2.50 2.14 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 2.45 2.42 2.40 216 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.46 2.42 2.40 2.37 2.35 2.33 2.317 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.41 2.38 2.35 2.33 2.3118 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.37 2.34 2.31 2.29 2.19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.34 2.31 2.28 2.26 2.2320 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.31 2.22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.26 2.23 2.20 2.124 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.22 2.18 2.1526 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.18 2.15 2.28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.1530 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 235 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 2.18 2.12 2.0845 4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.1050 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.0760 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 270 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.0780 3.96 3.11 2.72 2.49 2.33 2.21 2.1390 3.95 3.10 2.71 2.47 2.32 2.20 2.

100 3.94 3.09 2.70 2.46 2.31 2.19 2.120 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 2.43180 3.89 3.05 2.65 2.42200 3.89 3.04 2.65 2.4

3.84 3.00 2.61 2.

DENOMINATOR DEGREES OF FREEDOM

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 5.6354.54 4.53 4.52 4.50 4.50 4.48 4.46 4.45 4.44 4.43 4.42 4.41 4.41 4.41 4.40 4.39 4.39 4.39 4.39 4.3763.86 3.84 3.83 3.82 3.81 3.79 3.77 3.76 3.75 3.74 3.73 3.72 3.72 3.71 3.70 3.70 3.70 3.69 3.69 3.6773.43 3.41 3.40 3.39 3.38 3.36 3.34 3.33 3.32 3.30 3.29 3.29 3.28 3.27 3.27 3.26 3.26 3.25 3.25 3.2383.13 3.12 3.10 3.09 3.08 3.06 3.04 3.03 3.02 3.01 2.99 2.99 2.98 2.97 2.97 2.96 2.96 2.95 2.95 2.9392.92 2.90 2.89 2.87 2.86 2.84 2.83 2.81 2.80 2.79 2.78 2.77 2.76 2.76 2.75 2.74 2.74 2.73 2.73 2.71

10 2.75 2.74 2.72 2.71 2.70 2.68 2.66 2.65 2.64 2.62 2.61 2.60 2.59 2.59 2.58 2.57 2.57 2.57 2.56 2.5411 2.63 2.61 2.59 2.58 2.57 2.55 2.53 2.52 2.51 2.49 2.48 2.47 2.46 2.46 2.45 2.44 2.44 2.43 2.43 2.4112 2.52 2.51 2.49 2.48 2.47 2.44 2.43 2.41 2.40 2.38 2.37 2.36 2.36 2.35 2.34 2.33 2.33 2.33 2.32 2.3013 2.44 2.42 2.41 2.39 2.38 2.36 2.34 2.33 2.31 2.30 2.28 2.27 2.27 2.26 2.25 2.25 2.24 2.24 2.23 2.2114 2.37 2.35 2.33 2.32 2.31 2.28 2.27 2.25 2.24 2.22 2.21 2.20 2.19 2.19 2.18 2.17 2.17 2.16 2.16 2.1315 2.31 2.29 2.27 2.26 2.25 2.22 2.20 2.19 2.18 2.16 2.15 2.14 2.13 2.12 2.11 2.11 2.10 2.1016 2.25 2.24 2.22 2.21 2.19 2.17 2.15 2.14 2.12 2.11 2.09 2.08 2.07 2.07 2.06 2.05 2.05 217 2.21 2.19 2.17 2.16 2.15 2.12 2.10 2.09 2.08 2.06 2.05 2.03 2.03 2.02 2.01 2.00 2.00 1.918 2.17 2.15 2.13 2.12 2.11 2.08 2.06 2.05 2.04 2.02 2.00 1.99 1.98 1.98 1.97 1.96 1.96 1.9519 2.13 2.11 2.10 2.08 2.07 2.05 2.03 2.01 2.00 1.98 1.97 1.96 1.95 1.94 1.93 1.92 1.20 2.10 2.08 2.07 2.05 2.04 2.01 1.99 1.98 1.97 1.95 1.93 1.92 1.91 1.91 1.90 1.8922 2.05 2.03 2.01 2.00 1.98 1.96 1.94 1.92 1.91 1.89 1.88 1.86 1.86 1.85 1.84 1.8324 2.00 1.98 1.97 1.95 1.94 1.91 1.89 1.88 1.86 1.84 1.83 1.82 1.81 1.80 1.79 1.726 1.97 1.95 1.93 1.91 1.90 1.87 1.85 1.84 1.82 1.80 1.79 1.78 1.77 1.76 1.75 1.7428 1.93 1.91 1.90 1.88 1.87 1.84 1.82 1.80 1.79 1.77 1.75 1.74 1.73 1.73 130 1.91 1.89 1.87 1.85 1.84 1.81 1.79 1.77 1.76 1.74 1.72 1.71 1.7035 1.85 1.83 1.82 1.80 1.79 1.76 1.74 1.72 1.70 1.68 1.66 1.65 1.64 140 1.81 1.79 1.77 1.76 1.74 1.72 1.69 1.67 1.66 1.64 1.62 1.61 1.60 1.545 1.78 1.76 1.74 1.73 1.71 1.68 1.66 1.64 1.63 1.60 1.59 1.5750 1.76 1.74 1.72 1.70 1.69 1.66 1.63 1.61 1.60 1.58 1.56 1.54 160 1.72 1.70 1.68 1.66 1.65 1.62 1.59 1.57 1.56 1.53 1.5270 1.70 1.67 1.65 1.64 1.62 1.59 1.57 1.55 1.53 1.50 1.4980 1.68 1.65 1.63 1.62 1.60 1.57 1.54 1.52 1.51 1.490 1.66 1.64 1.62 1.60 1.59 1.55 1.53 1.51 1.49 1.46

100 1.65 1.63 1.61 1.59 1.57 1.54 1.52 1.49 1.48120 1.63 1.61 1.59 1.57 1.55 1.52 1.50 1.47 1.4140 1.62 1.60 1.57 1.56 1.54 1.51 1.48 1.46 1.44160 1.61 1.59 1.57 1.55 1.53 1.50 1.47 1180 1.60 1.58 1.56 1.54 1.52 1.49 1.46 1.4200 1.60 1.57 1.55 1.53 1.52 1.48 1.46

1.54 1.52 1.50 1.48 1.46 1.42 1.40

DENOMINATOR DEGREES OF FREEDOM

B-14 A P P E N D I X B

TABL E Values of the6(b)

-Distribution:

.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 8.61 8.59 8.58 8510.0 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.57 6.52 6.49 6.46 6.43 6.40 6.38 6.36 6.34 6.3368.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.41 5.37 5.33 5.30 5.27 5.24 5.22 5.20 5.18 5.1778.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.71 4.67 4.63 4.60 4.57 4.54 4.52 4.50 4.48 4.487.57 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

10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.66 3.62 3.58 3.55 3.52 3.50 3.47 3.45 311 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.47 3.43 3.39 3.36 3.33 3.30 3.28 3.2612 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.32 3.28 3.24 3.21 3.18 3.15 3.13 313 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.20 3.15 3.12 3.08 3.05 3.03 3.014 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 2.95 2.9215 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 3.01 2.96 2.92 2.89 2.86 2.84 216 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.93 2.89 2.85 2.82 2.79 2.7617 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.87 2.82 2.79 2.75 2.72 2.7018 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.81 2.77 2.73 2.70 2.67 2.19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.76 2.72 2.68 2.6520 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.72 2.68 2.64 2.60 222 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.65 2.60 2.56 2.524 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.59 2.54 226 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.54 2.49 2.28 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.4930 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.46 235 5.48 4.11 3.52 3.18 2.96 2.80 2.68 2.58 2.50 2.44 2.340 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.3945 5.38 4.01 3.42 3.09 2.86 2.70 2.58 2.49 2.450 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.3860 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 270 5.25 3.89 3.31 2.97 2.75 2.59 2.47 2.380 5.22 3.86 3.28 2.95 2.73 2.57 2.4590 5.20 3.84 3.26 2.93 2.71 2.55 2.4

100 5.18 3.83 3.25 2.92 2.70 2.5120 5.15 3.80 3.23 2.89 2.67 2.52140 5.13 3.79 3.21 2.88 2.66 2160 5.12 3.78 3.20 2.87 2.6180 5.11 3.77 3200 5.10 3.76 3.1

5.03 3.69 3.12 2.

f F( )

DENOMINATOR DEGREES OF FREEDOM

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 8.2656.30 6.28 6.26 6.24 6.23 6.20 6.18 6.16 6.14 6.12 6.11 6.10 6.09 6.08 6.07 6.06 6.06 6.05 6.05 6.0265.14 5.12 5.10 5.08 5.07 5.04 5.01 4.99 4.98 4.96 4.94 4.93 4.92 4.92 4.90 4.90 4.89 4.89 4.88 4.8574.44 4.41 4.39 4.38 4.36 4.33 4.31 4.29 4.28 4.25 4.24 4.23 4.22 4.21 4.20 4.19 4.18 4.18 4.18 4.1483.97 3.95 3.93 3.91 3.89 3.86 3.84 3.82 3.81 3.78 3.77 3.76 3.75 3.74 3.73 3.72 3.71 3.71 3.70 3.6793.64 3.61 3.59 3.58 3.56 3.53 3.51 3.49 3.47 3.45 3.43 3.42 3.41 3.40 3.39 3.38 3.38 3.37 3.37 3.33

