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chi2 distribution, Apuntes de Estadística

Asignatura: Estadística II, Profesor: , Carrera: Administració i Direcció d'Empreses, Universidad: UV

Tipo: Apuntes

2016/2017

Subido el 27/06/2017

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Right tail areas for the Chi-square distribution
n0.995 0.99 0.975 0.95 0.9 0.8 0.75 0.7 0.65 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.025 0.01 0.005
10.000 0.000 0.001 0.004 0.016 0.064 0.102 0.148 0.206 0.275 0.455 0.708 1.074 1.642 2.706 3.841 5.024 6.635 7.879
20.010 0.020 0.051 0.103 0.211 0.446 0.575 0.713 0.862 1.022 1.386 1.833 2.408 3.219 4.605 5.991 7.378 9.210 10.597
30.072 0.115 0.216 0.352 0.584 1.005 1.213 1.424 1.642 1.869 2.366 2.946 3.665 4.642 6.251 7.815 9.348 11.345 12.838
40.207 0.297 0.484 0.711 1.064 1.649 1.923 2.195 2.470 2.753 3.357 4.045 4.878 5.989 7.779 9.488 11.143 13.277 14.860
50.412 0.554 0.831 1.145 1.610 2.343 2.675 3.000 3.325 3.655 4.351 5.132 6.064 7.289 9.236 11.070 12.833 15.086 16.750
60.676 0.872 1.237 1.635 2.204 3.070 3.455 3.828 4.197 4.570 5.348 6.211 7.231 8.558 10.645 12.592 14.449 16.812 18.548
70.989 1.239 1.690 2.167 2.833 3.822 4.255 4.671 5.082 5.493 6.346 7.283 8.383 9.803 12.017 14.067 16.013 18.475 20.278
81.344 1.646 2.180 2.733 3.490 4.594 5.071 5.527 5.975 6.423 7.344 8.351 9.524 11.030 13.362 15.507 17.535 20.090 21.955
91.735 2.088 2.700 3.325 4.168 5.380 5.899 6.393 6.876 7.357 8.343 9.414 10.656 12.242 14.684 16.919 19.023 21.666 23.589
10 2.156 2.558 3.247 3.940 4.865 6.179 6.737 7.267 7.783 8.295 9.342 10.473 11.781 13.442 15.987 18.307 20.483 23.209 25.188
11 2.603 3.053 3.816 4.575 5.578 6.989 7.584 8.148 8.695 9.237 10.341 11.530 12.899 14.631 17.275 19.675 21.920 24.725 26.757
12 3.074 3.571 4.404 5.226 6.304 7.807 8.438 9.034 9.612 10.182 11.340 12.584 14.011 15.812 18.549 21.026 23.337 26.217 28.300
13 3.565 4.107 5.009 5.892 7.042 8.634 9.299 9.926 10.532 11.129 12.340 13.636 15.119 16.985 19.812 22.362 24.736 27.688 29.819
14 4.075 4.660 5.629 6.571 7.790 9.467 10.165 10.821 11.455 12.078 13.339 14.685 16.222 18.151 21.064 23.685 26.119 29.141 31.319
15 4.601 5.229 6.262 7.261 8.547 10.307 11.037 11.721 12.381 13.030 14.339 15.733 17.322 19.311 22.307 24.996 27.488 30.578 32.801
16 5.142 5.812 6.908 7.962 9.312 11.152 11.912 12.624 13.310 13.983 15.338 16.780 18.418 20.465 23.542 26.296 28.845 32.000 34.267
17 5.697 6.408 7.564 8.672 10.085 12.002 12.792 13.531 14.241 14.937 16.338 17.824 19.511 21.615 24.769 27.587 30.191 33.409 35.718
18 6.265 7.015 8.231 9.390 10.865 12.857 13.675 14.440 15.174 15.893 17.338 18.868 20.601 22.760 25.989 28.869 31.526 34.805 37.156
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Right tail areas for the Chi-square distribution

