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Statistical tables for economists - econ 101 resources môn Xác suất thống kê| Trường Đại học Ngoại Thương

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Statistical tables for economists - econ 101 resources môn Xácsuất thống kê| Trường Đại học Ngoại Thương. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời đọc đón xem!

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

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Lan Anh Trần

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Department of Economics
Statistical Tables for Economists
Index for Statistical Tables
Table
1 Normal Distribution 1
2 Student-t Distribution 2
3 Chi-Squared Distribution 3
4 F-Distribution (a=001.) 4-6
5 F-Distribution (a=005.) 7-9
6 F-Distribution (a=010.) 10-12
7 Binomial Distribution 13-27
8 Poisson Distribution 28-30
9 Durbin-Watson Critical Values 31
10 Mackinnon's Critical Values 32
11 Johansen Critical Values 33
1
Pr()() Z z F z£=
z F(z) z F(z) z F(z) z F(z) z F(z) z F(z) z F(z)
0.00 0.500 0.50 0.691 1.00 0.841 1.50 0.933 2.00 0.977 2.50 0.994 3.00 0.999
0.01 0.504 0.51 0.695 1.01 0.844 1.51 0.934 2.01 0.978 2.51 0.994 3.01 0.999
0.02 0.508 0.52 0.698 1.02 0.846 1.52 0.936 2.02 0.978 2.52 0.994 3.02 0.999
0.03 0.512 0.53 0.702 1.03 0.848 1.53 0.937 2.03 0.979 2.53 0.994 3.03 0.999
0.04 0.516 0.54 0.705 1.04 0.851 1.54 0.938 2.04 0.979 2.54 0.994 3.04 0.999
0.05 0.520 0.55 0.709 1.05 0.853 1.55 0.939 2.05 0.980 2.55 0.995 3.05 0.999
0.06 0.524 0.56 0.712 1.06 0.855 1.56 0.941 2.06 0.980 2.56 0.995 3.06 0.999
0.07 0.528 0.57 0.716 1.07 0.858 1.57 0.942 2.07 0.981 2.57 0.995 3.07 0.999
0.08 0.532 0.58 0.719 1.08 0.860 1.58 0.943 2.08 0.981 2.58 0.995 3.08 0.999
0.09 0.536 0.59 0.722 1.09 0.862 1.59 0.944 2.09 0.982 2.59 0.995 3.09 0.999
0.10 0.540 0.60 0.726 1.10 0.864 1.60 0.945 2.10 0.982 2.60 0.995 3.10 0.999
0.11 0.544 0.61 0.729 1.11 0.867 1.61 0.946 2.11 0.983 2.61 0.995 3.11 0.999
0.12 0.548 0.62 0.732 1.12 0.869 1.62 0.947 2.12 0.983 2.62 0.996 3.12 0.999
0.13 0.552 0.63 0.736 1.13 0.871 1.63 0.948 2.13 0.983 2.63 0.996 3.13 0.999
0.14 0.556 0.64 0.739 1.14 0.873 1.64 0.949 2.14 0.984 2.64 0.996 3.14 0.999
0.15 0.560 0.65 0.742 1.15 0.875 1.65 0.951 2.15 0.984 2.65 0.996 3.15 0.999
0.16 0.564 0.66 0.745 1.16 0.877 1.66 0.952 2.16 0.985 2.66 0.996 3.16 0.999
0.17 0.567 0.67 0.749 1.17 0.879 1.67 0.953 2.17 0.985 2.67 0.996 3.17 0.999
0.18 0.571 0.68 0.752 1.18 0.881 1.68 0.954 2.18 0.985 2.68 0.996 3.18 0.999
0.19 0.575 0.69 0.755 1.19 0.883 1.69 0.954 2.19 0.986 2.69 0.996 3.19 0.999
0.20 0.579 0.70 0.758 1.20 0.885 1.70 0.955 2.20 0.986 2.70 0.997 3.20 0.999
0.21 0.583 0.71 0.761 1.21 0.887 1.71 0.956 2.21 0.986 2.71 0.997 3.21 0.999
0.22 0.587 0.72 0.764 1.22 0.889 1.72 0.957 2.22 0.987 2.72 0.997 3.22 0.999
0.23 0.591 0.73 0.767 1.23 0.891 1.73 0.958 2.23 0.987 2.73 0.997 3.23 0.999
0.24 0.595 0.74 0.770 1.24 0.893 1.74 0.959 2.24 0.987 2.74 0.997 3.24 0.999
0.25 0.599 0.75 0.773 1.25 0.894 1.75 0.960 2.25 0.988 2.75 0.997 3.25 0.999
0.26 0.603 0.76 0.776 1.26 0.896 1.76 0.961 2.26 0.988 2.76 0.997 3.26 0.999
0.27 0.606 0.77 0.779 1.27 0.898 1.77 0.962 2.27 0.988 2.77 0.997 3.27 0.999
0.28 0.610 0.78 0.782 1.28 0.900 1.78 0.962 2.28 0.989 2.78 0.997 3.28 0.999
0.29 0.614 0.79 0.785 1.29 0.901 1.79 0.963 2.29 0.989 2.79 0.997 3.29 0.999
0.30 0.618 0.80 0.788 1.30 0.903 1.80 0.964 2.30 0.989 2.80 0.997 3.30 1.000
0.31 0.622 0.81 0.791 1.31 0.905 1.81 0.965 2.31 0.990 2.81 0.998 3.31 1.000
0.32 0.626 0.82 0.794 1.32 0.907 1.82 0.966 2.32 0.990 2.82 0.998 3.32 1.000
0.33 0.629 0.83 0.797 1.33 0.908 1.83 0.966 2.33 0.990 2.83 0.998 3.33 1.000
0.34 0.633 0.84 0.800 1.34 0.910 1.84 0.967 2.34 0.990 2.84 0.998 3.34 1.000
0.35 0.637 0.85 0.802 1.35 0.911 1.85 0.968 2.35 0.991 2.85 0.998 3.35 1.000
0.36 0.641 0.86 0.805 1.36 0.913 1.86 0.969 2.36 0.991 2.86 0.998 3.36 1.000
0.37 0.644 0.87 0.808 1.37 0.915 1.87 0.969 2.37 0.991 2.87 0.998 3.37 1.000
0.38 0.648 0.88 0.811 1.38 0.916 1.88 0.970 2.38 0.991 2.88 0.998 3.38 1.000
0.39 0.652 0.89 0.813 1.39 0.918 1.89 0.971 2.39 0.992 2.89 0.998 3.39 1.000
0.40 0.655 0.90 0.816 1.40 0.919 1.90 0.971 2.40 0.992 2.90 0.998 3.40 1.000
0.41 0.659 0.91 0.819 1.41 0.921 1.91 0.972 2.41 0.992 2.91 0.998 3.41 1.000
0.42 0.663 0.92 0.821 1.42 0.922 1.92 0.973 2.42 0.992 2.92 0.998 3.42 1.000
0.43 0.666 0.93 0.824 1.43 0.924 1.93 0.973 2.43 0.992 2.93 0.998 3.43 1.000
0.44 0.670 0.94 0.826 1.44 0.925 1.94 0.974 2.44 0.993 2.94 0.998 3.44 1.000
0.45 0.674 0.95 0.829 1.45 0.926 1.95 0.974 2.45 0.993 2.95 0.998 3.45 1.000
0.46 0.677 0.96 0.831 1.46 0.928 1.96 0.975 2.46 0.993 2.96 0.998 3.46 1.000
0.47 0.681 0.97 0.834 1.47 0.929 1.97 0.976 2.47 0.993 2.97 0.999 3.47 1.000
0.48 0.684 0.98 0.836 1.48 0.931 1.98 0.976 2.48 0.993 2.98 0.999 3.48 1.000
0.49 0.688 0.99 0.839 1.49 0.932 1.99 0.977 2.49 0.994 2.99 0.999 3.49 1.000
Table 1: Normal Distribution
z
F(z)
2
Table 2: Student t-distribution
a
1-a
n,a
t
Pr()
,
X t
>=naa
a
n
0.10 0.05 0.025 0.01 0.005
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
31 1.309 1.696 2.040 2.453 2.744
32 1.309 1.694 2.037 2.449 2.738
33 1.308 1.692 2.035 2.445 2.733
34 1.307 1.691 2.032 2.441 2.728
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
60 1.296 1.671 2.000 2.390 2.660
70 1.294 1.667 1.994 2.381 2.648
80 1.292 1.664 1.990 2.374 2.639
90 1.291 1.662 1.987 2.368 2.632
100 1.290 1.660 1.984 2.364 2.626
¥
1.282 1.645 1.960 2.327 2.576
3
Table 3: Chi-Squared Distribution
a
1-a
c
n
2
Pr( )
,
X³ c
na
2
a
n 0.995 0.99 0.975 0.95 0.9 0.1 0.05 0.025 0.01 0.005
1 0.00 0.00 0.00 0.00 0.02 2.71 3.84 5.02 6.63 7.88
2 0.01 0.02 0.05 0.10 0.21 4.61 5.99 7.38 9.21 10.60
3 0.07 0.11 0.22 0.35 0.58 6.25 7.81 9.35 11.34 12.84
4 0.21 0.30 0.48 0.71 1.06 7.78 9.49 11.14 13.28 14.86
5 0.41 0.55 0.83 1.15 1.61 9.24 11.07 12.83 15.09 16.75
6 0.68 0.87 1.24 1.64 2.20 10.64 12.59 14.45 16.81 18.55
7 0.99 1.24 1.69 2.17 2.83 12.02 14.07 16.01 18.48 20.28
8 1.34 1.65 2.18 2.73 3.49 13.36 15.51 17.53 20.09 21.95
9 1.73 2.09 2.70 3.33 4.17 14.68 16.92 19.02 21.67 23.59
10 2.16 2.56 3.25 3.94 4.87 15.99 18.31 20.48 23.21 25.19
11 2.60 3.05 3.82 4.57 5.58 17.28 19.68 21.92 24.72 26.76
12 3.07 3.57 4.40 5.23 6.30 18.55 21.03 23.34 26.22 28.30
13 3.57 4.11 5.01 5.89 7.04 19.81 22.36 24.74 27.69 29.82
14 4.07 4.66 5.63 6.57 7.79 21.06 23.68 26.12 29.14 31.32
15 4.60 5.23 6.26 7.26 8.55 22.31 25.00 27.49 30.58 32.80
16 5.14 5.81 6.91 7.96 9.31 23.54 26.30 28.85 32.00 34.27
17 5.70 6.41 7.56 8.67 10.09 24.77 27.59 30.19 33.41 35.72
18 6.26 7.01 8.23 9.39 10.86 25.99 28.87 31.53 34.81 37.16
19 6.84 7.63 8.91 10.12 11.65 27.20 30.14 32.85 36.19 38.58
20 7.43 8.26 9.59 10.85 12.44 28.41 31.41 34.17 37.57 40.00
21 8.03 8.90 10.28 11.59 13.24 29.62 32.67 35.48 38.93 41.40
22 8.64 9.54 10.98 12.34 14.04 30.81 33.92 36.78 40.29 42.80
23 9.26 10.20 11.69 13.09 14.85 32.01 35.17 38.08 41.64 44.18
24 9.89 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98 45.56
25 10.52 11.52 13.12 14.61 16.47 34.38 37.65 40.65 44.31 46.93
26 11.16 12.20 13.84 15.38 17.29 35.56 38.89 41.92 45.64 48.29
27 11.81 12.88 14.57 16.15 18.11 36.74 40.11 43.19 46.96 49.64
28 12.46 13.56 15.31 16.93 18.94 37.92 41.34 44.46 48.28 50.99
29 13.12 14.26 16.05 17.71 19.77 39.09 42.56 45.72 49.59 52.34
30 13.79 14.95 16.79 18.49 20.60 40.26 43.77 46.98 50.89 53.67
31 14.46 15.66 17.54 19.28 21.43 41.42 44.99 48.23 52.19 55.00
32 15.13 16.36 18.29 20.07 22.27 42.58 46.19 49.48 53.49 56.33
33 15.82 17.07 19.05 20.87 23.11 43.75 47.40 50.73 54.78 57.65
34 16.50 17.79 19.81 21.66 23.95 44.90 48.60 51.97 56.06 58.96
35 17.19 18.51 20.57 22.47 24.80 46.06 49.80 53.20 57.34 60.27
40 20.71 22.16 24.43 26.51 29.05 51.81 55.76 59.34 63.69 66.77
45 24.31 25.90 28.37 30.61 33.35 57.51 61.66 65.41 69.96 73.17
50 27.99 29.71 32.36 34.76 37.69 63.17 67.50 71.42 76.15 79.49
60 35.53 37.48 40.48 43.19 46.46 74.40 79.08 83.30 88.38 91.95
70 43.28 45.44 48.76 51.74 55.33 85.53 90.53 95.02 100.43 104.21
80 51.17 53.54 57.15 60.39 64.28 96.58 101.88 106.63 112.33 116.32
90 59.20 61.75 65.65 69.13 73.29 107.57 113.15 118.14 124.12 128.30
100 67.33 70.06 74.22 77.93 82.36 118.50 124.34 129.56 135.81 140.17
4
Table 4: F-distribution (a=001.)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=001.
n1
n2 1 2 3 4 5 6 7 8 9 10
1 4051.3 4999.5 5403.5 5624.8 5763.9 5859.2 5928.6 5981.3 6022.7 6056.1
2 98.50 99.00 99.22 99.33 99.40 99.44 99.48 99.50 99.52 99.53
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05
6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09
27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03
29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98
31 7.53 5.36 4.48 3.99 3.67 3.45 3.28 3.15 3.04 2.96
32 7.50 5.34 4.46 3.97 3.65 3.43 3.26 3.13 3.02 2.93
33 7.47 5.31 4.44 3.95 3.63 3.41 3.24 3.11 3.00 2.91
34 7.44 5.29 4.42 3.93 3.61 3.39 3.22 3.09 2.98 2.89
35 7.42 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.88
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80
45 7.23 5.11 4.25 3.77 3.45 3.23 3.07 2.94 2.83 2.74
50 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47
¥ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32
5
Table 4: F-distribution (a=001.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=001.
n1
n2 11 12 13 14 15 16 17 18 19 20
1 6083.6 6106.6 6126.2 6142.9 6157.6 6170.4 6181.7 6191.8 6200.9 6209.0
2 99.54 99.55 99.56 99.57 99.58 99.58 99.59 99.59 99.60 99.60
3 27.13 27.05 26.98 26.92 26.87 26.83 26.79 26.75 26.72 26.69
4 14.45 14.37 14.31 14.25 14.20 14.15 14.11 14.08 14.05 14.02
5 9.96 9.89 9.82 9.77 9.72 9.68 9.64 9.61 9.58 9.55
6 7.79 7.72 7.66 7.60 7.56 7.52 7.48 7.45 7.42 7.40
7 6.54 6.47 6.41 6.36 6.31 6.27 6.24 6.21 6.18 6.16
8 5.73 5.67 5.61 5.56 5.52 5.48 5.44 5.41 5.38 5.36
9 5.18 5.11 5.05 5.01 4.96 4.92 4.89 4.86 4.83 4.81
10 4.77 4.71 4.65 4.60 4.56 4.52 4.49 4.46 4.43 4.41
11 4.46 4.40 4.34 4.29 4.25 4.21 4.18 4.15 4.12 4.10
12 4.22 4.16 4.10 4.05 4.01 3.97 3.94 3.91 3.88 3.86
13 4.02 3.96 3.91 3.86 3.82 3.78 3.75 3.72 3.69 3.66
14 3.86 3.80 3.75 3.70 3.66 3.62 3.59 3.56 3.53 3.51
15 3.73 3.67 3.61 3.56 3.52 3.49 3.45 3.42 3.40 3.37
16 3.62 3.55 3.50 3.45 3.41 3.37 3.34 3.31 3.28 3.26
17 3.52 3.46 3.40 3.35 3.31 3.27 3.24 3.21 3.19 3.16
18 3.43 3.37 3.32 3.27 3.23 3.19 3.16 3.13 3.10 3.08
19 3.36 3.30 3.24 3.19 3.15 3.12 3.08 3.05 3.03 3.00
20 3.29 3.23 3.18 3.13 3.09 3.05 3.02 2.99 2.96 2.94
21 3.24 3.17 3.12 3.07 3.03 2.99 2.96 2.93 2.90 2.88
22 3.18 3.12 3.07 3.02 2.98 2.94 2.91 2.88 2.85 2.83
23 3.14 3.07 3.02 2.97 2.93 2.89 2.86 2.83 2.80 2.78
24 3.09 3.03 2.98 2.93 2.89 2.85 2.82 2.79 2.76 2.74
25 3.06 2.99 2.94 2.89 2.85 2.81 2.78 2.75 2.72 2.70
26 3.02 2.96 2.90 2.86 2.81 2.78 2.75 2.72 2.69 2.66
27 2.99 2.93 2.87 2.82 2.78 2.75 2.71 2.68 2.66 2.63
28 2.96 2.90 2.84 2.79 2.75 2.72 2.68 2.65 2.63 2.60
29 2.93 2.87 2.81 2.77 2.73 2.69 2.66 2.63 2.60 2.57
30 2.91 2.84 2.79 2.74 2.70 2.66 2.63 2.60 2.57 2.55
31 2.88 2.82 2.77 2.72 2.68 2.64 2.61 2.58 2.55 2.52
32 2.86 2.80 2.74 2.70 2.65 2.62 2.58 2.55 2.53 2.50
33 2.84 2.78 2.72 2.68 2.63 2.60 2.56 2.53 2.51 2.48
34 2.82 2.76 2.70 2.66 2.61 2.58 2.54 2.51 2.49 2.46
35 2.80 2.74 2.69 2.64 2.60 2.56 2.53 2.50 2.47 2.44
40 2.73 2.66 2.61 2.56 2.52 2.48 2.45 2.42 2.39 2.37
45 2.67 2.61 2.55 2.51 2.46 2.43 2.39 2.36 2.34 2.31
50 2.63 2.56 2.51 2.46 2.42 2.38 2.35 2.32 2.29 2.27
60 2.56 2.50 2.44 2.39 2.35 2.31 2.28 2.25 2.22 2.20
120 2.40 2.34 2.28 2.23 2.19 2.15 2.12 2.09 2.06 2.03
¥ 2.25 2.18 2.13 2.08 2.04 2.00 1.97 1.93 1.90 1.88
6
Table 4: F-distribution (a=001.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=001.