10 3.39 3.37 3.34 3.33 3.31 3.28 3.26 3.24 3.22 3.20 3.18 3.17 3.16 3.15 3.14 3.13 3.13 3.12 3.12 3.0811 3.20 3.17 3.15 3.13 3.12 3.09 3.06 3.04 3.03 3.00 2.99 2.97 2.96 2.96 2.94 2.94 2.93 2.92 2.92 2.8812 3.04 3.02 3.00 2.98 2.96 2.93 2.91 2.89 2.87 2.85 2.83 2.82 2.81 2.80 2.79 2.78 2.77 2.77 2.76 2.713 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 2.4416 2.65 2.63 2.60 2.58 2.57 2.53 2.51 2.49 2.47 2.45 2.43 2.42 2.40 2.40 2.38 2.37 2.37 2.36 2.36 217 2.59 2.56 2.54 2.52 2.50 2.47 2.44 2.42 2.41 2.38 2.36 2.35 2.34 2.33 2.32 2.31 2.30 2.218 2.53 2.50 2.48 2.46 2.44 2.41 2.38 2.36 2.35 2.32 2.30 2.29 2.28 2.27 2.26 2.25 2.24 2.2319 2.48 2.45 2.43 2.41 2.39 2.36 2.33 2.31 2.30 2.27 2.25 2.24 2.23 2.22 2.20 2.19 2.19 220 2.43 2.41 2.39 2.37 2.35 2.31 2.29 2.27 2.25 2.22 2.20 2.19 2.18 2.17 2.16 2.1522 2.36 2.33 2.31 2.29 2.27 2.24 2.21 2.19 2.17 2.14 2.13 2.11 2.10 2.09 2.08 224 2.30 2.27 2.25 2.23 2.21 2.17 2.15 2.12 2.11 2.08 2.06 2.05 2.03 2.02 2.0126 2.24 2.22 2.19 2.17 2.16 2.12 2.09 2.07 2.05 2.03 2.01 1.99 1.98 1.97 1.9528 2.20 2.17 2.15 2.13 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.94 1.93 1.92 130 2.16 2.14 2.11 2.09 2.07 2.04 2.01 1.99 1.97 1.94 1.92 1.90 1.8935 2.09 2.06 2.04 2.02 2.00 1.96 1.93 1.91 1.89 1.86 1.84 1.82 1.81 140 2.03 2.01 1.98 1.96 1.94 1.90 1.88 1.85 1.83 1.80 1.78 1.76 1.745 1.99 1.96 1.94 1.92 1.90 1.86 1.83 1.81 1.79 1.76 1.74 1.72 1.7050 1.96 1.93 1.91 1.89 1.87 1.83 1.80 1.77 1.75 1.72 1.70 1.68 160 1.91 1.88 1.86 1.83 1.82 1.78 1.74 1.72 1.70 1.67 1.6470 1.88 1.85 1.82 1.80 1.78 1.74 1.71 1.68 1.66 1.63 180 1.85 1.82 1.79 1.77 1.75 1.71 1.68 1.65 1.63 1.690 1.83 1.80 1.77 1.75 1.73 1.69 1.66 1.63 1.61

100 1.81 1.78 1.76 1.74 1.71 1.67 1.64 1.61 1120 1.79 1.76 1.73 1.71 1.69 1.65 1.61 1.59140 1.77 1.74 1.72 1.69 1.67 1.63 1.60 1.57 1.55160 1.76 1.73 1.70 1.68 1.66 1.62 1.58 1.55180 1.75 1.72 1.69 1.67 1.65 1.61 1.57 1.5200 1.74 1.71 1.68 1.66 1.64 1.60

1.67 1.64 1.61 1.59 1.57 1.52 1.49

DENOMINATOR DEGREES OF FREEDOM

B-16 A P P E N D I X B

TABL E Values of the 6(c)

-Distribution:

.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 6298.5 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 9.64 9.61 9.58 9.55613.7 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 6.2811.3 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.73 5.67 5.61 5.56 5.52 5.48 5.44 5.41 5.38910.6 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

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 4.1812 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 3.13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 4.02 3.96 3.91 3.86 3.82 3.78 3.75 3.72 3.69 3.14 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 3.6215 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 3.516 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.62 3.55 3.50 3.45 3.4117 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 3.219 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 3.1920 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 3.18 3.22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.18 3.12 3.0724 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.09 3.03 226 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.928 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 230 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.35 7.42 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.8840 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 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 2.95 2.82 270 7.01 4.92 4.07 3.60 3.29 3.0780 6.96 4.88 4.04 3.56 3.26 3.04 2.87 290 6.93 4.85 4.01 3.53 3.23 3.01 2.8

100 6.90 4.82 3.98 3.51 3.21 2.99 2.8120 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 3200 6.76 4.71 3.8

6.64 4.61 3.78 3.3

f(F)

DENOMINATOR DEGREES OF FREEDOM

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 5.6585.32 5.28 5.25 5.22 5.20 5.15 5.12 5.09 5.07 5.03 5.01 4.99 4.97 4.96 4.95 4.93 4.92 4.92 4.91 4.8694.77 4.73 4.70 4.67 4.65 4.60 4.57 4.54 4.52 4.48 4.46 4.44 4.43 4.41 4.40 4.39 4.38 4.37 4.36 4.31

10 4.36 4.33 4.30 4.27 4.25 4.20 4.17 4.14 4.12 4.08 4.06 4.04 4.03 4.01 4.00 3.98 3.97 3.97 3.96 3.9111 4.06 4.02 3.99 3.96 3.94 3.89 3.86 3.83 3.81 3.78 3.75 3.73 3.72 3.71 3.69 3.68 3.67 3.66 3.66 3.6012 3.82 3.78 3.75 3.72 3.70 3.65 3.62 3.59 3.57 3.54 3.51 3.49 3.48 3.47 3.45 3.44 3.43 3.42 3.41 3.313 3.62 3.59 3.56 3.53 3.51 3.46 3.43 3.40 3.38 3.34 3.32 3.30 3.28 3.27 3.25 3.24 3.23 3.23 3.22 3.1714 3.46 3.43 3.40 3.37 3.35 3.30 3.27 3.24 3.22 3.18 3.16 3.14 3.12 3.11 3.09 3.08 3.07 3.06 3.015 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 2.94 2.93 2.9216 3.22 3.18 3.15 3.12 3.10 3.05 3.02 2.99 2.97 2.93 2.91 2.89 2.87 2.86 2.84 2.83 2.82 2.8117 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 2.718 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 2.65 219 2.96 2.92 2.89 2.87 2.84 2.80 2.76 2.73 2.71 2.67 2.65 2.63 2.61 2.60 2.58 2.57 2.5620 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 2.5022 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 2.40 224 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 2.326 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 2.2528 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 2.1930 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 2.1335 2.40 2.36 2.33 2.30 2.28 2.23 2.19 2.16 2.14 2.10 2.07 2.05 2.03 240 2.33 2.29 2.26 2.23 2.20 2.15 2.11 2.08 2.06 2.02 1.99 1.97 1.945 2.27 2.23 2.20 2.17 2.14 2.09 2.05 2.02 2.00 1.96 1.93 1.9150 2.22 2.18 2.15 2.12 2.10 2.05 2.01 1.97 1.95 1.91 1.88 160 2.15 2.12 2.08 2.05 2.03 1.98 1.94 1.90 1.88 1.84 1.8170 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 1.79 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 1.73 1.140 1.97 1.93 1.89 1.86 1.84 1.78 1.74 1.70160 1.95 1.91 1.88 1.85 1.82 1.76 1.72 1180 1.94 1.90 1.86 1.83 1.81 1.75 1.7200 1.93 1.89 1.85 1.82 1.79 1.74

1.83 1.79 1.76 1.73 1.70 1.64

DENOMINATOR DEGREES OF FREEDOM

B-18 A P P E N D I X B

TABL E Values of the 6(d)

-Distribution:

.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 2472199 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 9.716.2 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 7.7814.7 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 6913.6 10.1 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.42 6.31 6.23 6.15 6.09 6.03 5.98 5.94 5.90 5

10 12.8 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.85 5.75 5.66 5.59 5.53 5.47 5.42 5.38 5.34 511 12.2 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54 5.42 5.32 5.24 5.16 5.10 5.05 5.00 4.9612 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 4.77 413 11.4 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.82 4.72 4.64 4.57 4.51 4.46 4.414 11.1 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.60 4.51 4.43 4.36 4.30 4.2515 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 4.016 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 3.92 3.817 10.4 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.14 4.05 3.97 318 10.2 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.03 3.94 3.86 3.79 3.73 3.19 10.1 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.93 3.84 3.76 3.7020 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 3.22 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.7024 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.50 3.42 3.35 326 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 3.52 330 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.34 3.25 3.1835 8.98 6.19 5.09 4.48 4.09 3.81 3.61 3.45 3.32 3.21 3.12 3.040 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.45 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 3.09 2.9960 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.0170 8.40 5.72 4.66 4.08 3.70 3.43 3.2380 8.33 5.67 4.61 4.03 3.65 3.39 3.19 3.0390 8.28 5.62 4.57 3.99 3.62 3.35 3.15 3.0

100 8.24 5.59 4.54 3.96 3.59 3.33120 8.18 5.54 4.50 3.92 3.55140 8.14 5.50 4.47 3.89 3.52160 8.10 5.48 4.44180 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)

