APPENDIX G STATISTICAL TABLES - US EPA

APPENDIX G STATISTICAL TABLES

Table G.1 -- Quantiles of the standard normal distribution

p 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 Note: z1 & p ' &zp

1 ! p 0.49 0.48 0.47 0.46 0.45 0.44 0.43 0.42 0.41 0.40 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.27 0.26 0.25

zp

p

0.02507

0.76

0.05015

0.77

0.07527

0.78

0.1004

0.79

0.1257

0.80

0.1510

0.81

0.1764

0.82

0.2019

0.83

0.2275

0.84

0.2533

0.85

0.2793

0.86

0.3055

0.87

0.3319

0.88

0.3585

0.89

0.3853

0.90

0.4125

0.91

0.4399

0.92

0.4677

0.93

0.4959

0.94

0.5244

0.95

0.5534

0.96

0.5828

0.97

0.6128

0.98

0.6433

0.99

0.6745

1.00

(Continued on next page)

1 ! p 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

zp 0.7063 0.7388 0.7722 0.8064 0.8416 0.8779 0.9154 0.9542 0.9945 1.036 1.080 1.126 1.175 1.227 1.282 1.341 1.405 1.476 1.555 1.645 1.751 1.881 2.054 2.326

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Statistical Tables Table G.1 (Continued) -- Quantiles of the standard normal distribution

p 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995 0.99975 0.9999

1 ! p 0.10 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005 0.00025 0.0001

zp 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291 3.481 3.719

p

1 - p

0

zp

p ' (zp) '

1

zpe &x 2/2 dx '

1

%

e &z

2 p

/

2

2 &4

2 2

zp %

zp3 3

%

zp5 3@5

%

zp7 3@5@7

% @@@

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Table G.2 -- Quantiles of Student's t distribution

Statistical Tables

Degrees of

Freedom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

p = 0.90 1 ! p = 0.10 tp ' 3.078

1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310

0.95 0.05 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697

0.975 0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042

0.98 0.02 15.895 4.849 3.482 2.999 2.757 2.612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.205 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147

0.99 0.01 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457

0.995 0.005 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750

0.9975 0.0025 127.321 14.089 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030

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Statistical Tables Table G.2 (Continued) -- Quantiles of Student's t distribution

Degrees of

Freedom 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 60 70 80 90

100 200 300 400 500

4

p = 0.90 1 ! p = 0.10

1.309 1.309 1.308 1.307 1.306 1.306 1.305 1.304 1.304 1.303 1.303 1.302 1.302 1.301 1.301 1.300 1.300 1.299 1.299 1.299 1.296 1.294 1.292 1.291 1.290 1.286 1.284 1.284 1.283 1.282

0.95 0.05 1.696 1.694 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.684 1.683 1.682 1.681 1.680 1.679 1.679 1.678 1.677 1.677 1.676 1.671 1.667 1.664 1.662 1.660 1.653 1.650 1.649 1.648 1.645

0.975 0.025 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2.024 2.023 2.021 2.020 2.018 2.017 2.015 2.014 2.013 2.012 2.011 2.010 2.009 2.000 1.994 1.990 1.987 1.984 1.972 1.968 1.966 1.965 1.960

0.98 0.02 2.144 2.141 2.138 2.136 2.133 2.131 2.129 2.127 2.125 2.123 2.121 2.120 2.118 2.116 2.115 2.114 2.112 2.111 2.110 2.109 2.099 2.093 2.088 2.084 2.081 2.067 2.063 2.060 2.059 2.054

0.99 0.01 2.453 2.449 2.445 2.441 2.438 2.434 2.431 2.429 2.426 2.423 2.421 2.418 2.416 2.414 2.412 2.410 2.408 2.407 2.405 2.403 2.390 2.381 2.374 2.368 2.364 2.345 2.339 2.336 2.334 2.326

0.995 0.005 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704 2.701 2.698 2.695 2.692 2.690 2.687 2.685 2.682 2.680 2.678 2.660 2.648 2.639 2.632 2.626 2.601 2.592 2.588 2.586 2.576

0.9975 0.0025 3.022 3.015 3.008 3.002 2.996 2.990 2.985 2.980 2.976 2.971 2.967 2.963 2.959 2.956 2.952 2.949 2.946 2.943 2.940 2.937 2.915 2.899 2.887 2.878 2.871 2.839 2.828 2.823 2.820 2.807

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Table G.3 -- Quantiles of chi-square

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Degrees of

Freedom 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.0025 9.82e!6 5.01e!3

0.0449 0.145 0.307 0.527 0.794

1.10 1.45 1.83 2.23 2.66 3.11 3.58 4.07 4.57 5.09 5.62 6.17 6.72 7.29 7.86 8.45 9.04 9.65 10.26 10.87 11.50 12.13 12.76

0.0050 3.93e!5

0.0100 0.0717

0.207 0.412 0.676 0.989

1.34 1.73 2.16 2.60 3.07 3.57 4.07 4.60 5.14 5.70 6.26 6.84 7.43 8.03 8.64 9.26 9.89 10.52 11.16 11.81 12.46 13.12 13.79

0.0100 1.57e!4

0.0201 0.115 0.297 0.554 0.872 1.24

1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 6.41 7.01 7.63 8.26 8.90 9.54 10.20 10.86 11.52 12.20 12.88 13.56 14.26 14.95

0.0250 9.82e!4

0.0506 0.216 0.484 0.831 1.24 1.69

2.18 2.70 3.25 3.82 4.40 5.01 5.63 6.26 6.91 7.56 8.23 8.91 9.59 10.28 10.98 11.69 12.40 13.12 13.84 14.57 15.31 16.05 16.79

Lower Tail Probability

0.0500 3.93e!3

0.103 0.352 0.711

1.15 1.64 2.17

2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 8.67 9.39 10.12 10.85 11.59 12.34 13.09 13.85 14.61 15.38 16.15 16.93 17.71 18.49

0.1000

0.0158 0.211 0.584 1.06 1.61 2.20 2.83

3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.09 10.86 11.65 12.44 13.24 14.04 14.85 15.66 16.47 17.29 18.11 18.94 19.77 20.60

0.9000

2.71 4.61 6.25 7.78 9.24 10.64 12.02

13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26

0.9500

3.84 5.99 7.81 9.49 11.07 12.59 14.07

15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77

0.9750

5.02 7.38 9.35 11.14 12.83 14.45 16.01

17.53 19.02 20.48 21.92 23.34 24.74 26.12 27.49 28.85 30.19 31.53 32.85 34.17 35.48 36.78 38.08 39.36 40.65 41.92 43.19 44.46 45.72 46.98

0.9900

6.63 9.21 11.34 13.28 15.09 16.81 18.48

20.09 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89

0.9950

7.88 10.60 12.84 14.86 16.75 18.55 20.28

21.95 23.59 25.19 26.76 28.30 29.82 31.32 32.80 34.27 35.72 37.16 38.58 40.00 41.40 42.80 44.18 45.56 46.93 48.29 49.64 50.99 52.34 53.67

0.9975

9.14 11.98 14.32 16.42 18.39 20.25 22.04

23.77 25.46 27.11 28.73 30.32 31.88 33.43 34.95 36.46 37.95 39.42 40.88 42.34 43.78 45.20 46.62 48.03 49.44 50.83 52.22 53.59 54.97 56.33

Statistical Tables

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