19. In a clinical trial involving 4,396 patients aged 65-74, patients were randomly assigned to initial therapy with a diuretic or a beta-blocker or a matched placebo, and then followed up for an average of 5.8 years. The main objective was to see if a policy of anti-hypertensive treatment reduces the risk of stroke, coronary heart disease and death. The main results are as follows: Active treatment Diuretic No. of patients Strokes 1081 45 Coronary events 48 Deaths 134 Beta-blocker 1102 56 80 167 Placebo 2213 134 159 315 Using 95% confidence intervals in both cases is there evidence for there being differences in the risk (proportion) of: Table 3 Areas in Upper Tail of the Normal Distribution The function tabulated is 1-(z) where (z) is the cumulative distribution function of a standardised Normal variable, z. Thus 10(z): ° 1 -2212 12π value of z (-) is the probability that a standardised Normal variate selected at random will be greater than a 0 x-1 .00 .01 .02 .03 .04 .05 .06 90 σ 1-0 (z) .07 .08 .09 EUNES 8EPRE PR888 0.0 0.1 0.2 0.3 0.4 01234 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 .4207 .4168 .4129 .4090 .4052 .4013 .3974 ..3936 .3897 .3859 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 1.0 .1587 .1562 .1539 .1515 .1492) .1469 .1446 .1423 .1401 .1379 1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 1.5 1.6 1.7 1.8 1.9 5678 a .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 2.0 .02275 .02222 .02169 .02118 .02068 .02018 .01970 .01923 .01876 .01831 2.1 .01786 .01743 .01700 .01659 .01618 .01578 .01539 .01500 .01463 .01426 2.2 .01390 .01355 2.3 .01072 .01044 2.4 .00820 .00798 2.5 .00621 .00604 2.6 .00466 .00453 .00440 2.7 .00347 .00336 .00326 2.8 .00256 .00248 .00240 2.9 .00187 .00181 .00175 .01321 .01287 .01255 .01222 .01191 .01017 .00990 .00964 .00939 .00914 .00889 .00866 .00776 .00755 .00734 .00714 .00695 .00676 .00657 .00587 .00570 .00554 .00539 .00523 .00508 .00427 .00415 .00402 .00391 .00379 1.00317 .00307 .00298 .00289 .00280 .00233 .00226 .00219 .00212 .00169 .00164 .00159 .00154 .01160 .01130 .01101 .00842 .00639 .00494 .00480 .00368 .00357 .00272 .00264 .00205 .00149 .00199 .00193 .00144 .00139 3.0 .00135 .00131 .00126 3.1 3.2 3.3 3.4 .00097 .00094 .00090 .00069 .00066. .00048 .00047 .00034 .00032 3.5 .00023 .00022 .00122 .00087 .00064 .00062 .00045 .00043 .00031 .00030 .00022 .00021 3.6 3.7 3.8 3.9 4.0 .00118 .00114 .00111 .00107 .00104 .00100 .00084 .00082 .00079 .00076 .00074 .00071 .00060 .00058 .00056 .00054 .00052 .00050 .00042 .00040 .00039 .00038 .00036 .00035 .00029 .00028 .00027 .00026 .00025 .00024 .00020 .00019 .00019 .00018 .00017 .00017 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011 .000108 .000104 .000100 .000096 .000092 .000088 .000085 .000082 .000078 .000075 .000072 .000069 .000067 .000064 .000062 .000059 .000057 .000054 .000052 .000050 .000048 .000046 .000044 .000042 .000041 .000039 .000037 .000036 .000034 .000033 .000032 5.0 0.000 000 286 7 5.5 0.000 000 019 0 6.0 0.000 000 001 0 108 Table 7 Percentage Points of the t Distribution The table gives the value of tay - the 100a percentage point of the distribution for v degrees of freedom. The values of t are obtained by solution of the equation: α = П[½(v+ 1)][¯¯(½v)]¯¹ (vπ)¯¹⁄2 -1/2 2 + /v)-(v+1)/2 -(v+1)/2 doc Note: The tabulation is for one tail only, that is, for positive values of 1. the column headings for a should be doubled. For 0 i a, v απ 0.10 0.05 0.025 0,01 0.005 0.001 0.0005 v = 1 3.078 6.314 12.706 31.821 63.657 318.31 636.62 2 1.886 2.920 4.303 6.965 9.925 22.326 31.598 3 1.638 2.353 3.182 4.541 5.841 10.213 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.893 6.869 21 25 120 67890 =2D 67822 28220 22222 4828 1.440 1.943 2.447 3.143 3.707 5.208 5.959 1.415 1.895 2.365 2.998 3.499 4.785 5.408 1.397 1.860 2.306 2.896 3.355 4.501 5.041 1.383 1.833 2.262 2.821 3.250 4.297 4.781 1.372 1.812 2.228 2.764 3.169 4.144 4.587 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.850 1.323 1.721 2.080 2.518 2.831 3.527 3.819 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.500 2.807 3.485 3.767 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 1.316 1.708 2.060 2.485 2.787 3.450 3.725 1.315 1.706 2.056 2.479 2.779 3.435 3.707 1.314 1.703 2.052 2.473 2.771 3.421 3.690 1.313 1.701 2.048 2.467 2.763 3.408 3.674 1.311 1.699 2.045 2.462 2.756 3.396 3.659 1.310 1.697 2.042 2.457 2.750 3.385 3.646 40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 1.296 1.671 2.000 2.390 2.660 3.232 3.460 1.289 1.658 1.980 2.358 2.617 3.160 3.373 1.282 1.645 1.960 2.326 2.576 3.090 3.291 Table 8 Percentage Points of the x² Distribution - continued .30 .25 .20 .10 .05 .025 .02 .01 .005 .001 Ξα 1.074 1.323 1.642 2.706 3.841 5.024 5.412 6.635 7.879 10.827 y= 1 2.408 2.773 3.219 4.605 5.991 7.378 7.824 9.210 10.597 13.815 2 3.665 4.108 4.642 6.251 7.815 9.348 9.837 11.345 12.838 16.268 3 4.878 5.385 5.989 7.779 9.488 11.143 11.668 13.277 14.860 18.465 4 6.064 6.626 7.289 9.236 11.070 12.832 13.388 15.086 16.750 20.517 5 7.231 7.841 8.558 10.645 12.592 14.449 15.033 16.812 18.548 22.457 6 8.383 9.037 9.803 12,017 14.067 16.013 16.622 18.475 20.278 24.322 7 9.524 10.219 11.030 13.362 15.507 17.535 18.168 20.090 21.955 26.125 g 10.656 11.389 12.242 14.684 16.919 19.023 19.679 21.666 23.589 27.877 11.781 12.549 13.442 15.987 18.307 20.483 21.161 23.209 25.188 29.588 10 12.899 13.701 14.631 17.275 19.675 21,920 22.618 24.725 26.757 31.264 11 14.011 14.845 15.812 18.549 21.026 23.337 24.054 26.217 28.300 32.909 12 15.119 15.984 16.985 19.812 22.362 24.736 25.472 27.688 29.819 34.528 13 16.222 17.117 18.151 21.064 23.685 26.119 26.873 29.141 31.319 36.123 17.322 18.245 19.311 22.307 24.996 27.488 28.259 30.578 32.801 37.697 18.418 19.369 20.465 23.542 26.296 28.845 29.633 32.000 34.267 39.252 