n1
n2 21 22 23 24 25 30 35 40 60 120
¥
1 6216.4 6223.2 6229.3 6234.9 6240.1 6261.0 6275.9 6287.1 6313.4 6339.7 6365.9
2 99.60 99.61 99.61 99.61 99.61 99.62 99.63 99.63 99.64 99.65 99.50
3 26.66 26.64 26.62 26.60 26.58 26.47 26.42 26.38 26.29 26.19 26.13
4 13.99 13.97 13.95 13.93 13.91 13.84 13.78 13.75 13.65 13.56 13.46
5 9.53 9.51 9.49 9.47 9.45 9.38 9.33 9.29 9.20 9.11 9.02
6 7.37 7.35 7.33 7.31 7.30 7.23 7.18 7.14 7.06 6.97 6.88
7 6.13 6.11 6.09 6.07 6.06 5.99 5.94 5.91 5.82 5.74 5.65
8 5.34 5.32 5.30 5.28 5.26 5.20 5.15 5.12 5.03 4.95 4.86
9 4.79 4.77 4.75 4.73 4.71 4.65 4.60 4.57 4.48 4.40 4.31
10 4.38 4.36 4.34 4.33 4.31 4.25 4.20 4.16 4.08 4.00 3.91
11 4.08 4.06 4.04 4.02 4.01 3.94 3.89 3.86 3.78 3.69 3.60
12 3.84 3.82 3.80 3.78 3.76 3.70 3.65 3.62 3.54 3.45 3.36
13 3.64 3.62 3.60 3.59 3.57 3.51 3.46 3.43 3.34 3.25 3.17
14 3.48 3.46 3.44 3.43 3.41 3.35 3.30 3.27 3.18 3.09 3.00
15 3.35 3.33 3.31 3.29 3.28 3.21 3.17 3.13 3.05 2.96 2.87
16 3.24 3.22 3.20 3.18 3.16 3.10 3.05 3.02 2.93 2.84 2.75
17 3.14 3.12 3.10 3.08 3.07 3.00 2.96 2.92 2.83 2.75 2.65
18 3.05 3.03 3.02 3.00 2.98 2.92 2.87 2.84 2.75 2.66 2.57
19 2.98 2.96 2.94 2.92 2.91 2.84 2.80 2.76 2.67 2.58 2.49
20 2.92 2.90 2.88 2.86 2.84 2.78 2.73 2.69 2.61 2.52 2.42
21 2.86 2.84 2.82 2.80 2.79 2.72 2.67 2.64 2.55 2.46 2.36
22 2.81 2.78 2.77 2.75 2.73 2.67 2.62 2.58 2.50 2.40 2.31
23 2.76 2.74 2.72 2.70 2.69 2.62 2.57 2.54 2.45 2.35 2.26
24 2.72 2.70 2.68 2.66 2.64 2.58 2.53 2.49 2.40 2.31 2.21
25 2.68 2.66 2.64 2.62 2.60 2.54 2.49 2.45 2.36 2.27 2.17
26 2.64 2.62 2.60 2.58 2.57 2.50 2.45 2.42 2.33 2.23 2.13
27 2.61 2.59 2.57 2.55 2.54 2.47 2.42 2.38 2.29 2.20 2.10
28 2.58 2.56 2.54 2.52 2.51 2.44 2.39 2.35 2.26 2.17 2.06
29 2.55 2.53 2.51 2.49 2.48 2.41 2.36 2.33 2.23 2.14 2.03
30 2.53 2.51 2.49 2.47 2.45 2.39 2.34 2.30 2.21 2.11 2.01
31 2.50 2.48 2.46 2.45 2.43 2.36 2.31 2.27 2.18 2.09 1.98
32 2.48 2.46 2.44 2.42 2.41 2.34 2.29 2.25 2.16 2.06 1.96
33 2.46 2.44 2.42 2.40 2.39 2.32 2.27 2.23 2.14 2.04 1.93
34 2.44 2.42 2.40 2.38 2.37 2.30 2.25 2.21 2.12 2.02 1.91
35 2.42 2.40 2.38 2.36 2.35 2.28 2.23 2.19 2.10 2.00 1.89
40 2.35 2.33 2.31 2.29 2.27 2.20 2.15 2.11 2.02 1.92 1.80
45 2.29 2.27 2.25 2.23 2.21 2.14 2.09 2.05 1.96 1.85 1.74
50 2.24 2.22 2.20 2.18 2.17 2.10 2.05 2.01 1.91 1.80 1.68
60 2.17 2.15 2.13 2.12 2.10 2.03 1.98 1.94 1.84 1.73 1.60
120 2.01 1.99 1.97 1.95 1.93 1.86 1.81 1.76 1.66 1.53 1.38
¥ 1.85 1.83 1.81 1.79 1.77 1.70 1.64 1.59 1.47 1.32 1.00
7
Table 5: F-distribution (a=005.)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=005.
n1
n2 1 2 3 4 5 6 7 8 9 10
1 161.55 199.71 215.95 224.84 230.42 234.25 237.04 239.16 240.82 242.16
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.73
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16
31 4.16 3.30 2.91 2.68 2.52 2.41 2.32 2.25 2.20 2.15
32 4.15 3.29 2.90 2.67 2.51 2.40 2.31 2.24 2.19 2.14
33 4.14 3.28 2.89 2.66 2.50 2.39 2.30 2.23 2.18 2.13
34 4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17 2.12
35 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08
45 4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.10 2.05
50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99
120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91
¥ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83
8
Table 5: F-distribution (a=005.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=005.
n1
n2 11 12 13 14 15 16 17 18 19 20
1 243.26 244.19 244.97 245.65 246.24 246.75 247.20 247.61 247.97 248.30
2 19.40 19.41 19.42 19.44 19.44 19.45 19.45 19.45 19.46 19.46
3 8.76 8.74 8.73 8.71 8.70 8.69 8.68 8.67 8.67 8.66
4 5.94 5.91 5.89 5.87 5.86 5.84 5.83 5.82 5.81 5.80
5 4.70 4.68 4.66 4.64 4.62 4.60 4.59 4.58 4.57 4.56
6 4.03 4.00 3.98 3.96 3.94 3.92 3.91 3.90 3.88 3.87
7 3.60 3.57 3.55 3.53 3.51 3.49 3.48 3.47 3.46 3.44
8 3.31 3.28 3.26 3.24 3.22 3.20 3.19 3.17 3.16 3.15
9 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.95 2.94
10 2.94 2.91 2.89 2.86 2.85 2.83 2.81 2.80 2.79 2.77
11 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.67 2.66 2.65
12 2.72 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.56 2.54
13 2.63 2.60 2.58 2.55 2.53 2.51 2.50 2.48 2.47 2.46
14 2.57 2.53 2.51 2.48 2.46 2.44 2.43 2.41 2.40 2.39
15 2.51 2.48 2.45 2.42 2.40 2.38 2.37 2.35 2.34 2.33
16 2.46 2.42 2.40 2.37 2.35 2.33 2.32 2.30 2.29 2.28
17 2.41 2.38 2.35 2.33 2.31 2.29 2.27 2.26 2.24 2.23
18 2.37 2.34 2.31 2.29 2.27 2.25 2.23 2.22 2.20 2.19
19 2.34 2.31 2.28 2.26 2.23 2.21 2.20 2.18 2.17 2.16
20 2.31 2.28 2.25 2.22 2.20 2.18 2.17 2.15 2.14 2.12
21 2.28 2.25 2.22 2.20 2.18 2.16 2.14 2.12 2.11 2.10
22 2.26 2.23 2.20 2.17 2.15 2.13 2.11 2.10 2.08 2.07
23 2.24 2.20 2.18 2.15 2.13 2.11 2.09 2.08 2.06 2.05
24 2.22 2.18 2.15 2.13 2.11 2.09 2.07 2.05 2.04 2.03
25 2.20 2.16 2.14 2.11 2.09 2.07 2.05 2.04 2.02 2.01
26 2.18 2.15 2.12 2.09 2.07 2.05 2.03 2.02 2.00 1.99
27 2.17 2.13 2.10 2.08 2.06 2.04 2.02 2.00 1.99 1.97
28 2.15 2.12 2.09 2.06 2.04 2.02 2.00 1.99 1.97 1.96
29 2.14 2.10 2.08 2.05 2.03 2.01 1.99 1.97 1.96 1.94
30 2.13 2.09 2.06 2.04 2.01 1.99 1.98 1.96 1.95 1.93
31 2.11 2.08 2.05 2.03 2.00 1.98 1.96 1.95 1.93 1.92
32 2.10 2.07 2.04 2.01 1.99 1.97 1.95 1.94 1.92 1.91
33 2.09 2.06 2.03 2.00 1.98 1.96 1.94 1.93 1.91 1.90
34 2.08 2.05 2.02 1.99 1.97 1.95 1.93 1.92 1.90 1.89
35 2.07 2.04 2.01 1.99 1.96 1.94 1.92 1.91 1.89 1.88
40 2.04 2.00 1.97 1.95 1.92 1.90 1.89 1.87 1.85 1.84
45 2.01 1.97 1.94 1.92 1.89 1.87 1.86 1.84 1.82 1.81
50 1.99 1.95 1.92 1.89 1.87 1.85 1.83 1.81 1.80 1.78
60 1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.78 1.76 1.75
120 1.87 1.83 1.80 1.78 1.75 1.73 1.71 1.69 1.67 1.66
¥ 1.79 1.75 1.72 1.69 1.67 1.64 1.62 1.60 1.59 1.57
9
Table 5: F-distribution (a=005.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=005.
n1
n2 21 22 23 24 25 30 35 40 60 120
¥
1 248.60 248.87 249.11 249.34 249.55 250.39 250.98 251.44 270.27 271.40 254.31
2 19.46 19.46 19.47 19.47 19.47 19.48 19.48 19.49 19.49 19.50 19.50
3 8.65 8.65 8.64 8.64 8.63 8.62 8.60 8.59 8.57 8.55 8.53
4 5.79 5.79 5.78 5.77 5.77 5.75 5.73 5.72 5.69 5.66 5.63
5 4.55 4.54 4.53 4.53 4.52 4.50 4.48 4.46 4.43 4.40 4.36
6 3.86 3.86 3.85 3.84 3.83 3.81 3.79 3.77 3.74 3.70 3.67
7 3.43 3.43 3.42 3.41 3.40 3.38 3.36 3.34 3.30 3.27 3.23
8 3.14 3.13 3.12 3.12 3.11 3.08 3.06 3.04 3.01 2.97 2.93
9 2.93 2.92 2.91 2.90 2.89 2.86 2.84 2.83 2.79 2.75 2.71
10 2.76 2.75 2.75 2.74 2.73 2.70 2.68 2.66 2.62 2.58 2.54
11 2.64 2.63 2.62 2.61 2.60 2.57 2.55 2.53 2.49 2.45 2.40
12 2.53 2.52 2.51 2.51 2.50 2.47 2.44 2.43 2.38 2.34 2.30
13 2.45 2.44 2.43 2.42 2.41 2.38 2.36 2.34 2.30 2.25 2.21
14 2.38 2.37 2.36 2.35 2.34 2.31 2.28 2.27 2.22 2.18 2.13
15 2.32 2.31 2.30 2.29 2.28 2.25 2.22 2.20 2.16 2.11 2.07
16 2.26 2.25 2.24 2.24 2.23 2.19 2.17 2.15 2.11 2.06 2.01
17 2.22 2.21 2.20 2.19 2.18 2.15 2.12 2.10 2.06 2.01 1.96
18 2.18 2.17 2.16 2.15 2.14 2.11 2.08 2.06 2.02 1.97 1.92
19 2.14 2.13 2.12 2.11 2.11 2.07 2.05 2.03 1.98 1.93 1.88
20 2.11 2.10 2.09 2.08 2.07 2.04 2.01 1.99 1.95 1.90 1.84
21 2.08 2.07 2.06 2.05 2.05 2.01 1.98 1.96 1.92 1.87 1.81
22 2.06 2.05 2.04 2.03 2.02 1.98 1.96 1.94 1.89 1.84 1.78
23 2.04 2.02 2.01 2.01 2.00 1.96 1.93 1.91 1.86 1.81 1.76
24 2.01 2.00 1.99 1.98 1.97 1.94 1.91 1.89 1.84 1.79 1.73
25 2.00 1.98 1.97 1.96 1.96 1.92 1.89 1.87 1.82 1.77 1.71
26 1.98 1.97 1.96 1.95 1.94 1.90 1.87 1.85 1.80 1.75 1.69
27 1.96 1.95 1.94 1.93 1.92 1.88 1.86 1.84 1.79 1.73 1.67
28 1.95 1.93 1.92 1.91 1.91 1.87 1.84 1.82 1.77 1.71 1.65
29 1.93 1.92 1.91 1.90 1.89 1.85 1.83 1.81 1.75 1.70 1.64
30 1.92 1.91 1.90 1.89 1.88 1.84 1.81 1.79 1.74 1.68 1.62
31 1.91 1.90 1.88 1.88 1.87 1.83 1.80 1.78 1.73 1.67 1.61
32 1.90 1.88 1.87 1.86 1.85 1.82 1.79 1.77 1.71 1.66 1.59
33 1.89 1.87 1.86 1.85 1.84 1.81 1.78 1.76 1.70 1.64 1.58
34 1.88 1.86 1.85 1.84 1.83 1.80 1.77 1.75 1.69 1.63 1.57
35 1.87 1.85 1.84 1.83 1.82 1.79 1.76 1.74 1.68 1.62 1.56
40 1.83 1.81 1.80 1.79 1.78 1.74 1.72 1.69 1.64 1.58 1.51
45 1.80 1.78 1.77 1.76 1.75 1.71 1.68 1.66 1.60 1.54 1.47
50 1.77 1.76 1.75 1.74 1.73 1.69 1.66 1.63 1.58 1.51 1.44
60 1.73 1.72 1.71 1.70 1.69 1.65 1.62 1.59 1.53 1.47 1.39
120 1.64 1.63 1.62 1.61 1.60 1.55 1.52 1.50 1.43 1.35 1.25
¥ 1.56 1.54 1.53 1.52 1.51 1.46 1.42 1.39 1.32 1.22 1.00
10
Table 6: F-distribution (a=010.)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=010.
n1
n2 1 2 3 4 5 6 7 8 9 10
1 39.87 49.52 53.62 55.87 57.28 58.24 58.95 59.48 59.90 60.24
2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39
3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23
4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92
5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30
6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94
7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70
8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54
9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42
10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32
11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25
12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19
13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14
14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10
15 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06
16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03
17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00
18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98
19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96
20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94
21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92
22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90
23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89
24 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88
25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87
26 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86
27 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87 1.85
28 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87 1.84
29 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83
30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82
31 2.87 2.48 2.27 2.14 2.04 1.97 1.92 1.88 1.84 1.81
32 2.87 2.48 2.26 2.13 2.04 1.97 1.91 1.87 1.83 1.81
33 2.86 2.47 2.26 2.12 2.03 1.96 1.91 1.86 1.83 1.80
34 2.86 2.47 2.25 2.12 2.02 1.96 1.90 1.86 1.82 1.79
35 2.85 2.46 2.25 2.11 2.02 1.95 1.90 1.85 1.82 1.79
40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76
45 2.82 2.42 2.21 2.07 1.98 1.91 1.85 1.81 1.77 1.74
50 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76 1.73
60 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71
120 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65
¥ 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.60
11
Table 6: F-distribution (a=010.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=010.
n1
n2 11 12 13 14 15 16 17 18 19 20
1 60.51 60.75 60.94 61.11 61.26 61.39 61.51 61.61 61.70 61.78
2 9.40 9.41 9.41 9.42 9.42 9.43 9.43 9.44 9.44 9.44
3 5.22 5.22 5.21 5.20 5.20 5.20 5.19 5.19 5.19 5.18
4 3.91 3.90 3.89 3.88 3.87 3.86 3.86 3.85 3.85 3.84
5 3.28 3.27 3.26 3.25 3.24 3.23 3.22 3.22 3.21 3.21
6 2.92 2.90 2.89 2.88 2.87 2.86 2.85 2.85 2.84 2.84
7 2.68 2.67 2.65 2.64 2.63 2.62 2.61 2.61 2.60 2.59
8 2.52 2.50 2.49 2.48 2.46 2.45 2.45 2.44 2.43 2.42
9 2.40 2.38 2.36 2.35 2.34 2.33 2.32 2.31 2.30 2.30
10 2.30 2.28 2.27 2.26 2.24 2.23 2.22 2.22 2.21 2.20
11 2.23 2.21 2.19 2.18 2.17 2.16 2.15 2.14 2.13 2.12
12 2.17 2.15 2.13 2.12 2.10 2.09 2.08 2.08 2.07 2.06
13 2.12 2.10 2.08 2.07 2.05 2.04 2.03 2.02 2.01 2.01
14 2.07 2.05 2.04 2.02 2.01 2.00 1.99 1.98 1.97 1.96
15 2.04 2.02 2.00 1.99 1.97 1.96 1.95 1.94 1.93 1.92
16 2.01 1.99 1.97 1.95 1.94 1.93 1.92 1.91 1.90 1.89
17 1.98 1.96 1.94 1.93 1.91 1.90 1.89 1.88 1.87 1.86
18 1.95 1.93 1.92 1.90 1.89 1.87 1.86 1.85 1.84 1.84
19 1.93 1.91 1.89 1.88 1.86 1.85 1.84 1.83 1.82 1.81
20 1.91 1.89 1.87 1.86 1.84 1.83 1.82 1.81 1.80 1.79
21 1.90 1.87 1.86 1.84 1.83 1.81 1.80 1.79 1.78 1.78
22 1.88 1.86 1.84 1.83 1.81 1.80 1.79 1.78 1.77 1.76
23 1.87 1.84 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.74
24 1.85 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.74 1.73
25 1.84 1.82 1.80 1.79 1.77 1.76 1.75 1.74 1.73 1.72
26 1.83 1.81 1.79 1.77 1.76 1.75 1.73 1.72 1.71 1.71
27 1.82 1.80 1.78 1.76 1.75 1.74 1.72 1.71 1.70 1.70
28 1.81 1.79 1.77 1.75 1.74 1.73 1.71 1.70 1.69 1.69
29 1.80 1.78 1.76 1.75 1.73 1.72 1.71 1.69 1.68 1.68
30 1.79 1.77 1.75 1.74 1.72 1.71 1.70 1.69 1.68 1.67
31 1.79 1.77 1.75 1.73 1.71 1.70 1.69 1.68 1.67 1.66
32 1.78 1.76 1.74 1.72 1.71 1.69 1.68 1.67 1.66 1.65
33 1.77 1.75 1.73 1.72 1.70 1.69 1.67 1.66 1.65 1.64
34 1.77 1.75 1.73 1.71 1.69 1.68 1.67 1.66 1.65 1.64
35 1.76 1.74 1.72 1.70 1.69 1.67 1.66 1.65 1.64 1.63
40 1.74 1.71 1.70 1.68 1.66 1.65 1.64 1.62 1.61 1.61
45 1.72 1.70 1.68 1.66 1.64 1.63 1.62 1.60 1.59 1.58
50 1.70 1.68 1.66 1.64 1.63 1.61 1.60 1.59 1.58 1.57
60 1.68 1.66 1.64 1.62 1.60 1.59 1.58 1.56 1.55 1.54
120 1.63 1.60 1.58 1.56 1.54 1.53 1.52 1.50 1.49 1.48
¥ 1.57 1.55 1.52 1.50 1.49 1.47 1.46 1.44 1.43 1.42
12
Table 6: F-distribution (a=010.) (cont'd)
a
1-a
nn1,
F
2
a
Pr( )
,
XF>=
nn
aa
12
a=010.