DENOMINATOR DEGREES OF FREEDOM

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 4.71 411 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 3.72 314 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 3.216 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 3.1917 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 2.96 2.9519 3.35 3.31 3.27 3.24 3.21 3.15 3.11 3.07 3.04 3.00 2.97 2.95 2.93 2.91 2.89 2.820 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 2.8122 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 2.66 224 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 2.526 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 2.4728 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 2.3730 2.77 2.73 2.69 2.66 2.63 2.57 2.52 2.49 2.46 2.42 2.38 2.36 2.34 2.32 2.335 2.64 2.60 2.56 2.53 2.50 2.44 2.39 2.36 2.33 2.28 2.25 2.22 2.20 2.19 240 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 1.60 2.33 2.29 2.25 2.22 2.19 2.13 2.08 2.04 2.01 1.96 1.9370 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 1.85 1.890 2.20 2.15 2.12 2.08 2.05 1.99 1.94 1.90 1.87 1.82 1.78

100 2.17 2.13 2.09 2.05 2.02 1.96 1.91 1.87 1120 2.13 2.09 2.05 2.01 1.98 1.92 1.87 1.8140 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 1180 2.07 2.02 1.98 1.95 1.92 1.85200 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

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A p p e n d i x B TABLE S TABLE 1Binomial Probabilities
Tabulated values are P(X…k)=a
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 APPENDI X B TABLE 1 (Continued) n 8 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0 0.9227 0.6634 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9973 0.9428 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 2 0.9999 0.9942 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113
0.0042 0.0012 0.0000 0.0000 0.0000 3
1.0000 0.9996 0.9950 0.9437 0.8862 0.8059 0.5941 0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 0.0000 0.0000 4
1.0000 1.0000 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 0.0004 0.0000 5
1.0000 1.0000 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 0.0058 0.0001 6
1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9915
0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 0.0572 0.0027 7
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 0.8999 0.8322 0.5695 0.3366 0.0773 n 9 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0 0.9135 0.6302 0.3874 0.1342 0.0751 0.0404 0.0101
0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1
0.9966 0.9288 0.7748 0.4362 0.3003 0.1960 0.0705 0.0195 0.0038 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 2 0.9999 0.9916 0.9470 0.7382 0.6007 0.4628 0.2318 0.0898
0.0250 0.0043 0.0013 0.0003 0.0000 0.0000 0.0000 3 1.0000 0.9994 0.9917 0.9144
0.8343 0.7297 0.4826 0.2539 0.0994 0.0253 0.0100 0.0031 0.0001 0.0000 0.0000 4 1.0000 1.0000 0.9991 0.9804 0.9511
0.9012 0.7334 0.5000 0.2666 0.0988 0.0489 0.0196 0.0009 0.0000 0.0000 5
1.0000 1.0000 0.9999 0.9969 0.9900 0.9747 0.9006 0.7461 0.5174 0.2703
0.1657 0.0856 0.0083 0.0006 0.0000 6
1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9750 0.9102
0.7682 0.5372 0.3993 0.2618 0.0530 0.0084 0.0001 7
1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9962 0.9805 0.9295 0.8040 0.6997 0.5638 0.2252 0.0712 0.0034 8
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9899 0.9596 0.9249 0.8658 0.6126 0.3698 0.0865
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or 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 TABLE 1 (Continued) n 10 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0 0.9044 0.5987 0.3487 0.1074 0.0563 0.0282 0.0060 0.0010 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9957 0.9139 0.7361
0.3758 0.2440 0.1493 0.0464 0.0107
0.0017 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 2
0.9999 0.9885 0.9298 0.6778 0.5256 0.3828 0.1673 0.0547 0.0123 0.0016 0.0004 0.0001 0.0000 0.0000 0.0000 3 1.0000 0.9990 0.9872 0.8791 0.7759 0.6496 0.3823 0.1719 0.0548 0.0106
0.0035 0.0009 0.0000 0.0000 0.0000 4
1.0000 0.9999 0.9984 0.9672 0.9219 0.8497 0.6331 0.3770 0.1662 0.0473 0.0197 0.0064 0.0001 0.0000 0.0000 5
1.0000 1.0000 0.9999 0.9936 0.9803 0.9527 0.8338 0.6230 0.3669 0.1503 0.0781 0.0328 0.0016 0.0001 0.0000 6 1.0000 1.0000 1.0000 0.9991 0.9965 0.9894 0.9452 0.8281 0.6177 0.3504 0.2241 0.1209 0.0128 0.0010 0.0000 7
1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9877 0.9453 0.8327 0.6172 0.4744 0.3222 0.0702 0.0115 0.0001 8
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9893 0.9536 0.8507 0.7560 0.6242 0.2639 0.0861 0.0043 9
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9990 0.9940 0.9718 0.9437 0.8926 0.6513 0.4013 0.0956 n 15 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0
0.8601 0.4633 0.2059 0.0352 0.0134 0.0047 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9904 0.8290 0.5490 0.1671
0.0802 0.0353 0.0052 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.9996 0.9638 0.8159 0.3980 0.2361 0.1268 0.0271 0.0037 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3
1.0000 0.9945 0.9444 0.6482 0.4613 0.2969 0.0905 0.0176
0.0019 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 4
1.0000 0.9994 0.9873 0.8358 0.6865 0.5155 0.2173 0.0592 0.0093 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 5
1.0000 0.9999 0.9978 0.9389 0.8516 0.7216 0.4032 0.1509 0.0338 0.0037 0.0008 0.0001 0.0000 0.0000 0.0000 6
1.0000 1.0000 0.9997 0.9819 0.9434 0.8689 0.6098 0.3036 0.0950 0.0152
0.0042 0.0008 0.0000 0.0000 0.0000 7
1.0000 1.0000 1.0000 0.9958 0.9827 0.9500 0.7869 0.5000 0.2131 0.0500 0.0173 0.0042 0.0000 0.0000 0.0000 8
1.0000 1.0000 1.0000 0.9992 0.9958 0.9848 0.9050 0.6964 0.3902 0.1311 0.0566 0.0181 0.0003 0.0000 0.0000 9
1.0000 1.0000 1.0000 0.9999 0.9992 0.9963 0.9662 0.8491 0.5968 0.2784 0.1484 0.0611 0.0022 0.0001 0.0000 10
1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9907 0.9408 0.7827 0.4845 0.3135 0.1642 0.0127 0.0006 0.0000 11
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9981 0.9824 0.9095 0.7031 0.5387 0.3518 0.0556 0.0055 0.0000 12
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9963 0.9729 0.8732 0.7639 0.6020 0.1841 0.0362 0.0004 13
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9948 0.9647 0.9198 0.8329 0.4510 0.1710 0.0096 14
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9953 0.9866 0.9648 0.7941 0.5367 0.1399
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or 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 APPENDI X B TABLE 1 (Continued) n 20 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0 0.8179 0.3585 0.1216 0.0115