19,511 20.489 24.769 21.615 27.587 30.191 30.995 33.409 35.718 20.601 21.605 22.760 25.989 28.869 31.526 32.346 34.805 37.156 40.790 42.312 21.689 22.718 23.900 27.204 30.144 32.852 33.687 36.191 38.582 43.820 22.775 23.828 25.038 28.412 31.410 34.170 35.020 37.566 39.997 45.315 23.858 24.935 26.171 29.615 32.671 35.479 36.343 38.932 41.401 46.797 24.939 26.039 27.301 30.813 33.924 36.781 37.659 40.289 42.796 48.268 26.018 27.141 28.429 32.007 35.172 38.076 38.968 41.638 44.181 49.728 27.096 28.241 29.553 33.196 36.415 39.364 40.270 42.980 45.558 28.172 29.339 30.675 34.382 37.652 40.646 41.566 44.314 46.928 51.179 52.620 29.246 31.795 30.434 35.563 38.885 41.923 42.856 45.642 48.290 54.052 30.319 31.528 32.912 36.741 40.113 43.194 44.140 46.963 49.645 55.476 31.391 32.620 34.027 37.916 41.337 44.461 45.419 48.278 50.993 56.893 32.461 33.711 35.139 39.087 42.557 45.722 46.693 49.588 52.336 58.302 33.530 34.800 36.250 40.256 43.773 46.979 47.962 50.892 53.672 59.703 44.165 45.616 47.269 51.805 55.759 59.342 60.436 63.691 66.766 73.402 54.723 56.334 58.164 63.167 67.505 71.420 72.613 76.154 79.490 86.661 65.227 66.981 68.972 74.397 79.082 83.298 84,580 88.379 91.952 99.607 75.689 77.577 79.715 85.527 90.531 95.023 96.388 100.425 86.120 88.130 90.405 96.578 101.880 106.629 96.524 98.650 101.054 106.906 109.141 111.667' 107.565 113.145 118.136 118.498 124.342 129.561 104.215 108.069 112.329 116.321 119.648 124.116 128.299 131.142 135.807 140.170 112.317 124.839 137.208 149.449 100 ± 298 220 22228 48822 28 14' 15 16 17 18 19 20 21 23 24 25 26 27 29 30 40 50 60 70 80 Table A4. Upper percentage points of the F distribution with V1, V2 df (a) 5% points V₁ df for the numerator V2 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 2 3 161.448 199.500 215.707 224.583 230.162 18.513 19.000 19.164 19.247 19.296 10.1280 9.5521 9.2766 9.1172 9.0135 4 7.7086 6.9443 6.5914 6.3882 506 6.6079 5.7861 5.1922 5.9874 4.2067 7 5.5914 4.7374 4.1203 3.9715 3.8660 8 CONNERO2222222222204828 3.8379 3.8625 3.6331 3.4817 3.6875 3.5806 3.3738 3.2927 3.1355 4.4513 3.5915 3.1968 2.8100 4.4139 3.5546 3.1599 2.9277 2.7729 4.3807 3.5219 3.1273 2.8951 2.7401 2.6283 2.5435 4.3512 3.4928 3.0984 2.8661 5.4095 5.1433 4.7571 4.5337 4.3468 5.3177 4.4590 4.0662 5.1174 4.2565 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.4630 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.4753 2.4034 2.3275 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756 2.9647 2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304 2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906 2.4768 2.4227 2.3080 2.2341 2.1555 2.4471 2.3928 2.2776 2.2033 233.986 236.768 238.883 240.543 241.882 19.330 19.353 19.371 19.385 8.9406 8.8867 8.8452 8.8123 6.2561 6.1631 6.0942 6.0410 5.9988 5.0503 4.9503 4.8759 4.8183 4.7725 4.3874 4.2839 4.0990 4.0600 3.9999 19.396 8.7855 5.9644 5.9117 5.8578 4.7351 4.6777 