n1
n2 21 22 23 24 25 30 35 40 60 120
¥
1 61.86 61.92 61.99 62.04 62.10 62.31 62.46 62.57 62.84 63.10 63.33
2 9.44 9.45 9.45 9.45 9.46 9.46 9.47 9.47 9.48 9.49 9.49
3 5.18 5.18 5.18 5.18 5.17 5.17 5.16 5.16 5.15 5.14 5.13
4 3.84 3.84 3.83 3.83 3.83 3.82 3.81 3.80 3.79 3.78 3.76
5 3.20 3.20 3.19 3.19 3.19 3.17 3.16 3.16 3.14 3.12 3.10
6 2.83 2.83 2.82 2.82 2.81 2.80 2.79 2.78 2.76 2.74 2.72
7 2.59 2.58 2.58 2.58 2.57 2.56 2.54 2.54 2.51 2.49 2.47
8 2.42 2.41 2.41 2.40 2.40 2.38 2.37 2.36 2.34 2.32 2.29
9 2.29 2.29 2.28 2.28 2.27 2.25 2.24 2.23 2.21 2.18 2.16
10 2.19 2.19 2.18 2.18 2.17 2.16 2.14 2.13 2.11 2.08 2.06
11 2.12 2.11 2.11 2.10 2.10 2.08 2.06 2.05 2.03 2.00 1.97
12 2.05 2.05 2.04 2.04 2.03 2.01 2.00 1.99 1.96 1.93 1.90
13 2.00 1.99 1.99 1.98 1.98 1.96 1.94 1.93 1.90 1.88 1.85
14 1.96 1.95 1.94 1.94 1.93 1.91 1.90 1.89 1.86 1.83 1.80
15 1.92 1.91 1.90 1.90 1.89 1.87 1.86 1.85 1.82 1.79 1.76
16 1.88 1.88 1.87 1.87 1.86 1.84 1.82 1.81 1.78 1.75 1.72
17 1.85 1.85 1.84 1.84 1.83 1.81 1.79 1.78 1.75 1.72 1.69
18 1.83 1.82 1.82 1.81 1.80 1.78 1.77 1.75 1.72 1.69 1.66
19 1.81 1.80 1.79 1.79 1.78 1.76 1.74 1.73 1.70 1.67 1.63
20 1.79 1.78 1.77 1.77 1.76 1.74 1.72 1.71 1.68 1.64 1.61
21 1.77 1.76 1.75 1.75 1.74 1.72 1.70 1.69 1.66 1.62 1.59
22 1.75 1.74 1.74 1.73 1.73 1.70 1.68 1.67 1.64 1.60 1.57
23 1.74 1.73 1.72 1.72 1.71 1.69 1.67 1.66 1.62 1.59 1.55
24 1.72 1.71 1.71 1.70 1.70 1.67 1.65 1.64 1.61 1.57 1.53
25 1.71 1.70 1.70 1.69 1.68 1.66 1.64 1.63 1.59 1.56 1.52
26 1.70 1.69 1.68 1.68 1.67 1.65 1.63 1.61 1.58 1.54 1.50
27 1.69 1.68 1.67 1.67 1.66 1.64 1.62 1.60 1.57 1.53 1.49
28 1.68 1.67 1.66 1.66 1.65 1.63 1.61 1.59 1.56 1.52 1.48
29 1.67 1.66 1.65 1.65 1.64 1.62 1.60 1.58 1.55 1.51 1.47
30 1.66 1.65 1.64 1.64 1.63 1.61 1.59 1.57 1.54 1.50 1.46
31 1.65 1.64 1.64 1.63 1.62 1.60 1.58 1.56 1.53 1.49 1.45
32 1.64 1.64 1.63 1.62 1.62 1.59 1.57 1.56 1.52 1.48 1.44
33 1.64 1.63 1.62 1.61 1.61 1.58 1.56 1.55 1.51 1.47 1.43
34 1.63 1.62 1.61 1.61 1.60 1.58 1.56 1.54 1.50 1.46 1.42
35 1.62 1.62 1.61 1.60 1.60 1.57 1.55 1.53 1.50 1.46 1.41
40 1.60 1.59 1.58 1.57 1.57 1.54 1.52 1.51 1.47 1.42 1.38
45 1.58 1.57 1.56 1.55 1.55 1.52 1.50 1.48 1.44 1.40 1.35
50 1.56 1.55 1.54 1.54 1.53 1.50 1.48 1.46 1.42 1.38 1.33
60 1.53 1.53 1.52 1.51 1.50 1.48 1.45 1.44 1.40 1.35 1.29
120 1.47 1.46 1.46 1.45 1.44 1.41 1.39 1.37 1.32 1.26 1.19
¥ 1.41 1.40 1.39 1.38 1.38 1.34 1.32 1.30 1.24 1.17 1.00
13
Table 7: Binomial Distribution
Pr ()X k
£
n=2 n=3 n=4 n=5
p k=0 1 k=0 1 2 k=0 1 2 3 k=0 1 2 3 4
0.01 0.980 1.000 0.970 1.000 0.961 0.999 1.000 0.951 0.999 1.000
0.02 0.960 1.000 0.941 0.999 1.000 0.922 0.998 1.000 0.904 0.996 1.000
0.03 0.941 0.999 0.913 0.997 1.000 0.885 0.995 1.000 0.859 0.992 1.000
0.04 0.922 0.998 0.885 0.995 1.000 0.849 0.991 1.000 0.815 0.985 0.999 1.000
0.05 0.902 0.997 0.857 0.993 1.000 0.815 0.986 1.000 0.774 0.977 0.999 1.000
0.06 0.884 0.996 0.831 0.990 1.000 0.781 0.980 0.999 1.000 0.734 0.968 0.998 1.000
0.07 0.865 0.995 0.804 0.986 1.000 0.748 0.973 0.999 1.000 0.696 0.958 0.997 1.000
0.08 0.846 0.994 0.779 0.982 0.999 0.716 0.966 0.998 1.000 0.659 0.946 0.995 1.000
0.09 0.828 0.992 0.754 0.977 0.999 0.686 0.957 0.997 1.000 0.624 0.933 0.994 1.000
0.10 0.810 0.990 0.729 0.972 0.999 0.656 0.948 0.996 1.000 0.590 0.919 0.991 1.000
0.11 0.792 0.988 0.705 0.966 0.999 0.627 0.938 0.995 1.000 0.558 0.903 0.989 0.999 1.000
0.12 0.774 0.986 0.681 0.960 0.998 0.600 0.927 0.994 1.000 0.528 0.888 0.986 0.999 1.000
0.13 0.757 0.983 0.659 0.954 0.998 0.573 0.915 0.992 1.000 0.498 0.871 0.982 0.999 1.000
0.14 0.740 0.980 0.636 0.947 0.997 0.547 0.903 0.990 1.000 0.470 0.853 0.978 0.998 1.000
0.15 0.722 0.977 0.614 0.939 0.997 0.522 0.890 0.988 0.999 0.444 0.835 0.973 0.998 1.000
0.16 0.706 0.974 0.593 0.931 0.996 0.498 0.877 0.986 0.999 0.418 0.817 0.968 0.997 1.000
0.17 0.689 0.971 0.572 0.923 0.995 0.475 0.863 0.983 0.999 0.394 0.797 0.963 0.996 1.000
0.18 0.672 0.968 0.551 0.914 0.994 0.452 0.849 0.980 0.999 0.371 0.778 0.956 0.996 1.000
0.19 0.656 0.964 0.531 0.905 0.993 0.430 0.834 0.976 0.999 0.349 0.758 0.949 0.994 1.000
0.20 0.640 0.960 0.512 0.896 0.992 0.410 0.819 0.973 0.998 0.328 0.737 0.942 0.993 1.000
0.21 0.624 0.956 0.493 0.886 0.991 0.390 0.804 0.969 0.998 0.308 0.717 0.934 0.992 1.000
0.22 0.608 0.952 0.475 0.876 0.989 0.370 0.788 0.964 0.998 0.289 0.696 0.926 0.990 0.999
0.23 0.593 0.947 0.457 0.866 0.988 0.352 0.772 0.960 0.997 0.271 0.675 0.916 0.989 0.999
0.24 0.578 0.942 0.439 0.855 0.986 0.334 0.755 0.955 0.997 0.254 0.654 0.907 0.987 0.999
0.25 0.562 0.937 0.422 0.844 0.984 0.316 0.738 0.949 0.996 0.237 0.633 0.896 0.984 0.999
0.26 0.548 0.932 0.405 0.832 0.982 0.300 0.721 0.943 0.995 0.222 0.612 0.886 0.982 0.999
0.27 0.533 0.927 0.389 0.821 0.980 0.284 0.704 0.937 0.995 0.207 0.591 0.874 0.979 0.999
0.28 0.518 0.922 0.373 0.809 0.978 0.269 0.687 0.931 0.994 0.193 0.570 0.862 0.976 0.998
0.29 0.504 0.916 0.358 0.796 0.976 0.254 0.669 0.924 0.993 0.180 0.549 0.850 0.973 0.998
0.30 0.490 0.910 0.343 0.784 0.973 0.240 0.652 0.916 0.992 0.168 0.528 0.837 0.969 0.998
0.31 0.476 0.904 0.329 0.771 0.970 0.227 0.634 0.909 0.991 0.156 0.508 0.823 0.965 0.997
0.32 0.462 0.898 0.314 0.758 0.967 0.214 0.616 0.900 0.990 0.145 0.487 0.809 0.961 0.997
0.33 0.449 0.891 0.301 0.745 0.964 0.202 0.599 0.892 0.988 0.135 0.468 0.795 0.956 0.996
0.34 0.436 0.884 0.287 0.732 0.961 0.190 0.581 0.883 0.987 0.125 0.448 0.780 0.951 0.995
0.35 0.423 0.878 0.275 0.718 0.957 0.179 0.563 0.874 0.985 0.116 0.428 0.765 0.946 0.995
0.36 0.410 0.870 0.262 0.705 0.953 0.168 0.545 0.864 0.983 0.107 0.409 0.749 0.940 0.994
0.37 0.397 0.863 0.250 0.691 0.949 0.158 0.528 0.854 0.981 0.099 0.391 0.733 0.934 0.993
0.38 0.384 0.856 0.238 0.677 0.945 0.148 0.510 0.843 0.979 0.092 0.372 0.717 0.927 0.992
0.39 0.372 0.848 0.227 0.662 0.941 0.138 0.493 0.832 0.977 0.084 0.354 0.700 0.920 0.991
0.40 0.360 0.840 0.216 0.648 0.936 0.130 0.475 0.821 0.974 0.078 0.337 0.683 0.913 0.990
0.41 0.348 0.832 0.205 0.634 0.931 0.121 0.458 0.809 0.972 0.071 0.320 0.665 0.905 0.988
0.42 0.336 0.824 0.195 0.619 0.926 0.113 0.441 0.797 0.969 0.066 0.303 0.647 0.897 0.987
0.43 0.325 0.815 0.185 0.604 0.920 0.106 0.424 0.785 0.966 0.060 0.287 0.630 0.888 0.985
0.44 0.314 0.806 0.176 0.590 0.915 0.098 0.407 0.772 0.963 0.055 0.271 0.611 0.879 0.984
0.45 0.303 0.798 0.166 0.575 0.909 0.092 0.391 0.759 0.959 0.050 0.256 0.593 0.869 0.982
0.46 0.292 0.788 0.157 0.560 0.903 0.085 0.375 0.745 0.955 0.046 0.241 0.575 0.859 0.979
0.47 0.281 0.779 0.149 0.545 0.896 0.079 0.359 0.731 0.951 0.042 0.227 0.556 0.848 0.977
0.48 0.270 0.770 0.141 0.530 0.889 0.073 0.343 0.717 0.947 0.038 0.213 0.537 0.837 0.975
0.49 0.260 0.760 0.133 0.515 0.882 0.068 0.328 0.702 0.942 0.035 0.200 0.519 0.825 0.972
0.50 0.250 0.750 0.125 0.500 0.875 0.062 0.312 0.688 0.938 0.031 0.187 0.500 0.813 0.969
14
Table 7: Binomial Distribution (cont'd)
Pr ()X k
£
n=6
p k=0 1 2 3 4 5 k=0 1 2 3 4 5 6
0.01 0.941 0.999 1.000 0.932 0.998 1.000
0.02 0.886 0.994 1.000 0.868 0.992 1.000
0.03 0.833 0.988 0.999 1.000 0.808 0.983 0.999 1.000
0.04 0.783 0.978 0.999 1.000 0.751 0.971 0.998 1.000
0.05 0.735 0.967 0.998 1.000 0.698 0.956 0.996 1.000
0.06 0.690 0.954 0.996 1.000 0.648 0.938 0.994 1.000
0.07 0.647 0.939 0.994 1.000 0.602 0.919 0.990 0.999 1.000
0.08 0.606 0.923 0.991 0.999 1.000 0.558 0.897 0.986 0.999 1.000
0.09 0.568 0.905 0.988 0.999 1.000 0.517 0.875 0.981 0.998 1.000
0.10 0.531 0.886 0.984 0.999 1.000 0.478 0.850 0.974 0.997 1.000
0.11 0.497 0.866 0.979 0.998 1.000 0.442 0.825 0.967 0.996 1.000
0.12 0.464 0.844 0.974 0.997 1.000 0.409 0.799 0.958 0.995 1.000
0.13 0.434 0.822 0.968 0.997 1.000 0.377 0.772 0.949 0.993 0.999 1.000
0.14 0.405 0.800 0.961 0.995 1.000 0.348 0.744 0.938 0.991 0.999 1.000
0.15 0.377 0.776 0.953 0.994 1.000 0.321 0.717 0.926 0.988 0.999 1.000
0.16 0.351 0.753 0.944 0.993 0.999 1.000 0.295 0.689 0.913 0.985 0.998 1.000
0.17 0.327 0.729 0.934 0.991 0.999 1.000 0.271 0.660 0.899 0.981 0.998 1.000
0.18 0.304 0.704 0.924 0.988 0.999 1.000 0.249 0.632 0.885 0.977 0.997 1.000
0.19 0.282 0.680 0.913 0.986 0.999 1.000 0.229 0.604 0.869 0.972 0.996 1.000
0.20 0.262 0.655 0.901 0.983 0.998 1.000 0.210 0.577 0.852 0.967 0.995 1.000
0.21 0.243 0.631 0.888 0.980 0.998 1.000 0.192 0.549 0.834 0.961 0.994 1.000
0.22 0.225 0.606 0.875 0.976 0.997 1.000 0.176 0.522 0.816 0.954 0.993 0.999 1.000
0.23 0.208 0.582 0.861 0.972 0.997 1.000 0.160 0.496 0.797 0.946 0.991 0.999 1.000
0.24 0.193 0.558 0.846 0.967 0.996 1.000 0.146 0.470 0.777 0.938 0.989 0.999 1.000
0.25 0.178 0.534 0.831 0.962 0.995 1.000 0.133 0.445 0.756 0.929 0.987 0.999 1.000
0.26 0.164 0.510 0.814 0.957 0.994 1.000 0.122 0.420 0.735 0.920 0.985 0.998 1.000
0.27 0.151 0.487 0.798 0.951 0.993 1.000 0.110 0.396 0.714 0.909 0.982 0.998 1.000
0.28 0.139 0.464 0.780 0.944 0.992 1.000 0.100 0.373 0.692 0.898 0.979 0.997 1.000
0.29 0.128 0.442 0.763 0.937 0.991 0.999 0.091 0.351 0.670 0.887 0.975 0.997 1.000
0.30 0.118 0.420 0.744 0.930 0.989 0.999 0.082 0.329 0.647 0.874 0.971 0.996 1.000
0.31 0.108 0.399 0.726 0.921 0.987 0.999 0.074 0.309 0.624 0.861 0.967 0.995 1.000
0.32 0.099 0.378 0.706 0.913 0.985 0.999 0.067 0.289 0.601 0.847 0.962 0.995 1.000
0.33 0.090 0.358 0.687 0.903 0.983 0.999 0.061 0.270 0.578 0.832 0.957 0.994 1.000
0.34 0.083 0.338 0.667 0.893 0.980 0.998 0.055 0.251 0.555 0.816 0.951 0.992 0.999
0.35 0.075 0.319 0.647 0.883 0.978 0.998 0.049 0.234 0.532 0.800 0.944 0.991 0.999
0.36 0.069 0.301 0.627 0.871 0.975 0.998 0.044 0.217 0.509 0.783 0.937 0.989 0.999
0.37 0.063 0.283 0.606 0.860 0.971 0.997 0.039 0.201 0.487 0.766 0.930 0.988 0.999
0.38 0.057 0.266 0.586 0.847 0.968 0.997 0.035 0.186 0.464 0.748 0.922 0.986 0.999
0.39 0.052 0.249 0.565 0.834 0.963 0.996 0.031 0.172 0.442 0.729 0.913 0.984 0.999
0.40 0.047 0.233 0.544 0.821 0.959 0.996 0.028 0.159 0.420 0.710 0.904 0.981 0.998
0.41 0.042 0.218 0.524 0.807 0.954 0.995 0.025 0.146 0.398 0.691 0.894 0.978 0.998
0.42 0.038 0.203 0.503 0.792 0.949 0.995 0.022 0.134 0.377 0.671 0.883 0.975 0.998
0.43 0.034 0.190 0.482 0.777 0.943 0.994 0.020 0.123 0.356 0.650 0.872 0.972 0.997
0.44 0.031 0.176 0.462 0.761 0.937 0.993 0.017 0.112 0.336 0.629 0.860 0.968 0.997
0.45 0.028 0.164 0.442 0.745 0.931 0.992 0.015 0.102 0.316 0.608 0.847 0.964 0.996
0.46 0.025 0.152 0.421 0.728 0.924 0.991 0.013 0.093 0.297 0.587 0.834 0.960 0.996
0.47 0.022 0.140 0.402 0.711 0.916 0.989 0.012 0.085 0.279 0.565 0.820 0.955 0.995
0.48 0.020 0.129 0.382 0.693 0.908 0.988 0.010 0.077 0.261 0.544 0.805 0.950 0.994
0.49 0.018 0.119 0.363 0.675 0.900 0.986 0.009 0.069 0.243 0.522 0.790 0.944 0.993
0.50 0.016 0.109 0.344 0.656 0.891 0.984 0.008 0.062 0.227 0.500 0.773 0.938 0.992
15
Table 7: Binomial Distribution (cont'd)
Pr ()X k
£
n=8
p k=0 1 2 3 4 5 6 7 k=0 1 2 3 4 5
0.01 0.923 0.997 1.000 0.914 0.997 1.000
0.02 0.851 0.990 1.000 0.834 0.987 0.999 1.000
0.03 0.784 0.978 0.999 1.000 0.760 0.972 0.998 1.000
0.04 0.721 0.962 0.997 1.000 0.693 0.952 0.996 1.000
0.05 0.663 0.943 0.994 1.000 0.630 0.929 0.992 0.999 1.000
0.06 0.610 0.921 0.990 0.999 1.000 0.573 0.902 0.986 0.999 1.000
0.07 0.560 0.897 0.985 0.999 1.000 0.520 0.873 0.979 0.998 1.000
0.08 0.513 0.870 0.979 0.998 1.000 0.472 0.842 0.970 0.996 1.000
0.09 0.470 0.842 0.971 0.997 1.000 0.428 0.809 0.960 0.994 0.999 1.000
0.10 0.430 0.813 0.962 0.995 1.000 0.387 0.775 0.947 0.992 0.999 1.000
0.11 0.394 0.783 0.951 0.993 0.999 1.000 0.350 0.740 0.933 0.988 0.999 1.000
0.12 0.360 0.752 0.939 0.990 0.999 1.000 0.316 0.705 0.917 0.984 0.998 1.000
0.13 0.328 0.721 0.926 0.987 0.999 1.000 0.286 0.670 0.899 0.979 0.997 1.000
0.14 0.299 0.689 0.911 0.983 0.998 1.000 0.257 0.634 0.880 0.973 0.996 1.000
0.15 0.272 0.657 0.895 0.979 0.997 1.000 0.232 0.599 0.859 0.966 0.994 0.999
0.16 0.248 0.626 0.877 0.973 0.996 1.000 0.208 0.565 0.837 0.958 0.993 0.999
0.17 0.225 0.594 0.859 0.967 0.995 1.000 0.187 0.532 0.814 0.949 0.990 0.999
0.18 0.204 0.563 0.839 0.960 0.993 0.999 1.000 0.168 0.499 0.790 0.938 0.988 0.998
0.19 0.185 0.533 0.819 0.952 0.992 0.999 1.000 0.150 0.467 0.764 0.927 0.984 0.998
0.20 0.168 0.503 0.797 0.944 0.990 0.999 1.000 0.134 0.436 0.738 0.914 0.980 0.997
0.21 0.152 0.474 0.775 0.934 0.987 0.998 1.000 0.120 0.407 0.711 0.901 0.976 0.996
0.22 0.137 0.446 0.751 0.924 0.984 0.998 1.000 0.107 0.378 0.684 0.886 0.971 0.995
0.23 0.124 0.419 0.728 0.912 0.981 0.997 1.000 0.095 0.351 0.657 0.870 0.965 0.994
0.24 0.111 0.392 0.703 0.900 0.977 0.997 1.000 0.085 0.325 0.629 0.852 0.958 0.992
0.25 0.100 0.367 0.679 0.886 0.973 0.996 1.000 0.075 0.300 0.601 0.834 0.951 0.990
0.26 0.090 0.343 0.653 0.872 0.968 0.995 1.000 0.067 0.277 0.573 0.815 0.943 0.988
0.27 0.081 0.319 0.628 0.857 0.962 0.994 0.999 1.000 0.059 0.255 0.545 0.795 0.934 0.985
0.28 0.072 0.297 0.603 0.841 0.956 0.992 0.999 1.000 0.052 0.234 0.517 0.774 0.924 0.982
0.29 0.065 0.276 0.577 0.824 0.949 0.991 0.999 1.000 0.046 0.214 0.490 0.752 0.913 0.979
0.30 0.058 0.255 0.552 0.806 0.942 0.989 0.999 1.000 0.040 0.196 0.463 0.730 0.901 0.975
0.31 0.051 0.236 0.526 0.787 0.934 0.987 0.998 1.000 0.035 0.179 0.436 0.706 0.888 0.970