0.0032 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9831 0.7358 0.3917 0.0692 0.0243 0.0076
0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.9990 0.9245 0.6769 0.2061
0.0913 0.0355 0.0036 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 1.0000 0.9841 0.8670 0.4114 0.2252 0.1071 0.0160
0.0013 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4 1.0000 0.9974 0.9568 0.6296 0.4148 0.2375 0.0510
0.0059 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5 1.0000 0.9997 0.9887 0.8042 0.6172 0.4164 0.1256 0.0207
0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6 1.0000 1.0000 0.9976 0.9133
0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 7 1.0000 1.0000 0.9996 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013
0.0002 0.0000 0.0000 0.0000 0.0000 8 1.0000 1.0000 0.9999 0.9900
0.9591 0.8867 0.5956 0.2517 0.0565 0.0051
0.0009 0.0001 0.0000 0.0000 0.0000 9 1.0000 1.0000 1.0000 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171
0.0039 0.0006 0.0000 0.0000 0.0000 10
1.0000 1.0000 1.0000 0.9994 0.9961 0.9829 0.8725 0.5881 0.2447 0.0480 0.0139 0.0026 0.0000 0.0000 0.0000 11
1.0000 1.0000 1.0000 0.9999 0.9991 0.9949 0.9435 0.7483 0.4044 0.1133 0.0409 0.0100 0.0001 0.0000 0.0000 12 1.0000 1.0000 1.0000 1.0000
0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.1018 0.0321 0.0004 0.0000 0.0000 13 1.0000 1.0000 1.0000 1.0000
1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.2142 0.0867 0.0024 0.0000 0.0000 14 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 0.9984 0.9793 0.8744 0.5836 0.3828 0.1958 0.0113 0.0003 0.0000 15 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 0.9997 0.9941 0.9490 0.7625 0.5852 0.3704 0.0432 0.0026 0.0000 16 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 0.9987 0.9840 0.8929 0.7748 0.5886 0.1330 0.0159 0.0000 17 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 0.9998 0.9964 0.9645 0.9087 0.7939 0.3231 0.0755 0.0010 18 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 0.9995 0.9924 0.9757 0.9308 0.6083 0.2642 0.0169 19 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9968 0.9885 0.8784 0.6415 0.1821
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or 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 TABLE 1 (Continued) n 25 p k 0.01 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 0.99 0 0.7778 0.2774 0.0718 0.0038 0.0008 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.9742 0.6424 0.2712 0.0274 0.0070 0.0016
0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.9980 0.8729 0.5371
0.0982 0.0321 0.0090 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 0.9999 0.9659 0.7636 0.2340
0.0962 0.0332 0.0024 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4 1.0000 0.9928 0.9020 0.4207
0.2137 0.0905 0.0095 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5 1.0000 0.9988 0.9666 0.6167
0.3783 0.1935 0.0294 0.0020 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6 1.0000 0.9998 0.9905 0.7800 0.5611 0.3407 0.0736 0.0073 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7 1.0000 1.0000 0.9977 0.8909 0.7265 0.5118 0.1536 0.0216 0.0012 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 8 1.0000 1.0000 0.9995 0.9532
0.8506 0.6769 0.2735 0.0539 0.0043 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 9 1.0000 1.0000 0.9999 0.9827 0.9287 0.8106 0.4246 0.1148
0.0132 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 10
1.0000 1.0000 1.0000 0.9944 0.9703 0.9022 0.5858 0.2122 0.0344 0.0018
0.0002 0.0000 0.0000 0.0000 0.0000 11
1.0000 1.0000 1.0000 0.9985 0.9893 0.9558 0.7323 0.3450 0.0778 0.0060 0.0009 0.0001 0.0000 0.0000 0.0000 12 1.0000 1.0000 1.0000 0.9996
0.9966 0.9825 0.8462 0.5000 0.1538 0.0175 0.0034 0.0004 0.0000 0.0000 0.0000 13 1.0000 1.0000 1.0000 0.9999
0.9991 0.9940 0.9222 0.6550 0.2677 0.0442 0.0107 0.0015 0.0000 0.0000 0.0000 14 1.0000 1.0000 1.0000 1.0000
0.9998 0.9982 0.9656 0.7878 0.4142 0.0978 0.0297 0.0056 0.0000 0.0000 0.0000 15 1.0000 1.0000 1.0000 1.0000
1.0000 0.9995 0.9868 0.8852 0.5754 0.1894 0.0713 0.0173 0.0001 0.0000 0.0000 16 1.0000 1.0000 1.0000 1.0000
1.0000 0.9999 0.9957 0.9461 0.7265 0.3231 0.1494 0.0468 0.0005 0.0000 0.0000 17 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 0.9988 0.9784 0.8464 0.4882 0.2735 0.1091 0.0023 0.0000 0.0000 18 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 0.9997 0.9927 0.9264 0.6593 0.4389 0.2200 0.0095 0.0002 0.0000 19 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 0.9999 0.9980 0.9706 0.8065 0.6217 0.3833 0.0334 0.0012 0.0000 20 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 0.9995 0.9905 0.9095 0.7863 0.5793 0.0980 0.0072 0.0000 21
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9976 0.9668 0.9038 0.7660 0.2364 0.0341 0.0001 22 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 0.9996 0.9910 0.9679 0.9018 0.4629 0.1271 0.0020 23 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 0.9999 0.9984 0.9930 0.9726 0.7288 0.3576 0.0258 24 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9962 0.9282 0.7226 0.2222
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or 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 APPENDI X B TABLE 2 Poisson Probabilities
Tabulated values are P(X…k)=a k
x=0p(xi) . (Values are rounded to four decimal places.) µ k 0.10 0.20 0.30 0.40 0.50 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067 0.0041 0.0025
1 0.9953 0.9825 0.9631 0.9384 0.9098 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404 0.0266 0.0174
2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247 0.0884 0.0620
3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650 0.2017 0.1512 4
1.0000 1.0000 0.9999 0.9998 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405 0.3575 0.2851 5 1.0000 1.0000 0.9994 0.9955 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160 0.5289 0.4457 6 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622 0.6860 0.6063 7 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.8666 0.8095 0.7440 8 1.0000 0.9998 0.9989
0.9962 0.9901 0.9786 0.9597 0.9319 0.8944 0.8472 9 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.9682 0.9462 0.9161 10 0.9999 0.9997 0.9990 0.9972 0.9933 0.9863 0.9747 0.9574 11 1.0000 0.9999 0.9997 0.9991 0.9976 0.9945 0.9890 0.9799 12 1.0000 0.9999 0.9997 0.9992 0.9980 0.9955 0.9912 13 1.0000 0.9999 0.9997 0.9993 0.9983 0.9964 14 1.0000 0.9999 0.9998 0.9994 0.9986 15 1.0000 0.9999 0.9998 0.9995 16 1.0000 0.9999 0.9998 17 1.0000 0.9999 18 1.0000 19 20