  • n 0.995 0.99 0.975 0.95 0.9 0.8 0.75 0.7 0.65 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.025 0.01 0.
  • 1 0.000 0.000 0.001 0.004 0.016 0.064 0.102 0.148 0.206 0.275 0.455 0.708 1.074 1.642 2.706 3.841 5.024 6.635 7.
  • 2 0.010 0.020 0.051 0.103 0.211 0.446 0.575 0.713 0.862 1.022 1.386 1.833 2.408 3.219 4.605 5.991 7.378 9.210 10.
  • 3 0.072 0.115 0.216 0.352 0.584 1.005 1.213 1.424 1.642 1.869 2.366 2.946 3.665 4.642 6.251 7.815 9.348 11.345 12.
  • 4 0.207 0.297 0.484 0.711 1.064 1.649 1.923 2.195 2.470 2.753 3.357 4.045 4.878 5.989 7.779 9.488 11.143 13.277 14.
  • 5 0.412 0.554 0.831 1.145 1.610 2.343 2.675 3.000 3.325 3.655 4.351 5.132 6.064 7.289 9.236 11.070 12.833 15.086 16.
  • 6 0.676 0.872 1.237 1.635 2.204 3.070 3.455 3.828 4.197 4.570 5.348 6.211 7.231 8.558 10.645 12.592 14.449 16.812 18.
  • 7 0.989 1.239 1.690 2.167 2.833 3.822 4.255 4.671 5.082 5.493 6.346 7.283 8.383 9.803 12.017 14.067 16.013 18.475 20.
  • 8 1.344 1.646 2.180 2.733 3.490 4.594 5.071 5.527 5.975 6.423 7.344 8.351 9.524 11.030 13.362 15.507 17.535 20.090 21.
  • 9 1.735 2.088 2.700 3.325 4.168 5.380 5.899 6.393 6.876 7.357 8.343 9.414 10.656 12.242 14.684 16.919 19.023 21.666 23.
  • 10 2.156 2.558 3.247 3.940 4.865 6.179 6.737 7.267 7.783 8.295 9.342 10.473 11.781 13.442 15.987 18.307 20.483 23.209 25.
  • 11 2.603 3.053 3.816 4.575 5.578 6.989 7.584 8.148 8.695 9.237 10.341 11.530 12.899 14.631 17.275 19.675 21.920 24.725 26.
  • 12 3.074 3.571 4.404 5.226 6.304 7.807 8.438 9.034 9.612 10.182 11.340 12.584 14.011 15.812 18.549 21.026 23.337 26.217 28.
  • 13 3.565 4.107 5.009 5.892 7.042 8.634 9.299 9.926 10.532 11.129 12.340 13.636 15.119 16.985 19.812 22.362 24.736 27.688 29.
  • 14 4.075 4.660 5.629 6.571 7.790 9.467 10.165 10.821 11.455 12.078 13.339 14.685 16.222 18.151 21.064 23.685 26.119 29.141 31.
  • 15 4.601 5.229 6.262 7.261 8.547 10.307 11.037 11.721 12.381 13.030 14.339 15.733 17.322 19.311 22.307 24.996 27.488 30.578 32.
  • 16 5.142 5.812 6.908 7.962 9.312 11.152 11.912 12.624 13.310 13.983 15.338 16.780 18.418 20.465 23.542 26.296 28.845 32.000 34.
  • 17 5.697 6.408 7.564 8.672 10.085 12.002 12.792 13.531 14.241 14.937 16.338 17.824 19.511 21.615 24.769 27.587 30.191 33.409 35.
  • 18 6.265 7.015 8.231 9.390 10.865 12.857 13.675 14.440 15.174 15.893 17.338 18.868 20.601 22.760 25.989 28.869 31.526 34.805 37. - n 0.995 0.99 0.975 0.95 0.9 0.8 0.75 0.7 0.65 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.025 0.01 0. Right tail areas for the Chi-square distribution
    • 19 6.844 7.633 8.907 10.117 11.651 13.716 14.562 15.352 16.109 16.850 18.338 19.910 21.689 23.900 27.204 30.144 32.852 36.191 38. p
    • 20 7.434 8.260 9.591 10.851 12.443 14.578 15.452 16.266 17.046 17.809 19.337 20.951 22.775 25.038 28.412 31.410 34.170 37.566 39.
    • 21 8.034 8.897 10.283 11.591 13.240 15.445 16.344 17.182 17.984 18.768 20.337 21.991 23.858 26.171 29.615 32.671 35.479 38.932 41.
    • 22 8.643 9.542 10.982 12.338 14.041 16.314 17.240 18.101 18.924 19.729 21.337 23.031 24.939 27.301 30.813 33.924 36.781 40.289 42.
    • 23 9.260 10.196 11.689 13.091 14.848 17.187 18.137 19.021 19.866 20.690 22.337 24.069 26.018 28.429 32.007 35.172 38.076 41.638 44.
    • 24 9.886 10.856 12.401 13.848 15.659 18.062 19.037 19.943 20.808 21.652 23.337 25.106 27.096 29.553 33.196 36.415 39.364 42.980 45.
    • 25 10.520 11.524 13.120 14.611 16.473 18.940 19.939 20.867 21.752 22.616 24.337 26.143 28.172 30.675 34.382 37.652 40.646 44.314 46.
    • 30 13.787 14.953 16.791 18.493 20.599 23.364 24.478 25.508 26.488 27.442 29.336 31.316 33.530 36.250 40.256 43.773 46.979 50.892 53.
    • 40 20.707 22.164 24.433 26.509 29.051 32.345 33.660 34.872 36.021 37.134 39.335 41.622 44.165 47.269 51.805 55.758 59.342 63.691 66.
    • 50 27.991 29.707 32.357 34.764 37.689 41.449 42.942 44.313 45.610 46.864 49.335 51.892 54.723 58.164 63.167 67.505 71.420 76.154 79.
    • 60 35.534 37.485 40.482 43.188 46.459 50.641 52.294 53.809 55.239 56.620 59.335 62.135 65.227 68.972 74.397 79.082 83.298 88.379 91.
    • 70 43.275 45.442 48.758 51.739 55.329 59.898 61.698 63.346 64.899 66.396 69.334 72.358 75.689 79.715 85.527 90.531 95.023 100.425 104.
    • 80 51.172 53.540 57.153 60.391 64.278 69.207 71.145 72.915 74.583 76.188 79.334 82.566 86.120 90.405 96.578 101.879 106.629 112.329 116.
    • 90 59.196 61.754 65.647 69.126 73.291 78.558 80.625 82.511 84.285 85.993 89.334 92.761 96.524 101.054 107.565 113.145 118.136 124.116 128.
  • 100 67.328 70.065 74.222 77.929 82.358 87.945 90.133 92.129 94.005 95.808 99.334 102.946 106.906 111.667 118.498 124.342 129.561 135.807 140.