0.32 0.046 0.218 0.501 0.768 0.925 0.984 0.998 1.000 0.031 0.163 0.411 0.683 0.875 0.965
0.33 0.041 0.201 0.476 0.748 0.915 0.981 0.998 1.000 0.027 0.148 0.385 0.658 0.860 0.960
0.34 0.036 0.184 0.452 0.728 0.905 0.978 0.997 1.000 0.024 0.134 0.361 0.634 0.845 0.953
0.35 0.032 0.169 0.428 0.706 0.894 0.975 0.996 1.000 0.021 0.121 0.337 0.609 0.828 0.946
0.36 0.028 0.155 0.404 0.685 0.882 0.971 0.996 1.000 0.018 0.109 0.314 0.584 0.811 0.939
0.37 0.025 0.141 0.381 0.663 0.869 0.966 0.995 1.000 0.016 0.098 0.292 0.558 0.793 0.930
0.38 0.022 0.129 0.359 0.640 0.856 0.961 0.994 1.000 0.014 0.088 0.271 0.533 0.774 0.921
0.39 0.019 0.117 0.337 0.617 0.841 0.956 0.993 0.999 0.012 0.079 0.251 0.508 0.754 0.911
0.40 0.017 0.106 0.315 0.594 0.826 0.950 0.991 0.999 0.010 0.071 0.232 0.483 0.733 0.901
0.41 0.015 0.096 0.295 0.571 0.810 0.944 0.990 0.999 0.009 0.063 0.213 0.458 0.712 0.889
0.42 0.013 0.087 0.275 0.547 0.794 0.937 0.988 0.999 0.007 0.056 0.196 0.433 0.690 0.877
0.43 0.011 0.078 0.256 0.524 0.776 0.929 0.986 0.999 0.006 0.049 0.180 0.409 0.668 0.863
0.44 0.010 0.070 0.238 0.500 0.758 0.921 0.984 0.999 0.005 0.044 0.164 0.385 0.645 0.849
0.45 0.008 0.063 0.220 0.477 0.740 0.912 0.982 0.998 0.005 0.039 0.150 0.361 0.621 0.834
0.46 0.007 0.057 0.203 0.454 0.720 0.902 0.979 0.998 0.004 0.034 0.136 0.339 0.598 0.818
0.47 0.006 0.050 0.187 0.431 0.700 0.891 0.976 0.998 0.003 0.030 0.123 0.316 0.573 0.801
0.48 0.005 0.045 0.172 0.408 0.680 0.880 0.973 0.997 0.003 0.026 0.111 0.295 0.549 0.784
0.49 0.005 0.040 0.158 0.385 0.658 0.868 0.969 0.997 0.002 0.023 0.100 0.274 0.525 0.765
0.50 0.004 0.035 0.145 0.363 0.637 0.855 0.965 0.996 0.002 0.020 0.090 0.254 0.500 0.746
16
Table 7: Binomial Distribution (cont'd)
Pr ()X k
£
n=9 n=10
p k=6 7 8 k=0 1 2 3 4 5 6 7 8 9
0.01 0.904 0.996 1.000
0.02 0.817 0.984 0.999 1.000
0.03 0.737 0.965 0.997 1.000
0.04 0.665 0.942 0.994 1.000
0.05 0.599 0.914 0.988 0.999 1.000
0.06 0.539 0.882 0.981 0.998 1.000
0.07 0.484 0.848 0.972 0.996 1.000
0.08 0.434 0.812 0.960 0.994 0.999 1.000
0.09 0.389 0.775 0.946 0.991 0.999 1.000
0.10 0.349 0.736 0.930 0.987 0.998 1.000
0.11 0.312 0.697 0.912 0.982 0.997 1.000
0.12 0.279 0.658 0.891 0.976 0.996 1.000
0.13 0.248 0.620 0.869 0.969 0.995 0.999 1.000
0.14 0.221 0.582 0.845 0.960 0.993 0.999 1.000
0.15 1.000 0.197 0.544 0.820 0.950 0.990 0.999 1.000
0.16 1.000 0.175 0.508 0.794 0.939 0.987 0.998 1.000
0.17 1.000 0.155 0.473 0.766 0.926 0.983 0.997 1.000
0.18 1.000 0.137 0.439 0.737 0.912 0.979 0.996 1.000
0.19 1.000 0.122 0.407 0.708 0.896 0.973 0.995 0.999 1.000
0.20 1.000 0.107 0.376 0.678 0.879 0.967 0.994 0.999 1.000
0.21 1.000 0.095 0.346 0.647 0.861 0.960 0.992 0.999 1.000
0.22 0.999 1.000 0.083 0.318 0.617 0.841 0.952 0.990 0.998 1.000
0.23 0.999 1.000 0.073 0.292 0.586 0.821 0.943 0.987 0.998 1.000
0.24 0.999 1.000 0.064 0.267 0.556 0.799 0.933 0.984 0.997 1.000
0.25 0.999 1.000 0.056 0.244 0.526 0.776 0.922 0.980 0.996 1.000
0.26 0.998 1.000 0.049 0.222 0.496 0.752 0.910 0.976 0.996 0.999 1.000
0.27 0.998 1.000 0.043 0.202 0.466 0.727 0.896 0.971 0.994 0.999 1.000
0.28 0.997 1.000 0.037 0.183 0.438 0.702 0.882 0.966 0.993 0.999 1.000
0.29 0.997 1.000 0.033 0.166 0.410 0.676 0.866 0.960 0.991 0.999 1.000
0.30 0.996 1.000 0.028 0.149 0.383 0.650 0.850 0.953 0.989 0.998 1.000
0.31 0.995 0.999 1.000 0.024 0.134 0.357 0.623 0.832 0.945 0.987 0.998 1.000
0.32 0.994 0.999 1.000 0.021 0.121 0.331 0.596 0.813 0.936 0.984 0.997 1.000
0.33 0.992 0.999 1.000 0.018 0.108 0.307 0.568 0.794 0.927 0.981 0.997 1.000
0.34 0.991 0.999 1.000 0.016 0.096 0.284 0.541 0.773 0.916 0.978 0.996 1.000
0.35 0.989 0.999 1.000 0.013 0.086 0.262 0.514 0.751 0.905 0.974 0.995 0.999 1.000
0.36 0.987 0.998 1.000 0.012 0.076 0.241 0.487 0.729 0.893 0.969 0.994 0.999 1.000
0.37 0.984 0.998 1.000 0.010 0.068 0.221 0.460 0.706 0.879 0.964 0.993 0.999 1.000
0.38 0.982 0.997 1.000 0.008 0.060 0.202 0.434 0.682 0.865 0.959 0.991 0.999 1.000
0.39 0.978 0.997 1.000 0.007 0.053 0.184 0.408 0.658 0.850 0.952 0.990 0.999 1.000
0.40 0.975 0.996 1.000 0.006 0.046 0.167 0.382 0.633 0.834 0.945 0.988 0.998 1.000
0.41 0.971 0.995 1.000 0.005 0.041 0.152 0.358 0.608 0.817 0.937 0.985 0.998 1.000
0.42 0.967 0.995 1.000 0.004 0.036 0.137 0.333 0.582 0.798 0.929 0.983 0.997 1.000
0.43 0.962 0.994 0.999 0.004 0.031 0.124 0.310 0.556 0.779 0.919 0.980 0.997 1.000
0.44 0.956 0.992 0.999 0.003 0.027 0.111 0.288 0.530 0.759 0.909 0.976 0.996 1.000
0.45 0.950 0.991 0.999 0.003 0.023 0.100 0.266 0.504 0.738 0.898 0.973 0.995 1.000
0.46 0.944 0.989 0.999 0.002 0.020 0.089 0.245 0.478 0.717 0.886 0.968 0.995 1.000
0.47 0.936 0.988 0.999 0.002 0.017 0.079 0.226 0.453 0.694 0.873 0.963 0.994 0.999
0.48 0.928 0.985 0.999 0.001 0.015 0.070 0.207 0.427 0.671 0.859 0.958 0.992 0.999
0.49 0.920 0.983 0.998 0.001 0.013 0.062 0.189 0.402 0.647 0.844 0.952 0.991 0.999
0.50 0.910 0.980 0.998 0.001 0.011 0.055 0.172 0.377 0.623 0.828 0.945 0.989 0.999
17
Table 7: Binomial Distribution (cont'd)
Pr ()X k
£
n=1
p k=0 1 2 3 4 5 6 7 8 9 10 k=0 1 2
0.01 0.895 0.995 1.000 0.886 0.994 1.000
0.02 0.801 0.980 0.999 1.000 0.785 0.977 0.998
0.03 0.715 0.959 0.996 1.000 0.694 0.951 0.995
0.04 0.638 0.931 0.992 0.999 1.000 0.613 0.919 0.989
0.05 0.569 0.898 0.985 0.998 1.000 0.540 0.882 0.980
0.06 0.506 0.862 0.975 0.997 1.000 0.476 0.840 0.968
0.07 0.450 0.823 0.963 0.995 0.999 1.000 0.419 0.797 0.953
0.08 0.400 0.782 0.948 0.991 0.999 1.000 0.368 0.751 0.935
0.09 0.354 0.740 0.931 0.987 0.998 1.000 0.322 0.705 0.913
0.10 0.314 0.697 0.910 0.981 0.997 1.000 0.282 0.659 0.889
0.11 0.278 0.655 0.888 0.974 0.996 1.000 0.247 0.613 0.862
0.12 0.245 0.613 0.863 0.966 0.994 0.999 1.000 0.216 0.569 0.833
0.13 0.216 0.571 0.837 0.956 0.991 0.999 1.000 0.188 0.525 0.802
0.14 0.190 0.531 0.809 0.944 0.988 0.998 1.000 0.164 0.483 0.770
0.15 0.167 0.492 0.779 0.931 0.984 0.997 1.000 0.142 0.443 0.736
0.16 0.147 0.455 0.748 0.915 0.979 0.996 1.000 0.123 0.405 0.701
0.17 0.129 0.419 0.716 0.899 0.973 0.995 0.999 1.000 0.107 0.370 0.666
0.18 0.113 0.385 0.684 0.880 0.967 0.993 0.999 1.000 0.092 0.336 0.630
0.19 0.098 0.353 0.651 0.860 0.959 0.991 0.999 1.000 0.080 0.304 0.594
0.20 0.086 0.322 0.617 0.839 0.950 0.988 0.998 1.000 0.069 0.275 0.558
0.21 0.075 0.294 0.584 0.816 0.939 0.985 0.997 1.000 0.059 0.248 0.523
0.22 0.065 0.267 0.551 0.792 0.928 0.981 0.996 1.000 0.051 0.222 0.489
0.23 0.056 0.242 0.519 0.767 0.915 0.977 0.995 0.999 1.000 0.043 0.199 0.455
0.24 0.049 0.219 0.487 0.740 0.901 0.972 0.994 0.999 1.000 0.037 0.178 0.422
0.25 0.042 0.197 0.455 0.713 0.885 0.966 0.992 0.999 1.000 0.032 0.158 0.391
0.26 0.036 0.177 0.425 0.685 0.869 0.959 0.990 0.998 1.000 0.027 0.141 0.360
0.27 0.031 0.159 0.395 0.657 0.851 0.951 0.988 0.998 1.000 0.023 0.125 0.331
0.28 0.027 0.142 0.366 0.628 0.832 0.942 0.985 0.997 1.000 0.019 0.110 0.304
0.29 0.023 0.127 0.339 0.599 0.811 0.933 0.982 0.997 1.000 0.016 0.097 0.278
0.30 0.020 0.113 0.313 0.570 0.790 0.922 0.978 0.996 0.999 1.000 0.014 0.085 0.253
0.31 0.017 0.100 0.288 0.540 0.767 0.910 0.974 0.995 0.999 1.000 0.012 0.074 0.230
0.32 0.014 0.089 0.264 0.511 0.744 0.897 0.969 0.993 0.999 1.000 0.010 0.065 0.208
0.33 0.012 0.078 0.241 0.482 0.719 0.883 0.963 0.992 0.999 1.000 0.008 0.057 0.188
0.34 0.010 0.069 0.220 0.454 0.694 0.868 0.957 0.990 0.998 1.000 0.007 0.049 0.169
0.35 0.009 0.061 0.200 0.426 0.668 0.851 0.950 0.988 0.998 1.000 0.006 0.042 0.151
0.36 0.007 0.053 0.181 0.398 0.642 0.834 0.942 0.985 0.997 1.000 0.005 0.037 0.135
0.37 0.006 0.046 0.164 0.371 0.615 0.815 0.933 0.982 0.997 1.000 0.004 0.031 0.120
0.38 0.005 0.040 0.148 0.345 0.588 0.796 0.923 0.979 0.996 1.000 0.003 0.027 0.107
0.39 0.004 0.035 0.133 0.320 0.560 0.775 0.912 0.975 0.995 0.999 1.000 0.003 0.023 0.095
0.40 0.004 0.030 0.119 0.296 0.533 0.753 0.901 0.971 0.994 0.999 1.000 0.002 0.020 0.083
0.41 0.003 0.026 0.106 0.273 0.505 0.731 0.888 0.966 0.993 0.999 1.000 0.002 0.017 0.073
0.42 0.002 0.022 0.094 0.251 0.478 0.708 0.874 0.960 0.991 0.999 1.000 0.001 0.014 0.064
0.43 0.002 0.019 0.084 0.230 0.451 0.683 0.859 0.954 0.990 0.999 1.000 0.001 0.012 0.056
0.44 0.002 0.016 0.074 0.210 0.424 0.659 0.843 0.947 0.988 0.998 1.000 0.001 0.010 0.049
0.45 0.001 0.014 0.065 0.191 0.397 0.633 0.826 0.939 0.985 0.998 1.000 0.001 0.008 0.042
0.46 0.001 0.012 0.057 0.173 0.371 0.607 0.808 0.930 0.982 0.997 1.000 0.001 0.007 0.036
0.47 0.001 0.010 0.050 0.157 0.346 0.581 0.789 0.921 0.979 0.997 1.000 0.000 0.006 0.031
0.48 0.001 0.008 0.044 0.141 0.321 0.554 0.769 0.910 0.976 0.996 1.000 0.000 0.005 0.027
0.49 0.001 0.007 0.038 0.127 0.297 0.527 0.748 0.899 0.972 0.995 1.000 0.000 0.004 0.023
0.50 0.000 0.006 0.033 0.113 0.274 0.500 0.726 0.887 0.967 0.994 1.000 0.000 0.003 0.019
18
Table 7: Binomial Distribution (cont'd)
Pr ()X k
£
n=1
p k=3 4 5 6 7 8 9 10 11 k=0 1 2 3 4
0.01 0.878 0.993 1.000
0.02 1.000 0.769 0.973 0.998 1.000
0.03 1.000 0.673 0.944 0.994 1.000
0.04 0.999 1.000 0.588 0.907 0.986 0.999 1.000
0.05 0.998 1.000 0.513 0.865 0.975 0.997 1.000
0.06 0.996 1.000 0.447 0.819 0.961 0.994 0.999
0.07 0.992 0.999 1.000 0.389 0.770 0.942 0.990 0.999
0.08 0.988 0.998 1.000 0.338 0.721 0.920 0.984 0.998
0.09 0.982 0.997 1.000 0.293 0.671 0.895 0.976 0.996
0.10 0.974 0.996 0.999 1.000 0.254 0.621 0.866 0.966 0.994
0.11 0.965 0.993 0.999 1.000 0.220 0.573 0.835 0.954 0.990
0.12 0.954 0.991 0.999 1.000 0.190 0.526 0.802 0.939 0.986
0.13 0.940 0.987 0.998 1.000 0.164 0.481 0.766 0.922 0.981
0.14 0.925 0.982 0.997 1.000 0.141 0.439 0.730 0.903 0.974
0.15 0.908 0.976 0.995 0.999 1.000 0.121 0.398 0.692 0.882 0.966
0.16 0.889 0.969 0.994 0.999 1.000 0.104 0.360 0.654 0.859 0.956
0.17 0.868 0.961 0.991 0.999 1.000 0.089 0.325 0.615 0.833 0.945
0.18 0.845 0.951 0.988 0.998 1.000 0.076 0.292 0.577 0.806 0.932
0.19 0.820 0.940 0.985 0.997 1.000 0.065 0.262 0.539 0.777 0.917
0.20 0.795 0.927 0.981 0.996 0.999 1.000 0.055 0.234 0.502 0.747 0.901
0.21 0.767 0.913 0.976 0.995 0.999 1.000 0.047 0.208 0.465 0.716 0.883
0.22 0.739 0.898 0.970 0.993 0.999 1.000 0.040 0.185 0.430 0.684 0.863
0.23 0.710 0.881 0.963 0.991 0.998 1.000 0.033 0.163 0.396 0.651 0.841
0.24 0.680 0.862 0.955 0.989 0.998 1.000 0.028 0.144 0.364 0.618 0.818
0.25 0.649 0.842 0.946 0.986 0.997 1.000 0.024 0.127 0.333 0.584 0.794
0.26 0.618 0.821 0.935 0.982 0.996 0.999 1.000 0.020 0.111 0.303 0.551 0.768
0.27 0.586 0.798 0.924 0.978 0.995 0.999 1.000 0.017 0.097 0.275 0.517 0.741
0.28 0.555 0.775 0.911 0.973 0.994 0.999 1.000 0.014 0.085 0.249 0.485 0.713
0.29 0.524 0.750 0.897 0.968 0.992 0.999 1.000 0.012 0.074 0.225 0.452 0.684
0.30 0.493 0.724 0.882 0.961 0.991 0.998 1.000 0.010 0.064 0.202 0.421 0.654
0.31 0.462 0.697 0.866 0.954 0.988 0.998 1.000 0.008 0.055 0.181 0.390 0.624
0.32 0.432 0.669 0.848 0.946 0.986 0.997 1.000 0.007 0.047 0.162 0.360 0.593
0.33 0.403 0.641 0.829 0.937 0.982 0.996 1.000 0.005 0.041 0.144 0.332 0.562
0.34 0.374 0.612 0.809 0.927 0.979 0.996 0.999 1.000 0.005 0.035 0.128 0.304 0.531
0.35 0.347 0.583 0.787 0.915 0.974 0.994 0.999 1.000 0.004 0.030 0.113 0.278 0.501
0.36 0.320 0.554 0.765 0.903 0.970 0.993 0.999 1.000 0.003 0.025 0.100 0.254 0.470
0.37 0.295 0.525 0.741 0.889 0.964 0.991 0.999 1.000 0.002 0.021 0.088 0.230 0.440
0.38 0.270 0.496 0.717 0.875 0.958 0.990 0.998 1.000 0.002 0.018 0.077 0.208 0.410
0.39 0.247 0.467 0.691 0.859 0.951 0.987 0.998 1.000 0.002 0.015 0.067 0.188 0.381
0.40 0.225 0.438 0.665 0.842 0.943 0.985 0.997 1.000 0.001 0.013 0.058 0.169 0.353
0.41 0.205 0.410 0.638 0.824 0.934 0.982 0.997 1.000 0.001 0.011 0.050 0.151 0.326
0.42 0.185 0.383 0.611 0.804 0.924 0.978 0.996 0.999 1.000 0.001 0.009 0.043 0.134 0.300
0.43 0.167 0.356 0.583 0.784 0.913 0.974 0.995 0.999 1.000 0.001 0.007 0.037 0.119 0.275
0.44 0.150 0.330 0.555 0.762 0.901 0.970 0.994 0.999 1.000 0.001 0.006 0.032 0.106 0.251
0.45 0.134 0.304 0.527 0.739 0.888 0.964 0.992 0.999 1.000 0.000 0.005 0.027 0.093 0.228
0.46 0.120 0.280 0.499 0.716 0.874 0.959 0.990 0.999 1.000 0.000 0.004 0.023 0.081 0.206
0.47 0.107 0.257 0.470 0.691 0.859 0.952 0.989 0.998 1.000 0.000 0.003 0.019 0.071 0.186
0.48 0.094 0.235 0.442 0.666 0.842 0.944 0.986 0.998 1.000 0.000 0.003 0.016 0.062 0.167
0.49 0.083 0.214 0.415 0.640 0.825 0.936 0.984 0.997 1.000 0.000 0.002 0.014 0.054 0.150
0.50 0.073 0.194 0.387 0.613 0.806 0.927 0.981 0.997 1.000 0.000 0.002 0.011 0.046 0.133

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Department of Economics
Statistical Tables for Economists Index for Statistical Tables e l b a T 1 Nor Dim st a r l i bu t i o n 1 2 Stude Di n s t t - r t i bu t i 2o n 3 Chi-Squ Da i r s e trd i butio n 3 4 F-Distrib(ut a i. o =) n 4- 0016 5 F-Distrib(ut a i. o =) n 7- 0059 6 F-Distrib(ut a i o =. ) n 0 1 10-12 7 Bino Dm is ita r l i b u t i 1o 3n - 27 8 Poi Dsiso trn i bu t i o n 2 8-30 9 Durbin-Wa C trs i V o ti aln cu al e s 31 10 Mackinn C o ri V n ti a l 's cu 3 al e 2 s 11 Joha Cn r s i Vtei aln cu al e s 33 1
Table 1: Normal Distribution F(z) z P ) r()(Z £ z = F z z F(z) z F(z) z F(z) z F(z) z F(z) z F(z) z F(z)