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or 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 TABLE 2 (Continued) µ k 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10 11 12 13 14 15
0 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0.0008 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000
2 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0.0042 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000
3 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.0149 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002
4 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0.0403 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009
5 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.0885 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028
6 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.1649 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076
7 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180
8 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374
9 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699
10 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185
11 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848
12 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676
13 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632
14 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657
15 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.9665 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681
16 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641
17 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489
18 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195
19 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752 20
1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170 21
1.0000 0.9999 0.9998 0.9996 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469 22 1.0000 0.9999 0.9999 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673 23
1.0000 0.9999 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 24
1.0000 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 25
0.9999 0.9997 0.9990 0.9974 0.9938 26
1.0000 0.9999 0.9995 0.9987 0.9967 27 0.9999 0.9998 0.9994 0.9983 28 1.0000 0.9999 0.9997 0.9991 29 1.0000 0.9999 0.9996 30 0.9999 0.9998 31 1.0000 0.9999 32 1.0000
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 APPENDI X B
TABLE 3 Cumulative Standardized Normal Probabilities z 0 P(-q6Z6z) Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.0
0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9
0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8
0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7
0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6
0.0047 0.0045 0.0044 0.0043 0.0041
0.0040 0.0039 0.0038 0.0037 0.0036 -2.5
0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.2
0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1
0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207
0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0.0281
0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351
0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418
0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516
0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.5
0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808
0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901
0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515
0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061
0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7
0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4
0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.3 0.3821 0.3783 0.3745 0.3707
0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1
0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.0
0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
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 TABLE 3 (Continued) 0z P(-q6Z6z) . Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517
0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331
0.6368 0.6406 0.6443 0.6480 0.6517 0.4
0.6554 0.6591 0.6628 0.6664 0.6700
0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6
0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704
0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910
0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907
0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3
0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251
0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6
0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7
0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671
0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719
0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821
0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918
0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941
0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6
0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7
0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981
0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
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 APPENDI X B TABLE 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
TABLE 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 APPENDI 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 2 189. 3 9 5 10 2 1. 4 1 9 17.60 7 5 21 1 6. 29 6 5. 152.2 9. 57 3 156 95.0 9. 7 .59 9 5 8 2 2941 9 5. 3. 54 9 4 28 6.. 447 25 2 5 1.4 1 3 97.. 952 7 1.49 16 64.. 164 2 .23 9 4. 3 3 39 5 4. 2 9 1.0 6 9 0 34.7. 3 3 1.2 8 1 5 6 .60 2 9..5 4 3 4 4 23 3. 6 1 8. 6493 8 2 9 96.. 94 4 .41 5 49 2 482 7 . 6482 186 3.34 9.9.8 4 3 4. 38 094 2 7. 4 2 1.3 6 4 9 86.9. 83 4 .52 4701 9 3. 3 2 8. 45 5 7 4 1867 3.835 9..10 7 4322 4804 1 3.94 1. 03 5 5 9 75. 03 .9.4 6 2 4 98 3. 2 4 80. 643 6 1639 75. 4. 73 2 .69 0 46314 480. 6 . 375 .3. 932 4.86 4 9.0 31 71 80. 143 9 756 03.5 . 3 4 38 6 3.. 57 3. 1 1 89. 983 3 012 9 75..1 3 4 8 53. 07 5 1 4.2 2 9 5 68 4 .4 338 4 89.. 6 422 176 63. 4 9 5 3 .02 35 8 4 .4 9 3 0 1. 443 5 9 65..90 354 .38 849 1. 1. 32 2 9 65 43..834 8 9.309.31 2 4.3 2 9 5 .23.. 4 4 88 9 3. 0 .4 1 6 1.3 2 7 5 .0 .7 34 89 8 3. .46 0.03 127 5. 96 3.. 498 7 3.9.6 83 1263 .7. . 4 8 6 3 9 .7 73 1 .24 6. 4 3 9 .1 6 5 2. N1 10 4. 1 9 1 6 4. 1 4 8 2 .1 41.0 3 3 . 7 3 9 5 41. . 4 7 83 6 13 .74 1.. 855 9 36.93 8 0 41.6 3 .4 13 5.1 3 .9 37 . 3.4 34 63 4.9 1 8 .2 13 6.83 4 8 3 6 3.54 1 ..4 3693 1.4 3 83 2.1 4 .93 503 2 1.93 . 132.842 03.. 4 35 2 3 0.5 . 163 25 4 3 0 13.. 03 54 . 