4.6188 243.906 245.950 248.013 19.413 19.429 19.446 8.7446 8.7029 8.6602 249.052 250.095 251.143 252.196 253.253 254.314 19.454 8.6385 19.462 8.6166 5.8025 5.7744 5.7459 19.471 19.479 8.5944 8.5720 5.7170 5.6877 5.6581 5.6281 19.487 8.5493 19.496 8.5265 4.5581 4.5272 4.4957 4.4638 4.4314 4.3985 4.3650 4.1468 3.9381 3.8742 3.8415 3.8082 3.7743 3.7398 3.7047 3.6689 3.7870 3.7257 3.6767 3.6365 3.5747 3.5107 3.4445 3.4105 3.3758 3.3404 3.3043 3.2674 3.2298 3.5005 3.4381 3.3881 3.3472 3.2839 3.2184 3.1503 3.1152 3.0794 3.0428 3.0053 2.9669 2.9276 3.2296 3.1789 3.1373 3.0729 3.0061 2.9365 2.9005 2.8637 2.8259 2.7872 2.7475 2.7067 3.0717 3.0204 2.9782 2.9130 2.8450 2.7740 2.7372 2.6996 2.6609 2.6211 2.5801 2.5379 2.7876 2.7186 2.7964 2.7534 2.6866 2.6169 2.6464 2.5436 2.5055 2.6090 2.5705 2.5309 2.4901 2.4480 2.4045 2.6710 2.6037 2.5331 2.6022 2.5437 2.5342 2.4663 2.4589 2.4202 2.3803 2.3879 2.3487 2.3082 2.2878 2.4259 2.3842 2.3410 2.3392 2.2966 2.2524 2.2664 2.2229 2.1778 2.2468 2.2043 2.1601 2.1141 2.2354 2.1938 2.1507 2.1058 2.0589 2.1898 2.1477 2.1040 2.0584 2.2962 2.2064 2.1307 2.0659 2.0096 2.0107 1.9604 4.3248 3.4668 3.0725 2.8401 2.6848 4.3009 3.4434 3.0491 2.8167 2.3965 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.2821 2.2365 2.1649 4.2252 4.2100 3.3690 2.9752 2.7426 3.3541 2.9604 2.7278 4.1960 3.3404 2.9467 2.7141 4.1830 3.3277 2.9340 4.1709 3.3158 2.9223 2.8387 3.9201 3.0718 3.8415 2.9957 2.5868 2.5719 2.4591 2.3732 2.3053 2.2501 2.2043 2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179 2.7014 2.5454 2.4324 2.3463 2.6896 2.5336 2.4205 2.3343 4.0847 3.2317 2.6060 2.4495 2.3359 2.2490 2.1802 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.6802 2.4472 2.2899 2.1750 2.0868 2.6049 2.3719 2.2141 2.0986 2.0096 2.4741 2.3883 2.1497 2.1141 2.7109 2.5990 2.5140 2.0825 2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540 2.6613 2.5491 2.4638 2.3419 2.2967 2.2258 2.1508 2.0707 2.0283 2.3201 2.2747 2.2036 2.1282 2.0476 2.0050 2.3002 2.2547 2.1834 2.1077 2.0267 1.9838 2.0889 2.0075 1.9898 2.1071 2.0629 2.0166 1.9681 1.9168 2.3779 2.3479 2.0712 2.0264 1.9795 1.9302 1.8780 2.1242 2.0391 1.9938 1.9464 1.8963 1.8432 2.0102 1.9645 1.9165 1.8657 1.8117 1.9842 1.9380 1.8894 1.8380 1.7831 1.9605 1.9390 1.9139 1.8648 1.8128 1.7570 1.8920 1.8424 1.7896 1.7331 2.3205 2.2655 2.2197 2.1479 2.0716 1.9643 1.9192 1.8718 1.8217 1.7684 1.9464 1.9010 1.7110 1.8533 1.8027 1.7488 1.6906 2.1323 2.0558 1.9736 1.9299 1.8842 1.8361 1.7851 1.7306 1.6717 2.0411 1.9586 1.9147 1.8687 1.8203 1.7689 1.7138 1.6541 2.2783 2.2229 2.1768 2.1045 2.0275 1.9446 1.9005 1.8543 1.8055 1.7537 1.6981 1.6377 2.2662 2.2107 2.1646 2.0921 2.0148 1.9317 1.8874 1.8409 1.7918 1.7396 1.6835 1.6223 2.1240 2.0772 2.0035 1.9245 1.8389 1.7929 1.7444 1.6928 1.6373 1.5766 1.5089 2.0970 2.0401 1.9926 1.9174 1.8364 1.7480 2.0164 1.9588 1.9384 1.8799 1.9105 1.8307 1.7522 1.6664 1.7001 1.8337 1.7505 1.6587 1.6084 1.5543 1.6491 1.5943 1.5343 1.4673 1.3893 1.4952 1.4290 1.3519 1.2539 1.5705 1.5173 1.4591 1.3940 1.3180 1.2214 1.0033