0.00 0.500 0.50 0.691 1.00 0.841 1.50 0.933 2.00 0.977 2.50 0.994 3.00 0.999
0.01 0.504 0.51 0.695 1.01 0.844 1.51 0.934 2.01 0.978 2.51 0.994 3.01 0.999
0.02 0.508 0.52 0.698 1.02 0.846 1.52 0.936 2.02 0.978 2.52 0.994 3.02 0.999
0.03 0.512 0.53 0.702 1.03 0.848 1.53 0.937 2.03 0.979 2.53 0.994 3.03 0.999
0.04 0.516 0.54 0.705 1.04 0.851 1.54 0.938 2.04 0.979 2.54 0.994 3.04 0.999
0.05 0.520 0.55 0.709 1.05 0.853 1.55 0.939 2.05 0.980 2.55 0.995 3.05 0.999
0.06 0.524 0.56 0.712 1.06 0.855 1.56 0.941 2.06 0.980 2.56 0.995 3.06 0.999
0.07 0.528 0.57 0.716 1.07 0.858 1.57 0.942 2.07 0.981 2.57 0.995 3.07 0.999
0.08 0.532 0.58 0.719 1.08 0.860 1.58 0.943 2.08 0.981 2.58 0.995 3.08 0.999
0.09 0.536 0.59 0.722 1.09 0.862 1.59 0.944 2.09 0.982 2.59 0.995 3.09 0.999
0.10 0.540 0.60 0.726 1.10 0.864 1.60 0.945 2.10 0.982 2.60 0.995 3.10 0.999
0.11 0.544 0.61 0.729 1.11 0.867 1.61 0.946 2.11 0.983 2.61 0.995 3.11 0.999
0.12 0.548 0.62 0.732 1.12 0.869 1.62 0.947 2.12 0.983 2.62 0.996 3.12 0.999
0.13 0.552 0.63 0.736 1.13 0.871 1.63 0.948 2.13 0.983 2.63 0.996 3.13 0.999
0.14 0.556 0.64 0.739 1.14 0.873 1.64 0.949 2.14 0.984 2.64 0.996 3.14 0.999
0.15 0.560 0.65 0.742 1.15 0.875 1.65 0.951 2.15 0.984 2.65 0.996 3.15 0.999
0.16 0.564 0.66 0.745 1.16 0.877 1.66 0.952 2.16 0.985 2.66 0.996 3.16 0.999
0.17 0.567 0.67 0.749 1.17 0.879 1.67 0.953 2.17 0.985 2.67 0.996 3.17 0.999
0.18 0.571 0.68 0.752 1.18 0.881 1.68 0.954 2.18 0.985 2.68 0.996 3.18 0.999
0.19 0.575 0.69 0.755 1.19 0.883 1.69 0.954 2.19 0.986 2.69 0.996 3.19 0.999
0.20 0.579 0.70 0.758 1.20 0.885 1.70 0.955 2.20 0.986 2.70 0.997 3.20 0.999
0.21 0.583 0.71 0.761 1.21 0.887 1.71 0.956 2.21 0.986 2.71 0.997 3.21 0.999
0.22 0.587 0.72 0.764 1.22 0.889 1.72 0.957 2.22 0.987 2.72 0.997 3.22 0.999
0.23 0.591 0.73 0.767 1.23 0.891 1.73 0.958 2.23 0.987 2.73 0.997 3.23 0.999
0.24 0.595 0.74 0.770 1.24 0.893 1.74 0.959 2.24 0.987 2.74 0.997 3.24 0.999
0.25 0.599 0.75 0.773 1.25 0.894 1.75 0.960 2.25 0.988 2.75 0.997 3.25 0.999
0.26 0.603 0.76 0.776 1.26 0.896 1.76 0.961 2.26 0.988 2.76 0.997 3.26 0.999
0.27 0.606 0.77 0.779 1.27 0.898 1.77 0.962 2.27 0.988 2.77 0.997 3.27 0.999
0.28 0.610 0.78 0.782 1.28 0.900 1.78 0.962 2.28 0.989 2.78 0.997 3.28 0.999
0.29 0.614 0.79 0.785 1.29 0.901 1.79 0.963 2.29 0.989 2.79 0.997 3.29 0.999
0.30 0.618 0.80 0.788 1.30 0.903 1.80 0.964 2.30 0.989 2.80 0.997 3.30 1.000
0.31 0.622 0.81 0.791 1.31 0.905 1.81 0.965 2.31 0.990 2.81 0.998 3.31 1.000
0.32 0.626 0.82 0.794 1.32 0.907 1.82 0.966 2.32 0.990 2.82 0.998 3.32 1.000
0.33 0.629 0.83 0.797 1.33 0.908 1.83 0.966 2.33 0.990 2.83 0.998 3.33 1.000
0.34 0.633 0.84 0.800 1.34 0.910 1.84 0.967 2.34 0.990 2.84 0.998 3.34 1.000
0.35 0.637 0.85 0.802 1.35 0.911 1.85 0.968 2.35 0.991 2.85 0.998 3.35 1.000
0.36 0.641 0.86 0.805 1.36 0.913 1.86 0.969 2.36 0.991 2.86 0.998 3.36 1.000
0.37 0.644 0.87 0.808 1.37 0.915 1.87 0.969 2.37 0.991 2.87 0.998 3.37 1.000
0.38 0.648 0.88 0.811 1.38 0.916 1.88 0.970 2.38 0.991 2.88 0.998 3.38 1.000
0.39 0.652 0.89 0.813 1.39 0.918 1.89 0.971 2.39 0.992 2.89 0.998 3.39 1.000
0.40 0.655 0.90 0.816 1.40 0.919 1.90 0.971 2.40 0.992 2.90 0.998 3.40 1.000
0.41 0.659 0.91 0.819 1.41 0.921 1.91 0.972 2.41 0.992 2.91 0.998 3.41 1.000
0.42 0.663 0.92 0.821 1.42 0.922 1.92 0.973 2.42 0.992 2.92 0.998 3.42 1.000
0.43 0.666 0.93 0.824 1.43 0.924 1.93 0.973 2.43 0.992 2.93 0.998 3.43 1.000
0.44 0.670 0.94 0.826 1.44 0.925 1.94 0.974 2.44 0.993 2.94 0.998 3.44 1.000
0.45 0.674 0.95 0.829 1.45 0.926 1.95 0.974 2.45 0.993 2.95 0.998 3.45 1.000
0.46 0.677 0.96 0.831 1.46 0.928 1.96 0.975 2.46 0.993 2.96 0.998 3.46 1.000
0.47 0.681 0.97 0.834 1.47 0.929 1.97 0.976 2.47 0.993 2.97 0.999 3.47 1.000
0.48 0.684 0.98 0.836 1.48 0.931 1.98 0.976 2.48 0.993 2.98 0.999 3.48 1.000
0.49 0.688 0.99 0.839 1.49 0.932 1.99 0.977 2.49 0.994 2.99 0.999 3.49 1.000 2
Table 2: Student t-distribution 1-a a t n,a
Pr()X > t=naa , a n 0.10 0.05 0.025 0.01 0.005 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
31 1.309 1.696 2.040 2.453 2.744
32 1.309 1.694 2.037 2.449 2.738
33 1.308 1.692 2.035 2.445 2.733
34 1.307 1.691 2.032 2.441 2.728
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
60 1.296 1.671 2.000 2.390 2.660
70 1.294 1.667 1.994 2.381 2.648
80 1.292 1.664 1.990 2.374 2.639
90 1.291 1.662 1.987 2.368 2.632
100 1.290 1.660 1.984 2.364 2.626
¥ 1.282 1.645 1.960 2.327 2.576 3
Table 3: Chi-Squared Distribution 1-a a 2 c n Pr( ) X³ c2 n,a a n 0.995 0.99 0.975 0.95 0.9 0.1 0.05 0.025 0.01 0.005
1 0.00 0.00 0.00 0.00 0.02 2.71 3.84 5.02 6.63 7.88
2 0.01 0.02 0.05 0.10 0.21 4.61 5.99 7.38 9.21 10.60
3 0.07 0.11 0.22 0.35 0.58 6.25 7.81 9.35 11.34 12.84
4 0.21 0.30 0.48 0.71 1.06 7.78 9.49 11.14 13.28 14.86
5 0.41 0.55 0.83 1.15 1.61 9.24 11.07 12.83 15.09 16.75
6 0.68 0.87 1.24 1.64 2.20 10.64 12.59 14.45 16.81 18.55
7 0.99 1.24 1.69 2.17 2.83 12.02 14.07 16.01 18.48 20.28
8 1.34 1.65 2.18 2.73 3.49 13.36 15.51 17.53 20.09 21.95
9 1.73 2.09 2.70 3.33 4.17 14.68 16.92 19.02 21.67 23.59 10
2 .16 2.56 3.25 3.94 4.87 15.99 18.31 20.48 23.21 25.19 11
2 .60 3.05 3.82 4.57 5.58 17.28 19.68 21.92 24.72 26.76 12
3 .07 3.57 4.40 5.23 6.30 18.55 21.03 23.34 26.22 28.30 13
3 .57 4.11 5.01 5.89 7.04 19.81 22.36 24.74 27.69 29.82 14
4 .07 4.66 5.63 6.57 7.79 21.06 23.68 26.12 29.14 31.32 15
4 .60 5.23 6.26 7.26 8.55 22.31 25.00 27.49 30.58 32.80 16
5 .14 5.81 6.91 7.96 9.31 23.54 26.30 28.85 32.00 34.27 17 5 .70 6.41 7.56 8.67 10.09 24.77 27.59 30.19 33.41 35.72 18 6 .26 7.01 8.23 9.39 10.86 25.99 28.87 31.53 34.81 37.16
19 6.84 7.63 8.91 10.12 11.65 27.20 30.14 32.85 36.19 38.58
20 7.43 8.26 9.59 10.85 12.44 28.41 31.41 34.17 37.57 40.00
21 8.03 8.90 10.28 11.59 13.24 29.62 32.67 35.48 38.93 41.40
22 8.64 9.54 10.98 12.34 14.04 30.81 33.92 36.78 40.29 42.80
23 9.26 10.20 11.69 13.09 14.85 32.01 35.17 38.08 41.64 44.18
24 9.89 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98 45.56
25 10.52 11.52 13.12 14.61 16.47 34.38 37.65 40.65 44.31 46.93
26 11.16 12.20 13.84 15.38 17.29 35.56 38.89 41.92 45.64 48.29
27 11.81 12.88 14.57 16.15 18.11 36.74 40.11 43.19 46.96 49.64
28 12.46 13.56 15.31 16.93 18.94 37.92 41.34 44.46 48.28 50.99
29 13.12 14.26 16.05 17.71 19.77 39.09 42.56 45.72 49.59 52.34
30 13.79 14.95 16.79 18.49 20.60 40.26 43.77 46.98 50.89 53.67
31 14.46 15.66 17.54 19.28 21.43 41.42 44.99 48.23 52.19 55.00
32 15.13 16.36 18.29 20.07 22.27 42.58 46.19 49.48 53.49 56.33
33 15.82 17.07 19.05 20.87 23.11 43.75 47.40 50.73 54.78 57.65
34 16.50 17.79 19.81 21.66 23.95 44.90 48.60 51.97 56.06 58.96
35 17.19 18.51 20.57 22.47 24.80 46.06 49.80 53.20 57.34 60.27
40 20.71 22.16 24.43 26.51 29.05 51.81 55.76 59.34 63.69 66.77
45 24.31 25.90 28.37 30.61 33.35 57.51 61.66 65.41 69.96 73.17
50 27.99 29.71 32.36 34.76 37.69 63.17 67.50 71.42 76.15 79.49
60 35.53 37.48 40.48 43.19 46.46 74.40 79.08 83.30 88.38 91.95
70 43.28 45.44 48.76 51.74 55.33 85.53 90.53 95.02 100.43 104.21
80 51.17 53.54 57.15 60.39 64.28 96.58 101.88 106.63 112.33 116.32
90 59.20 61.75 65.65 69.13 73.29 107.57 113.15 118.14 124.12 128.30
100 67.33 70.06 74.22 77.93 82.36 118.50 124.34 129.56 135.81 140.17 4
Table 4: F-distribution (a=.0 ) 01 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 01 n1 n2 1 2 3 4 5 6 7 8 9 10
1 4051.3 4999.5 5403.5 5624.8 5763.9 5859.2 5928.6 5981.3 6022.7 6056.1
2 98.50 99.00 99.22 99.33 99.40 99.44 99.48 99.50 99.52 99.53
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 6 13.75 10.92
9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7 12.25
9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 8 11.26
8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 9 10.56
8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 10 10.04
7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 11
9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 12
9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 13
9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 14
8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 15
8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 16
8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 17
8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 18
8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 19
8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 20
8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 21
8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 22
7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 23
7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 24
7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 25
7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 26
7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 27
7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 28
7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 29
7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 30
7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 31
7.53 5.36 4.48 3.99 3.67 3.45 3.28 3.15 3.04 2.96 32
7.50 5.34 4.46 3.97 3.65 3.43 3.26 3.13 3.02 2.93 33
7.47 5.31 4.44 3.95 3.63 3.41 3.24 3.11 3.00 2.91 34
7.44 5.29 4.42 3.93 3.61 3.39 3.22 3.09 2.98 2.89 35
7.42 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.88 40
7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 45
7.23 5.11 4.25 3.77 3.45 3.23 3.07 2.94 2.83 2.74 50
7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70 60
7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 120
6. 85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47
¥ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32 5
Table 4: F-distribution (a=.0 ) 01 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 01 n1
n2 11 12 13 14 15 16 17 18 19 20
1 6083.6 6106.6 6126.2 6142.9 6157.6 6170.4 6181.7 6191.8 6200.9 6209.0
2 99.54 99.55 99.56 99.57 99.58 99.58 99.59 99.59 99.60 99.60
3 27.13 27.05 26.98 26.92 26.87 26.83 26.79 26.75 26.72 26.69
4 14.45 14.37 14.31 14.25 14.20 14.15 14.11 14.08 14.05 14.02
5 9.96 9.89 9.82 9.77 9.72 9.68 9.64 9.61 9.58 9.55
6 7.79 7.72 7.66 7.60 7.56 7.52 7.48 7.45 7.42 7.40
7 6.54 6.47 6.41 6.36 6.31 6.27 6.24 6.21 6.18 6.16
8 5.73 5.67 5.61 5.56 5.52 5.48 5.44 5.41 5.38 5.36
9 5.18 5.11 5.05 5.01 4.96 4.92 4.89 4.86 4.83 4.81 10
4.77 4.71 4.65 4.60 4.56 4.52 4.49 4.46 4.43 4.41 11
4.46 4.40 4.34 4.29 4.25 4.21 4.18 4.15 4.12 4.10 12
4.22 4.16 4.10 4.05 4.01 3.97 3.94 3.91 3.88 3.86 13
4.02 3.96 3.91 3.86 3.82 3.78 3.75 3.72 3.69 3.66 14
3.86 3.80 3.75 3.70 3.66 3.62 3.59 3.56 3.53 3.51 15
3.73 3.67 3.61 3.56 3.52 3.49 3.45 3.42 3.40 3.37 16
3.62 3.55 3.50 3.45 3.41 3.37 3.34 3.31 3.28 3.26 17
3.52 3.46 3.40 3.35 3.31 3.27 3.24 3.21 3.19 3.16 18
3.43 3.37 3.32 3.27 3.23 3.19 3.16 3.13 3.10 3.08 19
3.36 3.30 3.24 3.19 3.15 3.12 3.08 3.05 3.03 3.00 20
3.29 3.23 3.18 3.13 3.09 3.05 3.02 2.99 2.96 2.94 21
3.24 3.17 3.12 3.07 3.03 2.99 2.96 2.93 2.90 2.88 22
3.18 3.12 3.07 3.02 2.98 2.94 2.91 2.88 2.85 2.83 23
3.14 3.07 3.02 2.97 2.93 2.89 2.86 2.83 2.80 2.78 24
3.09 3.03 2.98 2.93 2.89 2.85 2.82 2.79 2.76 2.74 25
3.06 2.99 2.94 2.89 2.85 2.81 2.78 2.75 2.72 2.70 26
3.02 2.96 2.90 2.86 2.81 2.78 2.75 2.72 2.69 2.66 27
2.99 2.93 2.87 2.82 2.78 2.75 2.71 2.68 2.66 2.63 28
2.96 2.90 2.84 2.79 2.75 2.72 2.68 2.65 2.63 2.60 29
2.93 2.87 2.81 2.77 2.73 2.69 2.66 2.63 2.60 2.57 30
2.91 2.84 2.79 2.74 2.70 2.66 2.63 2.60 2.57 2.55 31
2.88 2.82 2.77 2.72 2.68 2.64 2.61 2.58 2.55 2.52 32
2.86 2.80 2.74 2.70 2.65 2.62 2.58 2.55 2.53 2.50 33
2.84 2.78 2.72 2.68 2.63 2.60 2.56 2.53 2.51 2.48 34
2.82 2.76 2.70 2.66 2.61 2.58 2.54 2.51 2.49 2.46 35
2.80 2.74 2.69 2.64 2.60 2.56 2.53 2.50 2.47 2.44 40
2.73 2.66 2.61 2.56 2.52 2.48 2.45 2.42 2.39 2.37 45
2.67 2.61 2.55 2.51 2.46 2.43 2.39 2.36 2.34 2.31 50
2.63 2.56 2.51 2.46 2.42 2.38 2.35 2.32 2.29 2.27 60
2.56 2.50 2.44 2.39 2.35 2.31 2.28 2.25 2.22 2.20 120
2. 40 2.34 2.28 2.23 2.19 2.15 2.12 2.09 2.06 2.03
¥ 2.25 2.18 2.13 2.08 2.04 2.00 1.97 1.93 1.90 1.88 6
Table 4: F-distribution (a=.0 ) 01 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 01 n1
n2 21 22 23 24 25 30 35 40 60 120 ¥ 1
6216.4 6223.2 6229.3 6234.9 6240.1 6261.0 6275.9 6287.1 6313.4 6339.7 6365.9
2 99.60 99.61 99.61 99.61 99.61 99.62 99.63 99.63 99.64 99.65 99.50
3 26.66 26.64 26.62 26.60 26.58 26.47 26.42 26.38 26.29 26.19 26.13
4 13.99 13.97 13.95 13.93 13.91 13.84 13.78 13.75 13.65 13.56 13.46
5 9.53 9.51 9.49 9.47 9.45 9.38 9.33 9.29 9.20 9.11 9.02
6 7.37 7.35 7.33 7.31 7.30 7.23 7.18 7.14 7.06 6.97 6.88
7 6.13 6.11 6.09 6.07 6.06 5.99 5.94 5.91 5.82 5.74 5.65
8 5.34 5.32 5.30 5.28 5.26 5.20 5.15 5.12 5.03 4.95 4.86
9 4.79 4.77 4.75 4.73 4.71 4.65 4.60 4.57 4.48 4.40 4.31
10 4.38 4.36 4.34 4.33 4.31 4.25 4.20 4.16 4.08 4.00 3.91
11 4.08 4.06 4.04 4.02 4.01 3.94 3.89 3.86 3.78 3.69 3.60
12 3.84 3.82 3.80 3.78 3.76 3.70 3.65 3.62 3.54 3.45 3.36
13 3.64 3.62 3.60 3.59 3.57 3.51 3.46 3.43 3.34 3.25 3.17
14 3.48 3.46 3.44 3.43 3.41 3.35 3.30 3.27 3.18 3.09 3.00
15 3.35 3.33 3.31 3.29 3.28 3.21 3.17 3.13 3.05 2.96 2.87
16 3.24 3.22 3.20 3.18 3.16 3.10 3.05 3.02 2.93 2.84 2.75
17 3.14 3.12 3.10 3.08 3.07 3.00 2.96 2.92 2.83 2.75 2.65
18 3.05 3.03 3.02 3.00 2.98 2.92 2.87 2.84 2.75 2.66 2.57