0.231 9021.0 4. 2 4 3 32.. 64 . 93 2 3 0 29.. 62 14 . 62.3 4 0 1 38. 94 32 72 0 2 9.. 314 . 023 4 9 028. 0 . 9032 5 2 5 80.4 3 . 85 23 2 9 32 7..9 80 73 143 .1270. 962 7810 7.4 29 4 3 2 . 2477 7.. 82 35 . 127308 2. 7. 02945 5 2 64.. 20 8 71 2 6 2.. 73 0 . 6 274 9 2 26.57 26 120 . 173 0 9 82 0 253 6.7..52 13 4 8 22 6 9 26.. 72 0 . 8 26 03 2 245.06 235 9 28 . 54 2109 72 5 246. 9 . 6.52 8 3 4 97 2 5 4 25.9. 42 83 . 1 2 65 920 2 29.56 2 40341 9 . 91 276 3 9 76 0 2. 48 2.24 21 1 63 2 5 9 24 6. 3 9 ..6 2 54 728 5 2 5 42 1..4 36 1 . 5213 8 27. 4.6 4223 5 27 9 6 24 09.4 1 2 702 5.. 1 43 950 2 .25 12 4.36 2 . 7 125 8 4 23..5 4823 6 2546 2 34702 82. 4 . 7 3153 2 2 .95 2 37.30 34. 72 84 8 2 21. 3.5. 423 03 5 4 23092 68 0.4 323 5 . 92 71 2 .62 37 4 .35. 7 25 9 8 0 2.9.5. 312 294 3 6 2 47 36 .5 12 7. 52 2 2 42 315.. 8 23 8 2. 241.5 38.21 013 1 122 6 2 45 36. 31 85 2 1.2 .24 317.8 1 . 62 1 8 9 2. 21.5 32 61 30 0 122 6 2 43 07.9.5 102.2 .042 16 . 10. 62537 2 4 23 215 8 10013 2.9 01 4 3.3 9 01 .0 2 36. 9 3 01 .82 0 13. . 27 739.300 0.8 0 2 63.93. 34 20.38 . 6 2 5. 8.60 942 6 72.53. 33 826.20 . 1 2 6. 0.46 402 4 2.5. 21 5426 . 9 2 3. 6.4 512 2 .92 24. DENOMINATOR DEGREES OF FREEDOM N2 TAB f(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 93 5.3 458 7 3.3 8 .8 3 16 64..4392 5. 1 9 . 3 2 7 2 3412 58.54 8 3 9 5 16.3 2 1 92 5.3 2 5 8 7 0. .8 3 9 16 54..2 30 90 54 12.0 3 0 2 58 7. 03 5 .3 4 8 . 39 1 15.9 54 0 . 39 2 2 .7 8 39 5 58.24 7 3 8 1 5. 37 54 9.0 2 932.6 3 8 5 8 7. 83 2 .715 14..7 360 2 98 436 5 .5 36 2 5 8.4 7 3 8 . 34 2 1554 6.0 5 97.32.4 3 4 2 58 7.4 .04 7 3 8 2 15. 30 5 97 5. 432 3 . 358 6 3. 2 .94 7 . 31 5 154 4.0 3 96.32.6 2 2 2 58.84 7 3 8 5 1.3 003 9 6 5. 41 2.1 3 2 5 8 6.07 5 .74. 393 15 2.95 5. 42 2 .6 1 39 5 58 2.74 7 3 15 385 .2 9 2 95. 42 9 .1 3 5 8 6.927 4 .6715 37. 9 2 95 5. 9 5 .684 5 8 2.6 7 .36 2 1554. 9 5 94.2 8 . 0 3 4 58 672 .54 7 2 15 .036. 9 5 94 32 7 4 . 958 72.4 7 15 .35. 9 94 5. 32 7 .958 67 62. 54 7 5. 039 4 3 5.. 3 6 9 2 6.54 62. 7 5 .34. 9 . 3 6 9. 2 6.54 70 52. 7 .3 3. 9 7 2 5 52 . . 7 5 39. 36 .2 5 3 6.9 2. 7 9 1 3 3.69 3.67 N1 10 21.7 1 5 2. 1 2 6 2 .7 321.4 2 3 . 5 2 6 2 1.. 4 7 124.2 5 4 2 1. 2 12 3.1. 7 2 7 4.6 1 2 3 .152 3 12.792 .4 5 2.212 .1 58. 4922 5 93.12 .3 2.97 82.. 34 21 0 29. 7. 415 82 3 72.9 1 0 72 .2. 32 . 32 1 4 8 2.1.1 5 222 73 62.1 0 24.6 1 20.21 2 8 2 1.0 5 .1 30 6 2 5 52.6 8 20 1.6 52 108. 321 96 2 9.0 33. 41 29 71 2 5 421 7.8 19 0 .8 206 32. 03 1 . 3195 241 1.9 5 . 45 1 5 32 2..0 2 91 4 2 19. 70 3 7 21..2 8201 2 .3 70 1 94.8 5 . 41 35 2 1 02.0 5985. 51 6 12 5 2..20 72.91 8 4 . 351 971 20 8. 3 .1 81 6 2 0 92. 499 7 17 0 . 4 19 6 2 4 21..0 01 8.76 2 .1 42 917. 0 .3 20 681 7 2 48 8 2.9 0 15 787 2 .52 710 6 923 21 9..201 81 74 1 2.0 26179. 01 .3 2519 84 70 2 47 62 01. 01 8 1 767 0 . 8319 68 6 82 1 2..124 8 72 6 0 2.81 9 17. 71 .3 2091 8 716 2 46 520.9 1 77 6 .. 19 45 5 72 0 21..2 01 8 9 2.71 4 98 76 1 6..3 22081 514 2 461 4.5 28 8 16 . 0.1476 3 5 62 9 21..9 01 869 2.71 2696 1 .3 242078162 451 3.3 2 06 8 96 . 0.12765 62 9 21..82 014 68 2.61 0 1697 1 .3 2825 186 0 2 41 2. 098 79 6 6 . 0 381765 52 8 216.72 91 86 7 2.51 9 1 .3 26108 06 9 2 431 9.7 66 .. 71 89755 42 79.81 7 10 6 397 52. 8 191 64.02 186520 1 9.7 467. 2. 61 8755 2.7 1 . 961 7 7 219.1 5 .3 21 88 8 76 195 5 2 432 9.7. 14 6 .47. 5861 5 2 10. . 2 967 816 24. 15 .3 271 432 .09 17.7 16 5 3. 102 5 2 6 2..6 .418615 2.4 1 99 5 167. 5 3 .3 200 2611 8 6 1 2 410 9.7 65 15 . 231865 32 6.594 1 3 16 5 4 2.3 19 77 4. 5 0 .3 20 65 19 4 .9 01 73. 61 1 02. 109 75 2 35. 21. 83 64 1 1 1952 . 37 49 5 18. 19 .7 4 11 55 712 4 6 100 1 1 . 2 6 0151 4 1 .0 . 6 6 3 1 6.31 6 0 .6 2 18.1 6 02 .06 1.0 1 0 1. 6 .0 1 6 1 5.1 1 .91 6. . 5.0 5 157 54 .8 1 5 91. 1 91. 1 5. . 5.7 5 156 1. 52 .6 1 5 71 5.1 71 .71 5. . 5. 5 154 1. 50 .4 1 5 51. 1 41. 51. . 5.3 4 1 1. 58 . 52 1 5 21 5.1.21 .31 5 .. 42 4 158 1. 46 .9 1 4 01 5.1.91 .01 4 . 4.8 4 146 1. 42 .6 1 4 71 4.1 81 .71 4. . 4.6 4 4 140 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 APPENDI 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. 18.2 9 4 1 .0 78 9 2 16 2 7. 3 5. 8659 79 1 . . 4 93 162 46 .1 8 3. 70 9 1.6 5 9. 075 5 3 10 6457. 73 4 1. 054 9 9 7 2 . 368 64 1 92 5 3 . 3 4. 7350 9 6 .5.6. 1509 4 16 52 40 99 .8 9 3. 65847 9 5 2. 952 3 .4 1 88 9 7.29 4 6. 62 7 35 .4.7 9. 85 1 54 9 44 75. 8 8 3. 60540 9 4 9. 13 . 75239 4 1 266.28 4 0 . 604 3 39 4 9..65 93 9 .1 08 94 2 8 44 7 5.0 5 3. 62 3 .96 4.9 9. 65018 4 1 2.07 4. 633 8.. 4 9 5 80..8 74 20 .3 3 8 6 4. 1239 9.4. 5 7 8 4 1 92. 6 9 03.3 4 6.6 4. 72 9 3 8.4 70 3 9 .8 51 0 4 14 4 6 3.1 9 3.8. 3139 9 3.6. 4 2 4 1 79 68 3 4 7.69 2 8.. 63. 4 5 4 1 73 .84 5 3.3 9 3. 6 01.. 9 2 8.4 5 63 3 .4 1 7. 31 02. 8 3 4 0. 6 71 9 2 .6 03 . 3 5 4 1 8 .2 07 3 4 7. 6 4 9 2 8..53. 3 5 4 1 66 .74 4 82. . 6 2 0 2 8.. 8 6 3 5.6 42. 8 6 0 4. 0 .. 536 3 5..3 31 24. 728 8 4. 0 . 3 6 5..1 04. 70 8 7 4. 0 . 2 5 4 9 84. 8 03. 0 5 6848 .4 3 N1 10 6. 1 9 1 4 6. 1 5 7 2 .4 26 1.6 5 3 . 5 2 5 61.65 4 4 4 .1 16.54 .0 3 . 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 . 0.9 4 4 1 03 1.5.54 6 82 4 238. 9 0 .9 30250 3. 7.8 452 73 8.6 4 . 83 05 2 8 96 0.13 5 74 8 6 37..3 9 1452 3 5.6 544 7 6 3 .3 83.6 625. 7.39 6 3 58. 638 4 5 03 7 03..4 1865 3 3 .354 9 626 0 . 6.0 378 6 31 5. 4.32553 6 83 4..1 857 4 5543 .13 52 70. 5.8 3647 9 32 4. 3.46858 .3 5 93 2..9 2 7 14 5 3 .1328 96 85. 5.9 3217 3 30. 3.2142 .3 4 13 2..0 1 2568 3 .42635 94 0 . 41 3.76 7 3. 9 34 5 . 2 3106 .33 1.2 0 0. 12.34 583 .7 3 159. 6309 . 430. 752 6 3 26 37..5 203 9 2 .33 53. 06 9 101 2 09.323 .2 31 0..8 2935 . 359.2 18 5 9 3 2..9 2 38 4 8 2 03. 2. 012 9 3 9240.83 8 30 9.4..2 79306. 92. 6805 3 1. 5 3 ..3 28 46 0 5 3 53. 2. 978204 . 262 84 73 3 4 308. 1..7 2 83 8. 528. 7 5 63 1.28 3 . 9 286 70 1 2 3 2 3.. 917 26 . 22 87 75 293 1 30. 89. 2 0649 5. 128. 79 6 5 30... 270 68 9 0 3 8.7 2. 752 6 . 1725 6 3 8 3 927.2..9 26303 28. 61 5 7 . 7 ..2 758 1 5 2.8 207 3 62 6 9 55 21. 3 5 3 962 3.2 7 8425 .. 82654 0 275.27 20 259 7 3 29.8 24 5.7 062 5453 2 942 1. 6 495 15 47 2 . 584.4 83 724 6 .26 7 5 5 3 26. 269 45. 17 72 5343 2 3 96 1.. 6 04256 29.3 0 2 0.52 94 8 3 10015 2.1 0 8 5 4.3 1 0 .8 5 6. 3 1 0 .8 35 8.0 31 02 .3 7 2 50.0 3 .93 1.. 215 2 3 7. 5. 5 .2 8 10 0 2. 13 3 ..839 23 .3. 2 .8 0. 7 7 6 6 2. 82 9 .7.67 28 3. 0 .2 6 71 2 .62 2 .3.552 631 2. DENOMINATOR DEGREES OF FREEDOM N2 TAB f(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 4561 54 86 .3. . 04 1 1 382. 9 0 9 1.3.305 1 45. 93 4 6.3 4. 049 1 0 8.. 2 73 0 9.4 350 5 13 83.96 63 4.8 4831 9 0. 13 0 .1 4 85.63 5 0 54 16. 8 7 3. 40 81 4.3 1 9. 