a. Use Table A.5 to find 2 .05;2. b. Verify the answer to (a) by integrating

a. Use Table A.5 to find χ² _.05;2.

b. Verify the answer to (a) by integrating the pdf.

c. Verify the answer to (a) by using software.

Table A.5

Transcribed Image Text:

V 1 2 3 4 5 6 7 8 9 10 11 .995 0.000 0.010 0.072 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 12 13 14 .99 0.000 0.020 0.115 0.297 0.554 0.872 1.239 1.646 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 For v> 40, xv ~1(₁ v 1 6.407 7.015 7.632 8.260 8.897 10,283 .975 0.001 0.051 2 9v 0.216 0.484 0.831 1.237 1.690 2.180 2.733 20.090 2.700 3.325 21.665 3.247 3.940 20.483 23.209 3.816 4.575 21.920 24.724 4.404 5.226 23.337 26.217 5.009 5.892 22.362 24.735 27.687 5.629 6.571 23.685 26.119 29.141 15 4.600 6.262 7.261 22.307 24.996 27.488 30.577 16 5.142 6.908 7.962 23.542 28.845 32.000 26.296 27.587 17 5.697 7.564 8.682 10.085 24.769 30.190 33.408 18 6.265 8.231 9.390 10.865 25.989 28.869 31.526 19 6.843 8.906 10.117 11.651 27.203 30.143 32.852 36.190 20 7.434 9.591 10.851 12.443 28.412 31.410 34.170 37.566 21 8.033 11.591 13.240 29.615 38.930 32.670 35.478 30.813 33.924 36.781 40.289 22 8.643 9.542 10.982 12.338 14.042 23 9.260 10.195 11.688 13.090 14.848 32.007 38.075 41.637 35.172 36.415 24 9.886 10.856 12.401 13.848 15.659 33.196 39.364 42.980 11.523 13.120 14.611 16.473 34.381 37.652 40.646 44.313 25 10.519 26 11.160 12.198 15.379 17.292 35.563 41.923 45.642 38.885 36.741 40.113 27 16.151 18.114 43.194 46.962 13.844 11.807 12.878 14.573 12.461 13.565 15.308 13.120 14.256 16.047 17.708 28 16.928 18.939 37.916 44.461 48.278 19.768 39.087 45.772 49.586 29 30 13.787 14.954 20.599 40.256 46.979 50.892 48.231 52.190 49.480 53.486 42.585 46.194 43.745 47.400 33 50.724 54.774 41.337 42.557 16.791 18.493 43.773 31 14.457 15.655 17.538 19.280 21.433 41.422 44.985 32 15.134 16.362 18.291 20.072 22.271 15.814 17.073 19.046 20.866 23.110 34 16.501 17.789 19.806 21.664 23.952 35 17.191 18.508 20.569 22.465 24.796 46.059 36 17.887 19.233 21.336 23.269 25.643 47.212 37 18.584 19.960 22.105 24.075 38 19.289 20.691 22.878 24.884 39 19.994 21.425 23.654 25.695 20.706 22.164 24.433 26.509 44.903 48.602 51.966 56.061 49.802 53.203 50.998 54.437 26.492 48.363 52.192 55.667 59.891 27.343 49.513 53.384 56.896 61.162 28.196 50.660 54.572 58.119 62.426 40 29.050 51.805 55.758 59.342 63.691 2 + 2x √ ov 9v .95 0.004 0.103 0.352 0.711 1.145 1.635 2.167 3 α 90 .10 0.016 2.706 0.211 4.605 0.584 6.251 1.064 7.779 1.610 9.236 2.204 10.645 2.833 12.017 3.490 13.362 4.168 14.684 0 .05 3.843 5.992 X density curve Shaded area = α .025 .01 5.025 6.637 7.378 9.210 7.815 9.348 11.344 9.488 11.143 13.277 11.070 12.832 15.085 12.592 14.440 16.812 14.067 16.012 18.474 17.534 19.022 15.507 16.919 4.865 15.987 18.307 5.578 17.275 19.675 6.304 18.549 21.026 7.041 19.812 7.790 21.064 8.547 9.312 2 Lav .005 7.882 10.597 12.837 14.860 16.748 18.548 20.276 21.954 23.587 25.188 26.755 28.300 29.817 31.319 32.799 34.267 35.716 34.805 37.156 38.580 39.997 41.399 42.796 44.179 45.558 46.925 48.290 49.642 50.993 52.333 53.672 55.000 56.328 57.646 58.964 60.272 61.581 62.880 64.181 65.473 66.766 57.340 58.619