19 2.98 2.96 2.94 2.92 2.91 2.84 2.80 2.76 2.67 2.58 2.49
20 2.92 2.90 2.88 2.86 2.84 2.78 2.73 2.69 2.61 2.52 2.42
21 2.86 2.84 2.82 2.80 2.79 2.72 2.67 2.64 2.55 2.46 2.36
22 2.81 2.78 2.77 2.75 2.73 2.67 2.62 2.58 2.50 2.40 2.31
23 2.76 2.74 2.72 2.70 2.69 2.62 2.57 2.54 2.45 2.35 2.26
24 2.72 2.70 2.68 2.66 2.64 2.58 2.53 2.49 2.40 2.31 2.21
25 2.68 2.66 2.64 2.62 2.60 2.54 2.49 2.45 2.36 2.27 2.17
26 2.64 2.62 2.60 2.58 2.57 2.50 2.45 2.42 2.33 2.23 2.13
27 2.61 2.59 2.57 2.55 2.54 2.47 2.42 2.38 2.29 2.20 2.10
28 2.58 2.56 2.54 2.52 2.51 2.44 2.39 2.35 2.26 2.17 2.06
29 2.55 2.53 2.51 2.49 2.48 2.41 2.36 2.33 2.23 2.14 2.03
30 2.53 2.51 2.49 2.47 2.45 2.39 2.34 2.30 2.21 2.11 2.01
31 2.50 2.48 2.46 2.45 2.43 2.36 2.31 2.27 2.18 2.09 1.98
32 2.48 2.46 2.44 2.42 2.41 2.34 2.29 2.25 2.16 2.06 1.96
33 2.46 2.44 2.42 2.40 2.39 2.32 2.27 2.23 2.14 2.04 1.93
34 2.44 2.42 2.40 2.38 2.37 2.30 2.25 2.21 2.12 2.02 1.91
35 2.42 2.40 2.38 2.36 2.35 2.28 2.23 2.19 2.10 2.00 1.89
40 2.35 2.33 2.31 2.29 2.27 2.20 2.15 2.11 2.02 1.92 1.80
45 2.29 2.27 2.25 2.23 2.21 2.14 2.09 2.05 1.96 1.85 1.74
50 2.24 2.22 2.20 2.18 2.17 2.10 2.05 2.01 1.91 1.80 1.68
60 2.17 2.15 2.13 2.12 2.10 2.03 1.98 1.94 1.84 1.73 1.60 120
2 .01 1.99 1.97 1.95 1.93 1.86 1.81 1.76 1.66 1.53 1.38
¥ 1.85 1.83 1.81 1.79 1.77 1.70 1.64 1.59 1.47 1.32 1.00 7
Table 5: F-distribution (a=.0 ) 05 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 05 n1 n2 1 2 3 4 5 6 7 8 9 10
1 161.55 199.71 215.95 224.84 230.42 234.25 237.04 239.16 240.82 242.16
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 3 10.13
9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.73
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 10
4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 11
4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 12
4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 13
4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 14
4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 15
4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 16
4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 17
4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 18
4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 19
4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 20
4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 21
4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 22
4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 23
4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 24
4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 25
4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 26
4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 27
4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 28
4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 29
4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 30
4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 31
4.16 3.30 2.91 2.68 2.52 2.41 2.32 2.25 2.20 2.15 32
4.15 3.29 2.90 2.67 2.51 2.40 2.31 2.24 2.19 2.14 33
4.14 3.28 2.89 2.66 2.50 2.39 2.30 2.23 2.18 2.13 34
4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17 2.12 35
4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11 40
4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 45
4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.10 2.05 50
4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03 60
4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 120
3. 92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91
¥ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 8
Table 5: F-distribution (a=.0 ) 05 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 05 n1
n2 11 12 13 14 15 16 17 18 19 20
1 243.26 244.19 244.97 245.65 246.24 246.75 247.20 247.61 247.97 248.30
2 19.40 19.41 19.42 19.44 19.44 19.45 19.45 19.45 19.46 19.46
3 8.76 8.74 8.73 8.71 8.70 8.69 8.68 8.67 8.67 8.66
4 5.94 5.91 5.89 5.87 5.86 5.84 5.83 5.82 5.81 5.80
5 4.70 4.68 4.66 4.64 4.62 4.60 4.59 4.58 4.57 4.56
6 4.03 4.00 3.98 3.96 3.94 3.92 3.91 3.90 3.88 3.87
7 3.60 3.57 3.55 3.53 3.51 3.49 3.48 3.47 3.46 3.44
8 3.31 3.28 3.26 3.24 3.22 3.20 3.19 3.17 3.16 3.15
9 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.95 2.94 10
2.94 2.91 2.89 2.86 2.85 2.83 2.81 2.80 2.79 2.77 11
2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.67 2.66 2.65 12
2.72 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.56 2.54 13
2.63 2.60 2.58 2.55 2.53 2.51 2.50 2.48 2.47 2.46 14
2.57 2.53 2.51 2.48 2.46 2.44 2.43 2.41 2.40 2.39 15
2.51 2.48 2.45 2.42 2.40 2.38 2.37 2.35 2.34 2.33 16
2.46 2.42 2.40 2.37 2.35 2.33 2.32 2.30 2.29 2.28 17
2.41 2.38 2.35 2.33 2.31 2.29 2.27 2.26 2.24 2.23 18
2.37 2.34 2.31 2.29 2.27 2.25 2.23 2.22 2.20 2.19 19
2.34 2.31 2.28 2.26 2.23 2.21 2.20 2.18 2.17 2.16 20
2.31 2.28 2.25 2.22 2.20 2.18 2.17 2.15 2.14 2.12 21
2.28 2.25 2.22 2.20 2.18 2.16 2.14 2.12 2.11 2.10 22
2.26 2.23 2.20 2.17 2.15 2.13 2.11 2.10 2.08 2.07 23
2.24 2.20 2.18 2.15 2.13 2.11 2.09 2.08 2.06 2.05 24
2.22 2.18 2.15 2.13 2.11 2.09 2.07 2.05 2.04 2.03 25
2.20 2.16 2.14 2.11 2.09 2.07 2.05 2.04 2.02 2.01 26
2.18 2.15 2.12 2.09 2.07 2.05 2.03 2.02 2.00 1.99 27
2.17 2.13 2.10 2.08 2.06 2.04 2.02 2.00 1.99 1.97 28
2.15 2.12 2.09 2.06 2.04 2.02 2.00 1.99 1.97 1.96 29
2.14 2.10 2.08 2.05 2.03 2.01 1.99 1.97 1.96 1.94 30
2.13 2.09 2.06 2.04 2.01 1.99 1.98 1.96 1.95 1.93 31
2.11 2.08 2.05 2.03 2.00 1.98 1.96 1.95 1.93 1.92 32
2.10 2.07 2.04 2.01 1.99 1.97 1.95 1.94 1.92 1.91 33
2.09 2.06 2.03 2.00 1.98 1.96 1.94 1.93 1.91 1.90 34
2.08 2.05 2.02 1.99 1.97 1.95 1.93 1.92 1.90 1.89 35
2.07 2.04 2.01 1.99 1.96 1.94 1.92 1.91 1.89 1.88 40
2.04 2.00 1.97 1.95 1.92 1.90 1.89 1.87 1.85 1.84 45
2.01 1.97 1.94 1.92 1.89 1.87 1.86 1.84 1.82 1.81 50
1.99 1.95 1.92 1.89 1.87 1.85 1.83 1.81 1.80 1.78 60
1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.78 1.76 1.75 120
1. 87 1.83 1.80 1.78 1.75 1.73 1.71 1.69 1.67 1.66
¥ 1.79 1.75 1.72 1.69 1.67 1.64 1.62 1.60 1.59 1.57 9
Table 5: F-distribution (a=.0 ) 05 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a= . 0 05 n1
n2 21 22 23 24 25 30 35 40 60 120 ¥ 1
248.60 248.87 249.11 249.34 249.55 250.39 250.98 251.44 270.27 271.40 254.31
2 19.46 19.46 19.47 19.47 19.47 19.48 19.48 19.49 19.49 19.50 19.50
3 8.65 8.65 8.64 8.64 8.63 8.62 8.60 8.59 8.57 8.55 8.53
4 5.79 5.79 5.78 5.77 5.77 5.75 5.73 5.72 5.69 5.66 5.63
5 4.55 4.54 4.53 4.53 4.52 4.50 4.48 4.46 4.43 4.40 4.36
6 3.86 3.86 3.85 3.84 3.83 3.81 3.79 3.77 3.74 3.70 3.67
7 3.43 3.43 3.42 3.41 3.40 3.38 3.36 3.34 3.30 3.27 3.23
8 3.14 3.13 3.12 3.12 3.11 3.08 3.06 3.04 3.01 2.97 2.93
9 2.93 2.92 2.91 2.90 2.89 2.86 2.84 2.83 2.79 2.75 2.71
10 2.76 2.75 2.75 2.74 2.73 2.70 2.68 2.66 2.62 2.58 2.54
11 2.64 2.63 2.62 2.61 2.60 2.57 2.55 2.53 2.49 2.45 2.40
12 2.53 2.52 2.51 2.51 2.50 2.47 2.44 2.43 2.38 2.34 2.30
13 2.45 2.44 2.43 2.42 2.41 2.38 2.36 2.34 2.30 2.25 2.21
14 2.38 2.37 2.36 2.35 2.34 2.31 2.28 2.27 2.22 2.18 2.13
15 2.32 2.31 2.30 2.29 2.28 2.25 2.22 2.20 2.16 2.11 2.07
16 2.26 2.25 2.24 2.24 2.23 2.19 2.17 2.15 2.11 2.06 2.01
17 2.22 2.21 2.20 2.19 2.18 2.15 2.12 2.10 2.06 2.01 1.96
18 2.18 2.17 2.16 2.15 2.14 2.11 2.08 2.06 2.02 1.97 1.92
19 2.14 2.13 2.12 2.11 2.11 2.07 2.05 2.03 1.98 1.93 1.88
20 2.11 2.10 2.09 2.08 2.07 2.04 2.01 1.99 1.95 1.90 1.84
21 2.08 2.07 2.06 2.05 2.05 2.01 1.98 1.96 1.92 1.87 1.81
22 2.06 2.05 2.04 2.03 2.02 1.98 1.96 1.94 1.89 1.84 1.78
23 2.04 2.02 2.01 2.01 2.00 1.96 1.93 1.91 1.86 1.81 1.76
24 2.01 2.00 1.99 1.98 1.97 1.94 1.91 1.89 1.84 1.79 1.73
25 2.00 1.98 1.97 1.96 1.96 1.92 1.89 1.87 1.82 1.77 1.71
26 1.98 1.97 1.96 1.95 1.94 1.90 1.87 1.85 1.80 1.75 1.69
27 1.96 1.95 1.94 1.93 1.92 1.88 1.86 1.84 1.79 1.73 1.67
28 1.95 1.93 1.92 1.91 1.91 1.87 1.84 1.82 1.77 1.71 1.65
29 1.93 1.92 1.91 1.90 1.89 1.85 1.83 1.81 1.75 1.70 1.64
30 1.92 1.91 1.90 1.89 1.88 1.84 1.81 1.79 1.74 1.68 1.62
31 1.91 1.90 1.88 1.88 1.87 1.83 1.80 1.78 1.73 1.67 1.61
32 1.90 1.88 1.87 1.86 1.85 1.82 1.79 1.77 1.71 1.66 1.59
33 1.89 1.87 1.86 1.85 1.84 1.81 1.78 1.76 1.70 1.64 1.58
34 1.88 1.86 1.85 1.84 1.83 1.80 1.77 1.75 1.69 1.63 1.57
35 1.87 1.85 1.84 1.83 1.82 1.79 1.76 1.74 1.68 1.62 1.56
40 1.83 1.81 1.80 1.79 1.78 1.74 1.72 1.69 1.64 1.58 1.51
45 1.80 1.78 1.77 1.76 1.75 1.71 1.68 1.66 1.60 1.54 1.47
50 1.77 1.76 1.75 1.74 1.73 1.69 1.66 1.63 1.58 1.51 1.44
60 1.73 1.72 1.71 1.70 1.69 1.65 1.62 1.59 1.53 1.47 1.39 120
1 .64 1.63 1.62 1.61 1.60 1.55 1.52 1.50 1.43 1.35 1.25
¥ 1.56 1.54 1.53 1.52 1.51 1.46 1.42 1.39 1.32 1.22 1.00 10
Table 6: F-distribution (a=0 .) 1 0 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a=0 . 10 n1 n2 1 2 3 4 5 6 7 8 9 10
1 39.87 49.52 53.62 55.87 57.28 58.24 58.95 59.48 59.90 60.24
2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39
3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23
4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92
5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30
6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94
7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70
8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54
9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 10
3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32 11
3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 12
3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19 13
3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14 14
3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10 15
3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06 16
3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 17
3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00 18
3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98 19
2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96 20
2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94 21
2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 22
2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90 23
2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 24
2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88 25
2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87 26
2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86 27
2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87 1.85 28
2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87 1.84 29
2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83 30
2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 31
2.87 2.48 2.27 2.14 2.04 1.97 1.92 1.88 1.84 1.81 32
2.87 2.48 2.26 2.13 2.04 1.97 1.91 1.87 1.83 1.81 33
2.86 2.47 2.26 2.12 2.03 1.96 1.91 1.86 1.83 1.80 34
2.86 2.47 2.25 2.12 2.02 1.96 1.90 1.86 1.82 1.79 35
2.85 2.46 2.25 2.11 2.02 1.95 1.90 1.85 1.82 1.79 40
2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76 45
2.82 2.42 2.21 2.07 1.98 1.91 1.85 1.81 1.77 1.74 50
2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76 1.73 60
2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71 120
2. 75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65
¥ 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.60 11
Table 6: F-distribution (a=0 .) 1 0 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a=0 . 10 n1
n2 11 12 13 14 15 16 17 18 19 20
1 60.51 60.75 60.94 61.11 61.26 61.39 61.51 61.61 61.70 61.78
2 9.40 9.41 9.41 9.42 9.42 9.43 9.43 9.44 9.44 9.44
3 5.22 5.22 5.21 5.20 5.20 5.20 5.19 5.19 5.19 5.18
4 3.91 3.90 3.89 3.88 3.87 3.86 3.86 3.85 3.85 3.84
5 3.28 3.27 3.26 3.25 3.24 3.23 3.22 3.22 3.21 3.21
6 2.92 2.90 2.89 2.88 2.87 2.86 2.85 2.85 2.84 2.84
7 2.68 2.67 2.65 2.64 2.63 2.62 2.61 2.61 2.60 2.59
8 2.52 2.50 2.49 2.48 2.46 2.45 2.45 2.44 2.43 2.42
9 2.40 2.38 2.36 2.35 2.34 2.33 2.32 2.31 2.30 2.30 10
2.30 2.28 2.27 2.26 2.24 2.23 2.22 2.22 2.21 2.20 11
2.23 2.21 2.19 2.18 2.17 2.16 2.15 2.14 2.13 2.12 12
2.17 2.15 2.13 2.12 2.10 2.09 2.08 2.08 2.07 2.06 13
2.12 2.10 2.08 2.07 2.05 2.04 2.03 2.02 2.01 2.01 14
2.07 2.05 2.04 2.02 2.01 2.00 1.99 1.98 1.97 1.96 15
2.04 2.02 2.00 1.99 1.97 1.96 1.95 1.94 1.93 1.92 16
2.01 1.99 1.97 1.95 1.94 1.93 1.92 1.91 1.90 1.89 17
1.98 1.96 1.94 1.93 1.91 1.90 1.89 1.88 1.87 1.86 18
1.95 1.93 1.92 1.90 1.89 1.87 1.86 1.85 1.84 1.84 19
1.93 1.91 1.89 1.88 1.86 1.85 1.84 1.83 1.82 1.81 20
1.91 1.89 1.87 1.86 1.84 1.83 1.82 1.81 1.80 1.79 21
1.90 1.87 1.86 1.84 1.83 1.81 1.80 1.79 1.78 1.78 22
1.88 1.86 1.84 1.83 1.81 1.80 1.79 1.78 1.77 1.76 23
1.87 1.84 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.74 24
1.85 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.74 1.73 25
1.84 1.82 1.80 1.79 1.77 1.76 1.75 1.74 1.73 1.72 26
1.83 1.81 1.79 1.77 1.76 1.75 1.73 1.72 1.71 1.71 27
1.82 1.80 1.78 1.76 1.75 1.74 1.72 1.71 1.70 1.70 28
1.81 1.79 1.77 1.75 1.74 1.73 1.71 1.70 1.69 1.69 29
1.80 1.78 1.76 1.75 1.73 1.72 1.71 1.69 1.68 1.68 30
1.79 1.77 1.75 1.74 1.72 1.71 1.70 1.69 1.68 1.67 31
1.79 1.77 1.75 1.73 1.71 1.70 1.69 1.68 1.67 1.66 32
1.78 1.76 1.74 1.72 1.71 1.69 1.68 1.67 1.66 1.65 33
1.77 1.75 1.73 1.72 1.70 1.69 1.67 1.66 1.65 1.64 34
1.77 1.75 1.73 1.71 1.69 1.68 1.67 1.66 1.65 1.64 35
1.76 1.74 1.72 1.70 1.69 1.67 1.66 1.65 1.64 1.63 40