6.65 3 05 1 3.3 5 0 4 96.. 0 8 3.1 489 0 8.. 14 3 .4 3 5 1 38 56 .9 13.33 4.8 9 4 1 9 0. 12 3 0 .3 24.9 5 1 5 169 3. 0 3 4.8 4 9 0 8.. 1 3 . 14 2 5 1 3.83 4 .93 4 9.6 471 0 8..8 3 0 9.3 4 2 1 5 16 .3 1 39. 73 4..1 4 7 1 9 0 8.02 7 3 0 .3 4.41 5 139 4.523 3.8 4731 9.2 6 0 .1 36 4.3 4 1 53 2.9 3 .49 8 02. 7 .95 3 1 9.4 2 0 5 1 31 6. 23 4 1 3. 9 2 .43 3 02 79 8 .2 4 3. 1 .4. 4 0 5 16.9 31 13 3.80749 .73 3.. 341 0.3 4 0 53 94. 0 1 3. 87. 035 9 2..3401 5 10 6.. 3 0 3 8. 9 . 0 4 19 8.7.6 93 5 2 1.6 4. 93 1 9.80 8 09 4. 1 .6 3 5 29 6 483.. 3 1 84 . 0 8 0. 711 .51 3. 6 2483.. 1 0 84 7 0 5 5.3 1 13 . 8 6 83.0 4 7 2 .1 03 4 .33 3.67 N1 10 3. 1 3 1 9 3. 1 3 2.3 031.7 3. 0 1 42 1 7 .39 4 3 .0 2. 1 3 .2 8 5 . 1 3 58 2.643 .0 9 2. 72 1 3 .02 7 3 . 19 63 328 2.5 1 3 .9 7 2. 72 5 8 3 .82 7 09 1 . 17 693 285 1 .9 5 2.2 5 3 203 62 7.4 .5 2682 8.0 5 8 3 4 2 6.0.82 533 0 7.42 .3 25. 2 92.. 8 4.6 2 6 3 6.8 24 . 962 51 3 3 0 32.. 2 40 . 25.382 628.. 7 43 2 4 3 0 2.. 624 . 94 5203 0 12 7.. 02 47 . 0.1 23 2 427.. 41 25 2 3 8 23.. 4 2 1 . 8296 4 3 0 92 6..25 3210 . 79 2.0 2 327..6 39 14 0 3 6 23.. 92 15 . 812 474 0 3 0 72 6..25 215 . 52.0 1 027 4..5 17 26 9 8 2 4 23.. 1 279 6 . 892 4510 3 9 52 64 31..24 1 2 . 463 017 1 927 3..5 914 0 7 2 2. 861 9 . 862 41 3 9 32 61..24 10 . 130 8 1 72 31..5 73 40 2 981 6 2 0 2.. 69 4 1 80 . 852 4 19 3 9 2 61 37.8.24 18 5 . 01 1 62 31..5 52 10 951 8 5 2 9 2. 591 21 83 . 82 7.6 3 9 12 53068.241 1 . 82 09 1 1 65 3. 32 9 2 018.4 2 8 2. 3 271 99 0 1 8 . 12.8 3 7 3 9 2 5 0481.2419 8 .2 7 51 1 4. 64 2 37 00 61 3 2 8 7 2. 3 041 7 . 92 516 27 3 9 02 51.241 9 8 7 . 62 5311 4 2. 64 0 22 43 81 7 3 7 6 2 1.82 3 91 95 .5 20 7 3 92 5. 1 8 .241 9 7 5 .2 5401 3 1. 64 0 22 35 9 1 87 87 2 2 580.8 3 . 73.8 72 0 918.4 2 0 3 9 52 2 1.180 7 .3 42 0114 8. 213 9 87 41 2 2 70.8 1 .6 391.4 7 .36 2 9573 9 21.2 2 18 17 1.2 010 . 624 7 21 967 16 8 2 7 4. 678 9 .5 32 01.9 72 5.1 9.1. 37 2 .40 2 1685 1 . 62.0 994 17 2 7 4 2.19. 548 6 1 7 . 2 37 018 72 5.13 9.1. 076 8 8 2 .3 2. 39 248. . 67. 2918 7 3 2 41.8 9246 .20 7162 5 42. 61 9 187 5. 0166 3 2. 32 23.9 81 0 0 2 4 6.1 91 76 . 3 4 2707 2 164 42 0.7 1 .02 1 596329 3. 01 6 . 289137 4 6.87642 3 251917 016 100 1 1 . 2 8 0114 1 .0 . 71 7 9 1. 6 81 7 0 .7 71 8 6 1 .02. 7 1 7 6 1. 0 1 .4 7 0 . 757 3 1 1.1 6 ..1 7 3 1. 76 1 .2 7 47 . 727 1 1.1 4 ..6 0 1. 71 6 19 64 .97 16 1 1.8...6 6 671 61 91 .16 7.1 1 .6 1 6. .51 . 66 89. 6 31 6 5 .5 117 161 .2 1 6. .51 . 66 67. 6 01 6 1 .114 151 .8 1 6. .51 . 55 42. 5 71 6 9 .7 111 1. 55 6. .41 505 9 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 APPENDI 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 9 4 8. 3 9 5 3 9 4.4 9 912 5 .3 1. 4 002 1 0 9.6 3 9 81. .8 3 1 5 2. 3.76 90 1.712 951 3. 5 9.2 6 3 8 .1 5 287 1 7 9.2 6 9 71.1 31 4 .13 2 60. 0 5 80 6. 9 8 921 9 5 9.. 9 3 2. 5 75 1 8. 5 .1.69 914 8.582 5. 94 8 709 27 5.29 1 85 .964 2 59.7 .19 5 9. 019 9 710 5. 0 8 .2 4 16 1 47 .54. 87 6 95 7 2 0 91..6 2 4 2 4.1 862 69 7 0. 70.466 9 317.30 .2 41 5. 5 47 .19 6. 8 6 9. 50 2 .3 0 6 9 5 .8 75 0 4 21.68 72. 6 . 0 3 9.19 1 6. 1 . 8 4 2 49.1 896 9 751.. 006 6 9 12.35 1 .2 48. 7 0 474 19 45. 4 6 9. 07 9 01 86. 9 . 15 4 2 47. 7 63 25. 3 . 85 6 99 1 7 6. 8 1 9.476 15 2 4 2.9 5 69 6 27.. 9 1 9 6. 7 . 6 35 4 2 4. 75 6 2 9 451. 7 6 9.8 2 8 1 9 8 1. . 9 75 4 2 4. 74 3 6 2 9 75. 1 . 1 6 8 6. 6 1 274 1 5 9 .1 7 9. 6 9 17 0 6.. 5 4 2 4. 73..6 50 9 6 19.. 5 6 8 17 6 5 1 9.42 6 7 4 2. 7.509 6 19.. 5 9 7 16 2 6. 55. 2 4 2 4. 87 3 6 09 . 04 15.1 6 .4 1 76 88 8 4 1 9 5..66 1. 4 1 42.. 17 9 0. 85 9 2 4. 6 5 6.4 7 2 1. 9 .4 9 . 4 2 6 5242 8. 0 7.5 8 1 9..46 9 . 36 505 2 8 N1 10 10 11.0 9. 1 6 2 591 7 .3 . 339 1 7 2.4 . 1605 .7 8 1 6 6.. 93 8 5 6 2.6 8. 1 . 25765 .0 6 5 5.. 98175 6.1 6. 5 . 738 1 9 4 5 3.8 9 5..5 640 81 5 3.6 5. 29 . 2 5366 .1 498 2 4 5 4..1 251 06 5 0.28. 2 . 7589 023 .6 51. 15 9 0.6 24 05 07. 5 .43 5. 9 . 46 5072 24 .4 8. 956 0. 894158 24 6.7 5 9 .9 471. 78 . 472 5 04 .4 59. 27 3 6. 647 4. 0 . 15 6 4 .6 45 84 73.. 432 5 94 .0 4 3. 8435 4. 524376 0 2.5 6 . 240 4 3 .8 422 05 4.. 410 62 7 84 .9 4 1. 54 3 5. 341594 10 9 . 517 4 .4 3. 00 742 . 4137 52 74 .0 4 03 1 . 12 53 6 7. 304 1 4 0. 39 10 . 24851 4 6 .3 9. 838 41 47 7 . 409 1 7 .2 3 84. 415 0 1 2 9732 93.3 9 378.701 8 .4 3 7 0 . 737 76 8 4 0194 93 8.1 72 09 60. 6703 4 4 8 03 2.9.9673 8 40 3.2.6 3 659 . 4.39 51 20 64 .97 93 59 4. 75135. 163 5 84 3 6 308.8 3 75044 3.62 3 5.9 84 . 4359 72864 .83 204. 32 4750. 1653 4 2 89 3 5 7.. 4.63 17 49 3. 0 3. 45 32 . 35 27 405 83 6.. 139 616 27 735.2.2 3 73094 5 4 3. 5 3.6 21 3 . 536 10 2 5 40 73 6.2. 8 13 2 . 857 1345.6 3 97473214 5 3. 01390. 038 72 5 4 7. 3 . 9 03 1 9 . 52 34079.23 .0 3 29 3.0264 1 3. 43 0 3029.5 3024 0 732.6 3 72 936 1 23 8.05 3 1.5. 2.2 9804 3 4 3. 63 4 32919 2. 7. 3 260 4 4 63219 .. 32 81 31 96 3802. 3 81 02 8..3 2074 83 2. 402.5 1 2 97 9 92 84 100 6 1 . 2 9 0106 4 4 .01 . 8 8 5 6.24 8 01 3 .2 6 8. . 70 9 4 8 2 .8 603 7 0.0 3 .6 4 7. . 98 665 3 7...1 9 4 7.6 643 2 3 7. . 3442 9.. 13 1 37. 6 .124 8 . 93 9 8 3.. 93 4 7 .821 6 3.3 .4 3 8 7 3..1 4 383 N DENOMINATOR DEGREES OF FREEDOM 2 TAB f(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. 2 6 937. 5 96 1 4 56. 3 9.7 85 2 31. 7 9 1.9 6 93.39 5 14 12.3765 2.7 2 6 9.. 27 6 9.4 8 6. 2 1 9 5 18 4 .307 6 5 2.9 5 7.2 6 82. 3 7 5 13 54 6 38.. 75 7 6 89.. 26 0 2 93 .2 8 9.3 02 7 5 2 746 .5.6 9. 122 9 4 1 80.9 .2 3.66 579 5.. 6 7 6 94 12 .1 3 9 0.97 5 0 5 2.6 3 99 6 71. 5 9 4 12 4 .365 2. 79 6 79 5 6.. 15 0 6 9.2 1 3 9 3 12 1 .2 34. 453 59.9 6 7.09 3 12 4..0 7 5 2 3. 59 05 5.76 6.903 9197 4.2 9.38 7151 5 2.6 9 05 5.4 6 9. 6043 9 3 17 83. 2 .368.5 5 6 59 0.29 6.309 2 18 4..34 765 2. 49 0 4.869 6.1 39 2 18 4.3. 3 7241 5 2.6 9 05 4..6 9.1 08 943 9 2 17.. 16035 2 3.4 4 6 5 9.4 .9 6 2 17 4.3 3 6. 843 .95 4.9 5.1 7.7 946 9. 07 5 3 5 2.44 6 9.1. 5 3 99 2 1 67 9 6 .2 36. 5 3 56 5 9.9 4 4 9.056 9 2 1 4..3 92 6 5 2. 4 3 6 5 0 .41 7 8 3 64 . . 3 6 5 9.9 4 3 04.9 5 86 72 4. 09. 24 3 6 .3 5 8. 3 07 9 6 86 1 . 2 6 9.8082 4.35 4.7.7 8 1 6 4.36 4. 5 3 . 1 70 5.65 N1 10 4 1.3 1 6 4. 1 0 2 631 4 .8 3 4 .23 1 . 0 3 26 4 3 .7 2 3. 1 4 .83 4 5 . 913 95 63.603 .9 3.. 73 1 9 53 4 3.7 6 .5 3 2 .2 31 3 6 3.. 21 8 4 .9 323 1 .924 3 0 19.307 . 8 3 2.0 3 2. 4. 23 6 38 9 0 .829 35 10 62. 5 . 52 3 7 3..0 0 2924. 0352 9 0 2 .826 35 73.9 2 0 . 8 3 6 1 3.. 27 87 6 4. 53 48 6 20 2.85 1 1 3 4 37.2 926 8 7 . 5 36 6 3.. 20 82 3 4 .23 13 26 5 0 .80 1.31 34 37.0 92 5 6 2 4 . 2 3 5 3. 10 4 26 82 52 44. 93 2 70 85 1 .7 0.2418 34 73.5 29 202 .3 5 0 328. 19 20 2 52 4 4. 73 2 36 8 75 .7 0.42 6305 3 432.2 89 96 0 8 .3 5 327. 12 9 78 6 47 2 6 4. 