1.74 1.71 1.70 1.68 1.66 1.65 1.64 1.62 1.61 1.61 45
1.72 1.70 1.68 1.66 1.64 1.63 1.62 1.60 1.59 1.58 50
1.70 1.68 1.66 1.64 1.63 1.61 1.60 1.59 1.58 1.57 60
1.68 1.66 1.64 1.62 1.60 1.59 1.58 1.56 1.55 1.54 120
1. 63 1.60 1.58 1.56 1.54 1.53 1.52 1.50 1.49 1.48
¥ 1.57 1.55 1.52 1.50 1.49 1.47 1.46 1.44 1.43 1.42 12
Table 6: F-distribution (a=0 .) 1 0 (cont'd) 1-a a F a nn 1, 2 P >r( = ) XF aa 12 n , n a=0 . 10 n1
n2 21 22 23 24 25 30 35 40 60 120 ¥
1 61.86 61.92 61.99 62.04 62.10 62.31 62.46 62.57 62.84 63.10 63.33
2 9.44 9.45 9.45 9.45 9.46 9.46 9.47 9.47 9.48 9.49 9.49
3 5.18 5.18 5.18 5.18 5.17 5.17 5.16 5.16 5.15 5.14 5.13
4 3.84 3.84 3.83 3.83 3.83 3.82 3.81 3.80 3.79 3.78 3.76
5 3.20 3.20 3.19 3.19 3.19 3.17 3.16 3.16 3.14 3.12 3.10
6 2.83 2.83 2.82 2.82 2.81 2.80 2.79 2.78 2.76 2.74 2.72
7 2.59 2.58 2.58 2.58 2.57 2.56 2.54 2.54 2.51 2.49 2.47
8 2.42 2.41 2.41 2.40 2.40 2.38 2.37 2.36 2.34 2.32 2.29
9 2.29 2.29 2.28 2.28 2.27 2.25 2.24 2.23 2.21 2.18 2.16
10 2.19 2.19 2.18 2.18 2.17 2.16 2.14 2.13 2.11 2.08 2.06
11 2.12 2.11 2.11 2.10 2.10 2.08 2.06 2.05 2.03 2.00 1.97
12 2.05 2.05 2.04 2.04 2.03 2.01 2.00 1.99 1.96 1.93 1.90
13 2.00 1.99 1.99 1.98 1.98 1.96 1.94 1.93 1.90 1.88 1.85
14 1.96 1.95 1.94 1.94 1.93 1.91 1.90 1.89 1.86 1.83 1.80
15 1.92 1.91 1.90 1.90 1.89 1.87 1.86 1.85 1.82 1.79 1.76
16 1.88 1.88 1.87 1.87 1.86 1.84 1.82 1.81 1.78 1.75 1.72
17 1.85 1.85 1.84 1.84 1.83 1.81 1.79 1.78 1.75 1.72 1.69
18 1.83 1.82 1.82 1.81 1.80 1.78 1.77 1.75 1.72 1.69 1.66
19 1.81 1.80 1.79 1.79 1.78 1.76 1.74 1.73 1.70 1.67 1.63
20 1.79 1.78 1.77 1.77 1.76 1.74 1.72 1.71 1.68 1.64 1.61
21 1.77 1.76 1.75 1.75 1.74 1.72 1.70 1.69 1.66 1.62 1.59
22 1.75 1.74 1.74 1.73 1.73 1.70 1.68 1.67 1.64 1.60 1.57
23 1.74 1.73 1.72 1.72 1.71 1.69 1.67 1.66 1.62 1.59 1.55
24 1.72 1.71 1.71 1.70 1.70 1.67 1.65 1.64 1.61 1.57 1.53
25 1.71 1.70 1.70 1.69 1.68 1.66 1.64 1.63 1.59 1.56 1.52
26 1.70 1.69 1.68 1.68 1.67 1.65 1.63 1.61 1.58 1.54 1.50
27 1.69 1.68 1.67 1.67 1.66 1.64 1.62 1.60 1.57 1.53 1.49
28 1.68 1.67 1.66 1.66 1.65 1.63 1.61 1.59 1.56 1.52 1.48
29 1.67 1.66 1.65 1.65 1.64 1.62 1.60 1.58 1.55 1.51 1.47
30 1.66 1.65 1.64 1.64 1.63 1.61 1.59 1.57 1.54 1.50 1.46
31 1.65 1.64 1.64 1.63 1.62 1.60 1.58 1.56 1.53 1.49 1.45
32 1.64 1.64 1.63 1.62 1.62 1.59 1.57 1.56 1.52 1.48 1.44
33 1.64 1.63 1.62 1.61 1.61 1.58 1.56 1.55 1.51 1.47 1.43
34 1.63 1.62 1.61 1.61 1.60 1.58 1.56 1.54 1.50 1.46 1.42
35 1.62 1.62 1.61 1.60 1.60 1.57 1.55 1.53 1.50 1.46 1.41
40 1.60 1.59 1.58 1.57 1.57 1.54 1.52 1.51 1.47 1.42 1.38
45 1.58 1.57 1.56 1.55 1.55 1.52 1.50 1.48 1.44 1.40 1.35
50 1.56 1.55 1.54 1.54 1.53 1.50 1.48 1.46 1.42 1.38 1.33
60 1.53 1.53 1.52 1.51 1.50 1.48 1.45 1.44 1.40 1.35 1.29 120
1 .47 1.46 1.46 1.45 1.44 1.41 1.39 1.37 1.32 1.26 1.19
¥ 1.41 1.40 1.39 1.38 1.38 1.34 1.32 1.30 1.24 1.17 1.00 13
Table 7: Binomial Distribution Pr ()X £ k n= n2 =3 n =4 n =5 p k=0 1 k=0 1 2 k=0 1 2 3 k=0 1 2 3 4 0.01 0.980 1.000 0.970 1.000 0.961 0.999 1.000 0.951 0.999 1.000
0.02 0.960 1.000 0.941 0.999 1.000 0.922 0.998 1.000 0.904 0.996 1.000
0.03 0.941 0.999 0.913 0.997 1.000 0.885 0.995 1.000 0.859 0.992 1.000
0.04 0.922 0.998 0.885 0.995 1.000 0.849 0.991 1.000 0.815 0.985 0.999 1.000
0.05 0.902 0.997 0.857 0.993 1.000 0.815 0.986 1.000 0.774 0.977 0.999 1.000
0.06 0.884 0.996 0.831 0.990 1.000 0.781 0.980 0.999 1.000 0.734 0.968 0.998 1.000
0.07 0.865 0.995 0.804 0.986 1.000 0.748 0.973 0.999 1.000 0.696 0.958 0.997 1.000
0.08 0.846 0.994 0.779 0.982 0.999 0.716 0.966 0.998 1.000 0.659 0.946 0.995 1.000
0.09 0.828 0.992 0.754 0.977 0.999 0.686 0.957 0.997 1.000 0.624 0.933 0.994 1.000
0.10 0.810 0.990 0.729 0.972 0.999 0.656 0.948 0.996 1.000 0.590 0.919 0.991 1.000
0.11 0.792 0.988 0.705 0.966 0.999 0.627 0.938 0.995 1.000 0.558 0.903 0.989 0.999 1.000
0.12 0.774 0.986 0.681 0.960 0.998 0.600 0.927 0.994 1.000 0.528 0.888 0.986 0.999 1.000
0.13 0.757 0.983 0.659 0.954 0.998 0.573 0.915 0.992 1.000 0.498 0.871 0.982 0.999 1.000
0.14 0.740 0.980 0.636 0.947 0.997 0.547 0.903 0.990 1.000 0.470 0.853 0.978 0.998 1.000
0.15 0.722 0.977 0.614 0.939 0.997 0.522 0.890 0.988 0.999 0.444 0.835 0.973 0.998 1.000
0.16 0.706 0.974 0.593 0.931 0.996 0.498 0.877 0.986 0.999 0.418 0.817 0.968 0.997 1.000
0.17 0.689 0.971 0.572 0.923 0.995 0.475 0.863 0.983 0.999 0.394 0.797 0.963 0.996 1.000
0.18 0.672 0.968 0.551 0.914 0.994 0.452 0.849 0.980 0.999 0.371 0.778 0.956 0.996 1.000
0.19 0.656 0.964 0.531 0.905 0.993 0.430 0.834 0.976 0.999 0.349 0.758 0.949 0.994 1.000
0.20 0.640 0.960 0.512 0.896 0.992 0.410 0.819 0.973 0.998 0.328 0.737 0.942 0.993 1.000
0.21 0.624 0.956 0.493 0.886 0.991 0.390 0.804 0.969 0.998 0.308 0.717 0.934 0.992 1.000
0.22 0.608 0.952 0.475 0.876 0.989 0.370 0.788 0.964 0.998 0.289 0.696 0.926 0.990 0.999
0.23 0.593 0.947 0.457 0.866 0.988 0.352 0.772 0.960 0.997 0.271 0.675 0.916 0.989 0.999
0.24 0.578 0.942 0.439 0.855 0.986 0.334 0.755 0.955 0.997 0.254 0.654 0.907 0.987 0.999
0.25 0.562 0.937 0.422 0.844 0.984 0.316 0.738 0.949 0.996 0.237 0.633 0.896 0.984 0.999
0.26 0.548 0.932 0.405 0.832 0.982 0.300 0.721 0.943 0.995 0.222 0.612 0.886 0.982 0.999
0.27 0.533 0.927 0.389 0.821 0.980 0.284 0.704 0.937 0.995 0.207 0.591 0.874 0.979 0.999
0.28 0.518 0.922 0.373 0.809 0.978 0.269 0.687 0.931 0.994 0.193 0.570 0.862 0.976 0.998
0.29 0.504 0.916 0.358 0.796 0.976 0.254 0.669 0.924 0.993 0.180 0.549 0.850 0.973 0.998
0.30 0.490 0.910 0.343 0.784 0.973 0.240 0.652 0.916 0.992 0.168 0.528 0.837 0.969 0.998
0.31 0.476 0.904 0.329 0.771 0.970 0.227 0.634 0.909 0.991 0.156 0.508 0.823 0.965 0.997
0.32 0.462 0.898 0.314 0.758 0.967 0.214 0.616 0.900 0.990 0.145 0.487 0.809 0.961 0.997
0.33 0.449 0.891 0.301 0.745 0.964 0.202 0.599 0.892 0.988 0.135 0.468 0.795 0.956 0.996
0.34 0.436 0.884 0.287 0.732 0.961 0.190 0.581 0.883 0.987 0.125 0.448 0.780 0.951 0.995
0.35 0.423 0.878 0.275 0.718 0.957 0.179 0.563 0.874 0.985 0.116 0.428 0.765 0.946 0.995
0.36 0.410 0.870 0.262 0.705 0.953 0.168 0.545 0.864 0.983 0.107 0.409 0.749 0.940 0.994
0.37 0.397 0.863 0.250 0.691 0.949 0.158 0.528 0.854 0.981 0.099 0.391 0.733 0.934 0.993
0.38 0.384 0.856 0.238 0.677 0.945 0.148 0.510 0.843 0.979 0.092 0.372 0.717 0.927 0.992
0.39 0.372 0.848 0.227 0.662 0.941 0.138 0.493 0.832 0.977 0.084 0.354 0.700 0.920 0.991
0.40 0.360 0.840 0.216 0.648 0.936 0.130 0.475 0.821 0.974 0.078 0.337 0.683 0.913 0.990
0.41 0.348 0.832 0.205 0.634 0.931 0.121 0.458 0.809 0.972 0.071 0.320 0.665 0.905 0.988
0.42 0.336 0.824 0.195 0.619 0.926 0.113 0.441 0.797 0.969 0.066 0.303 0.647 0.897 0.987
0.43 0.325 0.815 0.185 0.604 0.920 0.106 0.424 0.785 0.966 0.060 0.287 0.630 0.888 0.985
0.44 0.314 0.806 0.176 0.590 0.915 0.098 0.407 0.772 0.963 0.055 0.271 0.611 0.879 0.984
0.45 0.303 0.798 0.166 0.575 0.909 0.092 0.391 0.759 0.959 0.050 0.256 0.593 0.869 0.982
0.46 0.292 0.788 0.157 0.560 0.903 0.085 0.375 0.745 0.955 0.046 0.241 0.575 0.859 0.979
0.47 0.281 0.779 0.149 0.545 0.896 0.079 0.359 0.731 0.951 0.042 0.227 0.556 0.848 0.977
0.48 0.270 0.770 0.141 0.530 0.889 0.073 0.343 0.717 0.947 0.038 0.213 0.537 0.837 0.975
0.49 0.260 0.760 0.133 0.515 0.882 0.068 0.328 0.702 0.942 0.035 0.200 0.519 0.825 0.972
0.50 0.250 0.750 0.125 0.500 0.875 0.062 0.312 0.688 0.938 0.031 0.187 0.500 0.813 0.969 14
Table 7: Binomial Distribution (cont'd) Pr ()X £ k 6 = n p k=0 1 2 3 4 5 k=0 1 2 3 4 5 6 0.01 0.941 0.999 1.000 0.932 0.998 1.000 0.02 0.886 0.994 1.000 0.868 0.992 1.000 0.03 0.833 0.988 0.999 1.000 0.808 0.983 0.999 1.000 0.04 0.783 0.978 0.999 1.000 0.751 0.971 0.998 1.000 0.05 0.735 0.967 0.998 1.000 0.698 0.956 0.996 1.000 0.06 0.690 0.954 0.996 1.000 0.648 0.938 0.994 1.000 0.07 0.647 0.939 0.994 1.000 0.602 0.919 0.990 0.999 1.000
0.08 0.606 0.923 0.991 0.999 1.000 0.558 0.897 0.986 0.999 1.000
0.09 0.568 0.905 0.988 0.999 1.000 0.517 0.875 0.981 0.998 1.000
0.10 0.531 0.886 0.984 0.999 1.000 0.478 0.850 0.974 0.997 1.000
0.11 0.497 0.866 0.979 0.998 1.000 0.442 0.825 0.967 0.996 1.000
0.12 0.464 0.844 0.974 0.997 1.000 0.409 0.799 0.958 0.995 1.000
0.13 0.434 0.822 0.968 0.997 1.000
0.377 0.772 0.949 0.993 0.999 1.000
0.14 0.405 0.800 0.961 0.995 1.000
0.348 0.744 0.938 0.991 0.999 1.000
0.15 0.377 0.776 0.953 0.994 1.000
0.321 0.717 0.926 0.988 0.999 1.000
0.16 0.351 0.753 0.944 0.993 0.999 1.000 0.295 0.689 0.913 0.985 0.998 1.000
0.17 0.327 0.729 0.934 0.991 0.999 1.000 0.271 0.660 0.899 0.981 0.998 1.000
0.18 0.304 0.704 0.924 0.988 0.999 1.000 0.249 0.632 0.885 0.977 0.997 1.000
0.19 0.282 0.680 0.913 0.986 0.999 1.000 0.229 0.604 0.869 0.972 0.996 1.000
0.20 0.262 0.655 0.901 0.983 0.998 1.000 0.210 0.577 0.852 0.967 0.995 1.000
0.21 0.243 0.631 0.888 0.980 0.998 1.000 0.192 0.549 0.834 0.961 0.994 1.000
0.22 0.225 0.606 0.875 0.976 0.997 1.000 0.176 0.522 0.816 0.954 0.993 0.999 1.000
0.23 0.208 0.582 0.861 0.972 0.997 1.000 0.160 0.496 0.797 0.946 0.991 0.999 1.000
0.24 0.193 0.558 0.846 0.967 0.996 1.000 0.146 0.470 0.777 0.938 0.989 0.999 1.000
0.25 0.178 0.534 0.831 0.962 0.995 1.000 0.133 0.445 0.756 0.929 0.987 0.999 1.000
0.26 0.164 0.510 0.814 0.957 0.994 1.000 0.122 0.420 0.735 0.920 0.985 0.998 1.000
0.27 0.151 0.487 0.798 0.951 0.993 1.000 0.110 0.396 0.714 0.909 0.982 0.998 1.000
0.28 0.139 0.464 0.780 0.944 0.992 1.000 0.100 0.373 0.692 0.898 0.979 0.997 1.000
0.29 0.128 0.442 0.763 0.937 0.991 0.999 0.091 0.351 0.670 0.887 0.975 0.997 1.000
0.30 0.118 0.420 0.744 0.930 0.989 0.999 0.082 0.329 0.647 0.874 0.971 0.996 1.000
0.31 0.108 0.399 0.726 0.921 0.987 0.999 0.074 0.309 0.624 0.861 0.967 0.995 1.000
0.32 0.099 0.378 0.706 0.913 0.985 0.999 0.067 0.289 0.601 0.847 0.962 0.995 1.000
0.33 0.090 0.358 0.687 0.903 0.983 0.999 0.061 0.270 0.578 0.832 0.957 0.994 1.000
0.34 0.083 0.338 0.667 0.893 0.980 0.998 0.055 0.251 0.555 0.816 0.951 0.992 0.999
0.35 0.075 0.319 0.647 0.883 0.978 0.998 0.049 0.234 0.532 0.800 0.944 0.991 0.999
0.36 0.069 0.301 0.627 0.871 0.975 0.998 0.044 0.217 0.509 0.783 0.937 0.989 0.999
0.37 0.063 0.283 0.606 0.860 0.971 0.997 0.039 0.201 0.487 0.766 0.930 0.988 0.999
0.38 0.057 0.266 0.586 0.847 0.968 0.997 0.035 0.186 0.464 0.748 0.922 0.986 0.999
0.39 0.052 0.249 0.565 0.834 0.963 0.996 0.031 0.172 0.442 0.729 0.913 0.984 0.999
0.40 0.047 0.233 0.544 0.821 0.959 0.996 0.028 0.159 0.420 0.710 0.904 0.981 0.998
0.41 0.042 0.218 0.524 0.807 0.954 0.995 0.025 0.146 0.398 0.691 0.894 0.978 0.998
0.42 0.038 0.203 0.503 0.792 0.949 0.995 0.022 0.134 0.377 0.671 0.883 0.975 0.998
0.43 0.034 0.190 0.482 0.777 0.943 0.994 0.020 0.123 0.356 0.650 0.872 0.972 0.997
0.44 0.031 0.176 0.462 0.761 0.937 0.993 0.017 0.112 0.336 0.629 0.860 0.968 0.997
0.45 0.028 0.164 0.442 0.745 0.931 0.992 0.015 0.102 0.316 0.608 0.847 0.964 0.996
0.46 0.025 0.152 0.421 0.728 0.924 0.991 0.013 0.093 0.297 0.587 0.834 0.960 0.996
0.47 0.022 0.140 0.402 0.711 0.916 0.989 0.012 0.085 0.279 0.565 0.820 0.955 0.995
0.48 0.020 0.129 0.382 0.693 0.908 0.988 0.010 0.077 0.261 0.544 0.805 0.950 0.994
0.49 0.018 0.119 0.363 0.675 0.900 0.986 0.009 0.069 0.243 0.522 0.790 0.944 0.993
0.50 0.016 0.109 0.344 0.656 0.891 0.984 0.008 0.062 0.227 0.500 0.773 0.938 0.992 15
Table 7: Binomial Distribution (cont'd) Pr ()X £ k 8 = n p k=0 1 2 3 4 5 6 7 k=0 1 2 3 4 5 0. 00 . 0. 1 1 99 . 2 03 90 7 0 0. 0 9 . 1.1 90 4 90 7 0 0. 00 . 0. 1 2 89 . 5 01 90 0 0. 0 8 . 0. 1 3 99 . 4 89 0 7 0 9 0 0.03 0.784 0.978 0.999 1.000 0.760 0.972 0.998 1.000 0.04 0.721 0.962 0.997 1.000 0.693 0.952 0.996 1.000 0.05 0.663 0.943 0.994 1.000 0.630 0.929 0.992 0.999 1.000
0.06 0.610 0.921 0.990 0.999 1.000 0.573 0.902 0.986 0.999 1.000
0.07 0.560 0.897 0.985 0.999 1.000 0.520 0.873 0.979 0.998 1.000
0.08 0.513 0.870 0.979 0.998 1.000 0.472 0.842 0.970 0.996 1.000
0.09 0.470 0.842 0.971 0.997 1.000
0.428 0.809 0.960 0.994 0.999 1.000
0.10 0.430 0.813 0.962 0.995 1.000
0.387 0.775 0.947 0.992 0.999 1.000
0.11 0.394 0.783 0.951 0.993 0.999 1.000
0.350 0.740 0.933 0.988 0.999 1.000
0.12 0.360 0.752 0.939 0.990 0.999 1.000
0.316 0.705 0.917 0.984 0.998 1.000
0.13 0.328 0.721 0.926 0.987 0.999 1.000
0.286 0.670 0.899 0.979 0.997 1.000
0.14 0.299 0.689 0.911 0.983 0.998 1.000
0.257 0.634 0.880 0.973 0.996 1.000
0.15 0.272 0.657 0.895 0.979 0.997 1.000
0.232 0.599 0.859 0.966 0.994 0.999
0.16 0.248 0.626 0.877 0.973 0.996 1.000
0.208 0.565 0.837 0.958 0.993 0.999
0.17 0.225 0.594 0.859 0.967 0.995 1.000
0.187 0.532 0.814 0.949 0.990 0.999
0.18 0.204 0.563 0.839 0.960 0.993 0.999 1.000
0.168 0.499 0.790 0.938 0.988 0.998
0.19 0.185 0.533 0.819 0.952 0.992 0.999 1.000
0.150 0.467 0.764 0.927 0.984 0.998
0.20 0.168 0.503 0.797 0.944 0.990 0.999 1.000
0.134 0.436 0.738 0.914 0.980 0.997
0.21 0.152 0.474 0.775 0.934 0.987 0.998 1.000
0.120 0.407 0.711 0.901 0.976 0.996
0.22 0.137 0.446 0.751 0.924 0.984 0.998 1.000
0.107 0.378 0.684 0.886 0.971 0.995
0.23 0.124 0.419 0.728 0.912 0.981 0.997 1.000
0.095 0.351 0.657 0.870 0.965 0.994
0.24 0.111 0.392 0.703 0.900 0.977 0.997 1.000
0.085 0.325 0.629 0.852 0.958 0.992
0.25 0.100 0.367 0.679 0.886 0.973 0.996 1.000
0.075 0.300 0.601 0.834 0.951 0.990
0.26 0.090 0.343 0.653 0.872 0.968 0.995 1.000
0.067 0.277 0.573 0.815 0.943 0.988
0.27 0.081 0.319 0.628 0.857 0.962 0.994 0.999 1.000 0.059 0.255 0.545 0.795 0.934 0.985
0.28 0.072 0.297 0.603 0.841 0.956 0.992 0.999 1.000 0.052 0.234 0.517 0.774 0.924 0.982
0.29 0.065 0.276 0.577 0.824 0.949 0.991 0.999 1.000 0.046 0.214 0.490 0.752 0.913 0.979
0.30 0.058 0.255 0.552 0.806 0.942 0.989 0.999 1.000 0.040 0.196 0.463 0.730 0.901 0.975
0.31 0.051 0.236 0.526 0.787 0.934 0.987 0.998 1.000 0.035 0.179 0.436 0.706 0.888 0.970
0.32 0.046 0.218 0.501 0.768 0.925 0.984 0.998 1.000 0.031 0.163 0.411 0.683 0.875 0.965
0.33 0.041 0.201 0.476 0.748 0.915 0.981 0.998 1.000 0.027 0.148 0.385 0.658 0.860 0.960
0.34 0.036 0.184 0.452 0.728 0.905 0.978 0.997 1.000 0.024 0.134 0.361 0.634 0.845 0.953
0.35 0.032 0.169 0.428 0.706 0.894 0.975 0.996 1.000 0.021 0.121 0.337 0.609 0.828 0.946
0.36 0.028 0.155 0.404 0.685 0.882 0.971 0.996 1.000 0.018 0.109 0.314 0.584 0.811 0.939
0.37 0.025 0.141 0.381 0.663 0.869 0.966 0.995 1.000 0.016 0.098 0.292 0.558 0.793 0.930
0.38 0.022 0.129 0.359 0.640 0.856 0.961 0.994 1.000 0.014 0.088 0.271 0.533 0.774 0.921
0.39 0.019 0.117 0.337 0.617 0.841 0.956 0.993 0.999 0.012 0.079 0.251 0.508 0.754 0.911
0.40 0.017 0.106 0.315 0.594 0.826 0.950 0.991 0.999 0.010 0.071 0.232 0.483 0.733 0.901
0.41 0.015 0.096 0.295 0.571 0.810 0.944 0.990 0.999 0.009 0.063 0.213 0.458 0.712 0.889
0.42 0.013 0.087 0.275 0.547 0.794 0.937 0.988 0.999 0.007 0.056 0.196 0.433 0.690 0.877
0.43 0.011 0.078 0.256 0.524 0.776 0.929 0.986 0.999 0.006 0.049 0.180 0.409 0.668 0.863
0.44 0.010 0.070 0.238 0.500 0.758 0.921 0.984 0.999 0.005 0.044 0.164 0.385 0.645 0.849
0.45 0.008 0.063 0.220 0.477 0.740 0.912 0.982 0.998 0.005 0.039 0.150 0.361 0.621 0.834
0.46 0.007 0.057 0.203 0.454 0.720 0.902 0.979 0.998 0.004 0.034 0.136 0.339 0.598 0.818
0.47 0.006 0.050 0.187 0.431 0.700 0.891 0.976 0.998 0.003 0.030 0.123 0.316 0.573 0.801
0.48 0.005 0.045 0.172 0.408 0.680 0.880 0.973 0.997 0.003 0.026 0.111 0.295 0.549 0.784
0.49 0.005 0.040 0.158 0.385 0.658 0.868 0.969 0.997 0.002 0.023 0.100 0.274 0.525 0.765
0.50 0.004 0.035 0.145 0.363 0.637 0.855 0.965 0.996 0.002 0.020 0.090 0.254 0.500 0.746 16
Table 7: Binomial Distribution (cont'd) Pr ()X £ k n= 9 n =10 p k=6 7 8 k=0 1 2 3 4 5 6 7 8 9 0. 0 1 0. 9 0. 1 0 9 . 4 9 0 6 0 0 0. 0 2 0. 8 0. 0 1 9 . 1. 7 8 90 4 9 9 0 0 0. 0 3 0. 7 0. 0 3 9 . 1. 7 6 90 5 9 7 0 0 0. 0 4 0. 6 0. 0 6 9 . 1. 5 4 90 2 9 4 0 0 0. 0 5 0. 5 0. 0 9 9 . 0. 1 9 1 99 . 4 8 0 8 9 9 0 0 0. 0 6 0. 5 0. 0 3 8 . 0. 1 9 8 99 . 2 8 0 1 9 8 0 0 0. 0 7 0. 4 0. 0 8 8 . 0. 1 4 4 99 . 8 7 0 2 9 6 0 0 0.08
0.434 0.812 0.960 0.994 0.999 1.000 0.09
0.389 0.775 0.946 0.991 0.999 1.000 0.10
0.349 0.736 0.930 0.987 0.998 1.000 0.11
0.312 0.697 0.912 0.982 0.997 1.000 0.12
0.279 0.658 0.891 0.976 0.996 1.000 0.13
0.248 0.620 0.869 0.969 0.995 0.999 1.000 0.14
0.221 0.582 0.845 0.960 0.993 0.999 1.000 0.15 1.000
0.197 0.544 0.820 0.950 0.990 0.999 1.000 0.16 1.000
0.175 0.508 0.794 0.939 0.987 0.998 1.000 0.17 1.000
0.155 0.473 0.766 0.926 0.983 0.997 1.000 0.18 1.000
0.137 0.439 0.737 0.912 0.979 0.996 1.000 0.19 1.000
0.122 0.407 0.708 0.896 0.973 0.995 0.999 1.000 0.20 1.000
0.107 0.376 0.678 0.879 0.967 0.994 0.999 1.000 0.21 1.000
0.095 0.346 0.647 0.861 0.960 0.992 0.999 1.000 0.22 0.999 1.000
0.083 0.318 0.617 0.841 0.952 0.990 0.998 1.000 0.23 0.999 1.000
0.073 0.292 0.586 0.821 0.943 0.987 0.998 1.000 0.24 0.999 1.000
0.064 0.267 0.556 0.799 0.933 0.984 0.997 1.000 0.25 0.999 1.000
0.056 0.244 0.526 0.776 0.922 0.980 0.996 1.000 0.26 0.998 1.000
0.049 0.222 0.496 0.752 0.910 0.976 0.996 0.999 1.000 0.27 0.998 1.000
0.043 0.202 0.466 0.727 0.896 0.971 0.994 0.999 1.000 0.28 0.997 1.000
0.037 0.183 0.438 0.702 0.882 0.966 0.993 0.999 1.000 0.29 0.997 1.000
0.033 0.166 0.410 0.676 0.866 0.960 0.991 0.999 1.000 0.30 0.996 1.000
0.028 0.149 0.383 0.650 0.850 0.953 0.989 0.998 1.000
0.31 0.995 0.999 1.000 0.024 0.134 0.357 0.623 0.832 0.945 0.987 0.998 1.000
0.32 0.994 0.999 1.000 0.021 0.121 0.331 0.596 0.813 0.936 0.984 0.997 1.000
0.33 0.992 0.999 1.000 0.018 0.108 0.307 0.568 0.794 0.927 0.981 0.997 1.000
0.34 0.991 0.999 1.000 0.016 0.096 0.284 0.541 0.773 0.916 0.978 0.996 1.000
0.35 0.989 0.999 1.000 0.013 0.086 0.262 0.514 0.751 0.905 0.974 0.995 0.999 1.000
0.36 0.987 0.998 1.000 0.012 0.076 0.241 0.487 0.729 0.893 0.969 0.994 0.999 1.000
0.37 0.984 0.998 1.000 0.010 0.068 0.221 0.460 0.706 0.879 0.964 0.993 0.999 1.000
0.38 0.982 0.997 1.000 0.008 0.060 0.202 0.434 0.682 0.865 0.959 0.991 0.999 1.000
0.39 0.978 0.997 1.000 0.007 0.053 0.184 0.408 0.658 0.850 0.952 0.990 0.999 1.000
0.40 0.975 0.996 1.000 0.006 0.046 0.167 0.382 0.633 0.834 0.945 0.988 0.998 1.000
0.41 0.971 0.995 1.000 0.005 0.041 0.152 0.358 0.608 0.817 0.937 0.985 0.998 1.000
0.42 0.967 0.995 1.000 0.004 0.036 0.137 0.333 0.582 0.798 0.929 0.983 0.997 1.000
0.43 0.962 0.994 0.999 0.004 0.031 0.124 0.310 0.556 0.779 0.919 0.980 0.997 1.000
0.44 0.956 0.992 0.999 0.003 0.027 0.111 0.288 0.530 0.759 0.909 0.976 0.996 1.000
0.45 0.950 0.991 0.999 0.003 0.023 0.100 0.266 0.504 0.738 0.898 0.973 0.995 1.000
0.46 0.944 0.989 0.999 0.002 0.020 0.089 0.245 0.478 0.717 0.886 0.968 0.995 1.000
0.47 0.936 0.988 0.999 0.002 0.017 0.079 0.226 0.453 0.694 0.873 0.963 0.994 0.999
0.48 0.928 0.985 0.999 0.001 0.015 0.070 0.207 0.427 0.671 0.859 0.958 0.992 0.999
0.49 0.920 0.983 0.998 0.001 0.013 0.062 0.189 0.402 0.647 0.844 0.952 0.991 0.999
0.50 0.910 0.980 0.998 0.001 0.011 0.055 0.172 0.377 0.623 0.828 0.945 0.989 0.999 17
Table 7: Binomial Distribution (cont'd)
Pr ()X £ k 1 = n p k=0 1 2 3 4 5 6 7 8 9 10 k=0 1 2 0. 00 . 0. 1 1 89 . 9 05 90 5 0 0. 08 . 1. 8 906 90 4 0 0. 00 . 0.2 89 . 1 . 0 9 1 89 0 0 9 0 0. 07 . 0.8 995 79 7 8 0. 00 . 0.3 79 . 1 . 1 9 5 59 0 9 0 6 0 0. 06 . 0.9 9 4 59 1 5
0.04 0.638 0.931 0.992 0.999 1.000 0.613 0.919 0.989
0.05 0.569 0.898 0.985 0.998 1.000 0.540 0.882 0.980
0.06 0.506 0.862 0.975 0.997 1.000 0.476 0.840 0.968
0.07 0.450 0.823 0.963 0.995 0.999 1.000 0.419 0.797 0.953
0.08 0.400 0.782 0.948 0.991 0.999 1.000 0.368 0.751 0.935
0.09 0.354 0.740 0.931 0.987 0.998 1.000 0.322 0.705 0.913
0.10 0.314 0.697 0.910 0.981 0.997 1.000 0.282 0.659 0.889
0.11 0.278 0.655 0.888 0.974 0.996 1.000 0.247 0.613 0.862
0.12 0.245 0.613 0.863 0.966 0.994 0.999 1.000 0.216 0.569 0.833
0.13 0.216 0.571 0.837 0.956 0.991 0.999 1.000 0.188 0.525 0.802
0.14 0.190 0.531 0.809 0.944 0.988 0.998 1.000 0.164 0.483 0.770
0.15 0.167 0.492 0.779 0.931 0.984 0.997 1.000 0.142 0.443 0.736
0.16 0.147 0.455 0.748 0.915 0.979 0.996 1.000 0.123 0.405 0.701
0.17 0.129 0.419 0.716 0.899 0.973 0.995 0.999 1.000 0.107 0.370 0.666
0.18 0.113 0.385 0.684 0.880 0.967 0.993 0.999 1.000 0.092 0.336 0.630
0.19 0.098 0.353 0.651 0.860 0.959 0.991 0.999 1.000 0.080 0.304 0.594
0.20 0.086 0.322 0.617 0.839 0.950 0.988 0.998 1.000 0.069 0.275 0.558
0.21 0.075 0.294 0.584 0.816 0.939 0.985 0.997 1.000 0.059 0.248 0.523
0.22 0.065 0.267 0.551 0.792 0.928 0.981 0.996 1.000 0.051 0.222 0.489
0.23 0.056 0.242 0.519 0.767 0.915 0.977 0.995 0.999 1.000 0.043 0.199 0.455
0.24 0.049 0.219 0.487 0.740 0.901 0.972 0.994 0.999 1.000 0.037 0.178 0.422
0.25 0.042 0.197 0.455 0.713 0.885 0.966 0.992 0.999 1.000 0.032 0.158 0.391
0.26 0.036 0.177 0.425 0.685 0.869 0.959 0.990 0.998 1.000 0.027 0.141 0.360
0.27 0.031 0.159 0.395 0.657 0.851 0.951 0.988 0.998 1.000 0.023 0.125 0.331
0.28 0.027 0.142 0.366 0.628 0.832 0.942 0.985 0.997 1.000 0.019 0.110 0.304
0.29 0.023 0.127 0.339 0.599 0.811 0.933 0.982 0.997 1.000 0.016 0.097 0.278
0.30 0.020 0.113 0.313 0.570 0.790 0.922 0.978 0.996 0.999 1.000 0.014 0.085 0.253
0.31 0.017 0.100 0.288 0.540 0.767 0.910 0.974 0.995 0.999 1.000 0.012 0.074 0.230
0.32 0.014 0.089 0.264 0.511 0.744 0.897 0.969 0.993 0.999 1.000 0.010 0.065 0.208
0.33 0.012 0.078 0.241 0.482 0.719 0.883 0.963 0.992 0.999 1.000 0.008 0.057 0.188
0.34 0.010 0.069 0.220 0.454 0.694 0.868 0.957 0.990 0.998 1.000 0.007 0.049 0.169
0.35 0.009 0.061 0.200 0.426 0.668 0.851 0.950 0.988 0.998 1.000 0.006 0.042 0.151
0.36 0.007 0.053 0.181 0.398 0.642 0.834 0.942 0.985 0.997 1.000 0.005 0.037 0.135
0.37 0.006 0.046 0.164 0.371 0.615 0.815 0.933 0.982 0.997 1.000 0.004 0.031 0.120
0.38 0.005 0.040 0.148 0.345 0.588 0.796 0.923 0.979 0.996 1.000 0.003 0.027 0.107
0.39 0.004 0.035 0.133 0.320 0.560 0.775 0.912 0.975 0.995 0.999 1.000 0.003 0.023 0.095
0.40 0.004 0.030 0.119 0.296 0.533 0.753 0.901 0.971 0.994 0.999 1.000 0.002 0.020 0.083
0.41 0.003 0.026 0.106 0.273 0.505 0.731 0.888 0.966 0.993 0.999 1.000 0.002 0.017 0.073
0.42 0.002 0.022 0.094 0.251 0.478 0.708 0.874 0.960 0.991 0.999 1.000 0.001 0.014 0.064
0.43 0.002 0.019 0.084 0.230 0.451 0.683 0.859 0.954 0.990 0.999 1.000 0.001 0.012 0.056
0.44 0.002 0.016 0.074 0.210 0.424 0.659 0.843 0.947 0.988 0.998 1.000 0.001 0.010 0.049
0.45 0.001 0.014 0.065 0.191 0.397 0.633 0.826 0.939 0.985 0.998 1.000 0.001 0.008 0.042
0.46 0.001 0.012 0.057 0.173 0.371 0.607 0.808 0.930 0.982 0.997 1.000 0.001 0.007 0.036
0.47 0.001 0.010 0.050 0.157 0.346 0.581 0.789 0.921 0.979 0.997 1.000 0.000 0.006 0.031
0.48 0.001 0.008 0.044 0.141 0.321 0.554 0.769 0.910 0.976 0.996 1.000 0.000 0.005 0.027
0.49 0.001 0.007 0.038 0.127 0.297 0.527 0.748 0.899 0.972 0.995 1.000 0.000 0.004 0.023
0.50 0.000 0.006 0.033 0.113 0.274 0.500 0.726 0.887 0.967 0.994 1.000 0.000 0.003 0.019 18
Table 7: Binomial Distribution (cont'd) Pr ()X £ k 1 = n p k=3 4 5 6 7 8 9 10 11 k=0 1 2 3 4 0 . 0 1 0. 08 . 1 . 7 90 8 90 3 0 0. 1 0 . 2 0 00 0. 07 . 0. 1 6 99 . 9 7 0 3 08 0 0. 1 0 . 3 0 00 0. 06 . 0. 1 7 99 . 3 49 0 4 04 0 0.04 0.999 1.000 0.588 0.907 0.986 0.999 1.000 0.05 0.998 1.000 0.513 0.865 0.975 0.997 1.000 0.06 0.996 1.000 0.447 0.819 0.961 0.994 0.999 0.07 0.992 0.999 1.000 0.389 0.770 0.942 0.990 0.999 0.08 0.988 0.998 1.000 0.338 0.721 0.920 0.984 0.998 0.09 0.982 0.997 1.000 0.293 0.671 0.895 0.976 0.996 0.10 0.974 0.996 0.999 1.000 0.254 0.621 0.866 0.966 0.994 0.11 0.965 0.993 0.999 1.000 0.220 0.573 0.835 0.954 0.990 0.12 0.954 0.991 0.999 1.000 0.190 0.526 0.802 0.939 0.986 0.13 0.940 0.987 0.998 1.000 0.164 0.481 0.766 0.922 0.981 0.14 0.925 0.982 0.997 1.000 0.141 0.439 0.730 0.903 0.974
0.15 0.908 0.976 0.995 0.999 1.000 0.121 0.398 0.692 0.882 0.966
0.16 0.889 0.969 0.994 0.999 1.000 0.104 0.360 0.654 0.859 0.956
0.17 0.868 0.961 0.991 0.999 1.000 0.089 0.325 0.615 0.833 0.945
0.18 0.845 0.951 0.988 0.998 1.000 0.076 0.292 0.577 0.806 0.932
0.19 0.820 0.940 0.985 0.997 1.000 0.065 0.262 0.539 0.777 0.917
0.20 0.795 0.927 0.981 0.996 0.999 1.000 0.055 0.234 0.502 0.747 0.901
0.21 0.767 0.913 0.976 0.995 0.999 1.000 0.047 0.208 0.465 0.716 0.883
0.22 0.739 0.898 0.970 0.993 0.999 1.000 0.040 0.185 0.430 0.684 0.863
0.23 0.710 0.881 0.963 0.991 0.998 1.000 0.033 0.163 0.396 0.651 0.841
0.24 0.680 0.862 0.955 0.989 0.998 1.000 0.028 0.144 0.364 0.618 0.818
0.25 0.649 0.842 0.946 0.986 0.997 1.000 0.024 0.127 0.333 0.584 0.794
0.26 0.618 0.821 0.935 0.982 0.996 0.999 1.000 0.020 0.111 0.303 0.551 0.768
0.27 0.586 0.798 0.924 0.978 0.995 0.999 1.000 0.017 0.097 0.275 0.517 0.741
0.28 0.555 0.775 0.911 0.973 0.994 0.999 1.000 0.014 0.085 0.249 0.485 0.713
0.29 0.524 0.750 0.897 0.968 0.992 0.999 1.000 0.012 0.074 0.225 0.452 0.684
0.30 0.493 0.724 0.882 0.961 0.991 0.998 1.000 0.010 0.064 0.202 0.421 0.654
0.31 0.462 0.697 0.866 0.954 0.988 0.998 1.000 0.008 0.055 0.181 0.390 0.624
0.32 0.432 0.669 0.848 0.946 0.986 0.997 1.000 0.007 0.047 0.162 0.360 0.593
0.33 0.403 0.641 0.829 0.937 0.982 0.996 1.000 0.005 0.041 0.144 0.332 0.562
0.34 0.374 0.612 0.809 0.927 0.979 0.996 0.999 1.000 0.005 0.035 0.128 0.304 0.531
0.35 0.347 0.583 0.787 0.915 0.974 0.994 0.999 1.000 0.004 0.030 0.113 0.278 0.501
0.36 0.320 0.554 0.765 0.903 0.970 0.993 0.999 1.000 0.003 0.025 0.100 0.254 0.470
0.37 0.295 0.525 0.741 0.889 0.964 0.991 0.999 1.000 0.002 0.021 0.088 0.230 0.440
0.38 0.270 0.496 0.717 0.875 0.958 0.990 0.998 1.000 0.002 0.018 0.077 0.208 0.410
0.39 0.247 0.467 0.691 0.859 0.951 0.987 0.998 1.000 0.002 0.015 0.067 0.188 0.381
0.40 0.225 0.438 0.665 0.842 0.943 0.985 0.997 1.000 0.001 0.013 0.058 0.169 0.353
0.41 0.205 0.410 0.638 0.824 0.934 0.982 0.997 1.000 0.001 0.011 0.050 0.151 0.326
0.42 0.185 0.383 0.611 0.804 0.924 0.978 0.996 0.999 1.000 0.001 0.009 0.043 0.134 0.300
0.43 0.167 0.356 0.583 0.784 0.913 0.974 0.995 0.999 1.000 0.001 0.007 0.037 0.119 0.275
0.44 0.150 0.330 0.555 0.762 0.901 0.970 0.994 0.999 1.000 0.001 0.006 0.032 0.106 0.251
0.45 0.134 0.304 0.527 0.739 0.888 0.964 0.992 0.999 1.000 0.000 0.005 0.027 0.093 0.228
0.46 0.120 0.280 0.499 0.716 0.874 0.959 0.990 0.999 1.000 0.000 0.004 0.023 0.081 0.206
0.47 0.107 0.257 0.470 0.691 0.859 0.952 0.989 0.998 1.000 0.000 0.003 0.019 0.071 0.186
0.48 0.094 0.235 0.442 0.666 0.842 0.944 0.986 0.998 1.000 0.000 0.003 0.016 0.062 0.167
0.49 0.083 0.214 0.415 0.640 0.825 0.936 0.984 0.997 1.000 0.000 0.002 0.014 0.054 0.150
0.50 0.073 0.194 0.387 0.613 0.806 0.927 0.981 0.997 1.000 0.000 0.002 0.011 0.046 0.133

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