3 2 080 49 0 .7 9.02 6303 23 7.9 287 5 2 6 .27 0 3 5 4 3. 02 8 432 1 . 84 52 7 139 2 78..92 6 20 2 3 83 621.8 5 812 3 7.6 24 29 . 08 1 25 02 0 2 1 4 3 210.1 572 93 2 .3 72 0 73 6 932 54..27 4 5 4 1. 38008 8 26 3.4 52 04 4 93 2.2 7 7 298 .2 0 2 0 3 927 12 59..48 13 . 1504 0 3..8 5 62 32 704 .83 112 4 26 40.62 1 09 32 4352..7 22 3 511 .2 39 3 4 8 3.. 02 2 69 301 40 7 . 01 2 45. 6 73 16.1.8 4 2305 8 2 2751. 2037 3 9.2 .0 2 39 . 97 5629 0 4 3 2.1.1 992 6 8 2 4370. 0 231 0 63 12 854.1.27 0 2510 7. 72 30 94 9. 767 02.. 325 919 4 3 3 2..5 88 6 3287. 8 209 1 9 632 832.. 6 2 1818 6. 630 94 5 3. 4.7 2502 19. 19 2 3 3 2..4 06 2 618.9. 291 9 632 24..6 12.2 4 2 17317 6. 50 84 4 3. 0. 92 9253 10 1 98 6 3 36 2.. 026 5809.8. 1 9 9 632 24.4 6 02.2 05 11 7 0. 3984 3. 7. 92 8253 80 6 1 8. 18 2 3 2 0 5.5 4 249 88. 78 1 9 32 24.. 82.1 19 6 . 2974 3 92 7 2. 1.3 62 9 1 883 1 4.2 6.5298 4 . 820 1 9 2 2.. 670 21 8 15 1 2 3. 57.97 62 5 . 8163 03 2.2 .24 97 .5.1793 .62 86 49 0 1 . 12.09 3 3 7 3. 37.9 5102 7 133 9 12 10012.0 0121 4.19 0 .9 9 1. 6 81 9 0 .19 71 8 .. 0 9 5 1 2. 9 51 9 5 1. 0 . 0 19 31 9 .. 41 9 2 1. 1. 9. 2 8 1. 93 8 1 91 3 ..018 8. 1. 91 8 1. 8 .9 7 18 89 . 61 8 9 1. 1. 41 8.5 7 18 61. 6 .8 6 1. 81 1. 0 1 8 5. .8 7 1 8 41.3 3 .7 1. 818 1. 6 1 7 2. .8 2 7 17 81. 0 .7 6 1. 71 1. 41 7 6.6.7 9 1 7 41.5 4 .6 3 1. 7179 1 7 2. .01 7 4 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 APPENDI 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 91 549 .39 619 51 4.29 93.29 82. 6 2 4 6 8 1.1 173 8. 6 9.8 1 1 952.6 54 4 3 1. 8 .63 1 42 1. . 492 65 1.7 12 3 51 2. 2 14. 5 95 2 1.6 0 9.2 59. 0 1 426.12 9 451 2. 3 9 4.4 0 1 0 1 8 2. 0 1 5 9 29. 9 6 9 44 01 2 .4.03 45 1. 4 4 1. 9 3 4 15 . 71 .2 46.9 112 08. 9 4.3 61 87.22 1. 498 3 9 9.17.7 9 01 5.1 2 9 5 123 6 . 9 2 917.81 3 9446 8. 4 9 1 3.3 7 2 971 8.0 5 908 1 .9 7.9 23 8 . 8 2 9 1.7.6 5 4 41 0. 6 0 38. 63 9 5 28 1 1.64. 0572 13 0.8 4 9.2 3 46 8 2 9 40 .6 21 4. 5749 3 81. 6 .5 9 2 93 2 3.1 8041 06. 403 39 47.8. 5 39 3 1.4 4 2 2 30 .1 86 2 4. 30. 274 3 61 7. 4 4 .2 38 2 2 10 .16 6 129 4.5 0. 18 7. 3 2 9 3 10.14 0 3. 805 11 6. 0 947. 2 5 92 1 1 .23 0. 8 9 90.1.19 4. 0 2 1 93 4 .23 5 . 7 5 90.6.0 9 7 4 .96. 12 8713 8 9 5 2 10. 464 9.0 966 92 38. 0 3 1.27 8 9 0 9 8.79 064.2 31 1 6. 0 .8 3 2 8 2.14 05. 9 6 27 9 8 1671 20 .98 5 2 . 97 6 4 27. 9 7 17 4.2 8 65 7 3 6..9 2 7049 .2 7. 76 5 N1 10 12 1 .8 12 1 . 2 211 1 . 3 81 9 14 ..4 41 3 8 15 . 8 9 1 .060 18.8 7 81 . 5077 6 18. .613 0170 8 4 6 9. .94 1 6 8 6.27 09 . 7.8 8. 967 21 7 6 2 3.0 .36 07 6 4 6..8 1 92 . 6 52 5 2. 264 17 9 4 6 5 3. 49 2 .20 86.34 6 1 57.05 67 . 392 3 0758 06 29. . 6 0 5 9. 1796 5 .5 01.29 6 8 560.5 6 584. 916 1 60 453 4 08.9 3. 1 2 5 8. 35260 . 72 7526 5 6 5 9.62 0 38 9 . 25 9 8250 15 3.6.5 4 7 5 5. 7548 .0 406 25 5 54 2.39 74 94 4 6 . 748 8 47 04 1 95 .3. 5 5 6 8. 6485 .8 4380 9 35 5 4 4 8..6 42 5127 0 . 5479 6 7 25 94 89 46.. 4.9 2168 5 2 4.57 640 .7 4796 5 3 48 5.7.2 40 83 . 64390 6 23 84 62 4. 2.8 65 4 6 5 2.7 4629 8 . 604.92 4 63.. 4190 5 47 0.2 4310 9. 8.72 4 5. 029 70 .43 89 593 3 48 9 .85 54 .913 08 7 3 . 1 38.3 425 24 89. 9.594 789 5 02 46. 83 3.4 . 433 0755 1 4. 27. 403284 6 . 2437 365 604 7 41.. 183 7 9123 5 9 4.2 4364 9 .4 13 9 5 1 43 .541 98 . 9.69 0 . 136 584 5 4 09 38 07.0 3157 137 9 34 3. 65831 0 .931.55 4. 3.1 8348 7. . 54.3 094 97 4 20. 96 35932 5. 14. 14 3 89 536 . 403.5 04.6 34 5 .0 3 68 . . 5 43 63 81 4 13. 82430 52 8 4. 33 80 63. 4 6193 . 5235 40 3714 9 .3 2. . 96335 7 1 76.2 3 4. 2 9315 0 743.2 53 1. 330 .4 .099 3 37. 31 4 . 03 914 6 475. 23. 29 1 3035.4 2 23 7 3575 83 510.5 9 4 0236 4.4 . 32 9 0 8 3.2 09 100 8 1 . 2 2 0148 5 .01 . 1 5 8 6.9 05 1 4 .4 8. . 5 0 5 4 5 1 2 .4 0 85.0 3 .0 . 5879 0 4...6 5 03 4 85.83. 7 4 . 94 6555 2 3...89 43 8.4 3 .4 0 5 9245 3. 4..54 34.1 2 32. 8 8 .4334 5. 3. 3 87 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 .6 2 2. 37 2 0896 5 4.9 6.0 2 014.915 2 5. 7 4 5 1 976.. 972 9 14 4 6.85 9. 237 5 0 5 1.0.4 197 6.74 9 0 6 9 2 913..27 4 3 1 4 1. 9 975 6 5. 2 94.7 6.5 92 813.4 9 1 3 2. 6750 965 3. 3 4.2 81 6.52 .97 4 5 13.0 5.1 94 954. 964 92 71 7 6. 8 1.2 1 2 3. 4752 954 3. 5 9.2 6 5 1 712.6 89 2. 075394 5 9. .1 2 8 6 5. 9 .21 7 2.2 93 5. 5 .6 4 2 16.8 1 92. 2 1 94 9 2 5 ..21 4 5 .27 5 2 1. 5 4 9. 3 3 12 6 6..2 91 2. 1 5 994 8 5. 2 1 4. 8 9 2 510. 1 3 90 1 2. 97 2 14 932. 965 92 10 8. 3 9.267 1 0 0 1.5.6 4 932. 95 3.2 2 510.1 8 5 0 1 2. 4723 192. 2 9 4.3 6.3 9 2 510.27 1 6 2 1 0 1.5.5 9 932. 933 9410 2 3 207 7 1.9 1381 5. 2 9 4. 63 5 1. 4190 2 3 91 2. 87955 9281. 9 . 641 .8 302 17 0 5 9 .65.3 9 4281.627 16.9.84 1 09 91 6 7.5 2 98 1. 5 .1 6. 2 3 42 90 7 8 1. 57455 41 92.. 81622 .318 5 5 92 0 6 .8 7 31 .35 9 0. 4 8 26 25 416 5. 4. 1 0 809 1 2 5.9255464 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 . 45 5 7 34 0.1. 13 1 241.. 6 0 4 7 3. 8 . 31 6 94.7 8 .41 63.8 3 4 .3 3. 75 8 5 .64 93 1 . 6290 541 3.3 74 .0 32. 75 . 35 06 3 8.1.04 93 65 2 .0 32 4 .32. 70 5. 248 2 3 423 7 .5 74 05 63 51.21 4.7 32 4 .732. 6 4. 28 9 3 403 2 2 .5 341 92 0 3 53 73 0. 8 7 4.38 2 4 .132. 63 2 4. 17 3 493 2 88 0 .4 917 9 63 43 43 02.83 4.25. 81 42 7. 50 3744 135 97 2 .7 83 20. 7 3 9 93 42 13 09 2 6 .840 .1244 4. 735 412 7 . 392 54 132.7 530 255 2.64 9 03 46 2 . 3280. 45 00 32 67 4 032 31 7 2. 89 2 5.0 .. 137 20 4 8 993. 5 92 7 6 8.4 4. 12 760. 13 762. 472 3 4 068 31. 82 43 1 76 .31 2603. 3 9 . 9 2 57 .3 10 278 9.2 6 304 3 4 227 2. 99 . 5 86328 3 32.2 74 5 3 34 4 3. . 70 12 6 . 92 504 .036 4 200 9 276.725 1 . 35328 9 22 3820. 739 40 1 0 34 4. 8 .38 2 69 1 . 92 54 .036 2743.72 31 . 34 1527 78 03 802.6 2 421 5 9 34 4.3. 13 62 .4124 .051 3 127.9 2 3 . 31. 83427 6 83 2. 850.217 34 3. 6 09 23..6 23 0 .342 14 .3 126 8 .59 306 2 . 3.50 6 217 4 73 2. 74626 2 0 5 84 47. 93 5 0217 .32 6404 .03 295 .57 3928. 30.721 87 2 753. 743 2123 254 34. 82. 08 1 9 . 1832 04 .93 260.5 3 928 1 2 . 3925417 1 73. 753 2 820 0 2 .24 32. 63 .985 1 29 . 3196044 .95 6 3 6.26 1 9 . 380717 0 23 59. 1 3.12 5.. 8199 3 3 12.. 312507 . 195 401 1 23. 32874 00 2 25 9 4 . 4 3 4.928.372 09 518 4 .9 3 28. 9526 19 7 . 21 5737 9 703 2. 642 29 01 1 09 2. 4 3.928.9 0 218 . 3062.52 3. 3.3 8 51 2 3 7 41 2. 0. 926 5302 43.1 2 . 928 6 7 2. . 79 214 3 2 07 58 125 3.2 0. 1 10012.1 0 72 4.21 0 .1 3 2. 6 32 1 0 2 .12 8 .. 0 0 90 2 92 9 2. 00 2 .2 0 . 0.72 0 5 2.0 1. 52 046 9 2 .62 5 . 0.2 0 102. 1. 21 0.0 9 1 .12 0 . 92. 9 8.9 1. 6 02 78 1 1 6 ..9111 93. . .97 8 198 2 .19 2.1 1 1 9..61 9 4 7 1. 5 9 .81187 1. 9.71 .9 12. 82 8 7 1.171 8 1..61 .48 41 85 7 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.

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