19. In a clinical trial involving 4,396 patients aged 65-74, patients were randomly assigned to initial therapy with a diuretic or a beta-blocker or a matched placebo, and then followed up for an average of 5.8 years. The main objective was to see if a policy of anti-hypertensive treatment reduces the risk of stroke, coronary heart disease and death. The main results are as follows: Active treatment Diuretic No. of patients Strokes 1081 45 Coronary events 48 Deaths 134 Beta-blocker 1102 56 80 167 Placebo 2213 134 159 315 Using 95% confidence intervals in both cases is there evidence for there being differences in the risk (proportion) of: Table 3 Areas in Upper Tail of the Normal Distribution The function tabulated is 1-(z) where (z) is the cumulative distribution function of a standardised Normal variable, z. Thus 10(z): ° 1 -2212 12π value of z (-) is the probability that a standardised Normal variate selected at random will be greater than a 0 x-1 .00 .01 .02 .03 .04 .05 .06 90 σ 1-0 (z) .07 .08 .09 EUNES 8EPRE PR888 0.0 0.1 0.2 0.3 0.4 01234 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 .4207 .4168 .4129 .4090 .4052 .4013 .3974 ..3936 .3897 .3859 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 1.0 .1587 .1562 .1539 .1515 .1492) .1469 .1446 .1423 .1401 .1379 1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 1.5 1.6 1.7 1.8 1.9 5678 a .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 2.0 .02275 .02222 .02169 .02118 .02068 .02018 .01970 .01923 .01876 .01831 2.1 .01786 .01743 .01700 .01659 .01618 .01578 .01539 .01500 .01463 .01426 2.2 .01390 .01355 2.3 .01072 .01044 2.4 .00820 .00798 2.5 .00621 .00604 2.6 .00466 .00453 .00440 2.7 .00347 .00336 .00326 2.8 .00256 .00248 .00240 2.9 .00187 .00181 .00175 .01321 .01287 .01255 .01222 .01191 .01017 .00990 .00964 .00939 .00914 .00889 .00866 .00776 .00755 .00734 .00714 .00695 .00676 .00657 .00587 .00570 .00554 .00539 .00523 .00508 .00427 .00415 .00402 .00391 .00379 1.00317 .00307 .00298 .00289 .00280 .00233 .00226 .00219 .00212 .00169 .00164 .00159 .00154 .01160 .01130 .01101 .00842 .00639 .00494 .00480 .00368 .00357 .00272 .00264 .00205 .00149 .00199 .00193 .00144 .00139 3.0 .00135 .00131 .00126 3.1 3.2 3.3 3.4 .00097 .00094 .00090 .00069 .00066. .00048 .00047 .00034 .00032 3.5 .00023 .00022 .00122 .00087 .00064 .00062 .00045 .00043 .00031 .00030 .00022 .00021 3.6 3.7 3.8 3.9 4.0 .00118 .00114 .00111 .00107 .00104 .00100 .00084 .00082 .00079 .00076 .00074 .00071 .00060 .00058 .00056 .00054 .00052 .00050 .00042 .00040 .00039 .00038 .00036 .00035 .00029 .00028 .00027 .00026 .00025 .00024 .00020 .00019 .00019 .00018 .00017 .00017 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011 .000108 .000104 .000100 .000096 .000092 .000088 .000085 .000082 .000078 .000075 .000072 .000069 .000067 .000064 .000062 .000059 .000057 .000054 .000052 .000050 .000048 .000046 .000044 .000042 .000041 .000039 .000037 .000036 .000034 .000033 .000032 5.0 0.000 000 286 7 5.5 0.000 000 019 0 6.0 0.000 000 001 0 108 Table 7 Percentage Points of the t Distribution The table gives the value of tay - the 100a percentage point of the distribution for v degrees of freedom. The values of t are obtained by solution of the equation: α = П[½(v+ 1)][¯¯(½v)]¯¹ (vπ)¯¹⁄2 -1/2 2 + /v)-(v+1)/2 -(v+1)/2 doc Note: The tabulation is for one tail only, that is, for positive values of 1. the column headings for a should be doubled. For 0 i a, v απ 0.10 0.05 0.025 0,01 0.005 0.001 0.0005 v = 1 3.078 6.314 12.706 31.821 63.657 318.31 636.62 2 1.886 2.920 4.303 6.965 9.925 22.326 31.598 3 1.638 2.353 3.182 4.541 5.841 10.213 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.893 6.869 21 25 120 67890 =2D 67822 28220 22222 4828 1.440 1.943 2.447 3.143 3.707 5.208 5.959 1.415 1.895 2.365 2.998 3.499 4.785 5.408 1.397 1.860 2.306 2.896 3.355 4.501 5.041 1.383 1.833 2.262 2.821 3.250 4.297 4.781 1.372 1.812 2.228 2.764 3.169 4.144 4.587 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.850 1.323 1.721 2.080 2.518 2.831 3.527 3.819 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.500 2.807 3.485 3.767 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 1.316 1.708 2.060 2.485 2.787 3.450 3.725 1.315 1.706 2.056 2.479 2.779 3.435 3.707 1.314 1.703 2.052 2.473 2.771 3.421 3.690 1.313 1.701 2.048 2.467 2.763 3.408 3.674 1.311 1.699 2.045 2.462 2.756 3.396 3.659 1.310 1.697 2.042 2.457 2.750 3.385 3.646 40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 1.296 1.671 2.000 2.390 2.660 3.232 3.460 1.289 1.658 1.980 2.358 2.617 3.160 3.373 1.282 1.645 1.960 2.326 2.576 3.090 3.291 Table 8 Percentage Points of the x² Distribution - continued .30 .25 .20 .10 .05 .025 .02 .01 .005 .001 Ξα 1.074 1.323 1.642 2.706 3.841 5.024 5.412 6.635 7.879 10.827 y= 1 2.408 2.773 3.219 4.605 5.991 7.378 7.824 9.210 10.597 13.815 2 3.665 4.108 4.642 6.251 7.815 9.348 9.837 11.345 12.838 16.268 3 4.878 5.385 5.989 7.779 9.488 11.143 11.668 13.277 14.860 18.465 4 6.064 6.626 7.289 9.236 11.070 12.832 13.388 15.086 16.750 20.517 5 7.231 7.841 8.558 10.645 12.592 14.449 15.033 16.812 18.548 22.457 6 8.383 9.037 9.803 12,017 14.067 16.013 16.622 18.475 20.278 24.322 7 9.524 10.219 11.030 13.362 15.507 17.535 18.168 20.090 21.955 26.125 g 10.656 11.389 12.242 14.684 16.919 19.023 19.679 21.666 23.589 27.877 11.781 12.549 13.442 15.987 18.307 20.483 21.161 23.209 25.188 29.588 10 12.899 13.701 14.631 17.275 19.675 21,920 22.618 24.725 26.757 31.264 11 14.011 14.845 15.812 18.549 21.026 23.337 24.054 26.217 28.300 32.909 12 15.119 15.984 16.985 19.812 22.362 24.736 25.472 27.688 29.819 34.528 13 16.222 17.117 18.151 21.064 23.685 26.119 26.873 29.141 31.319 36.123 17.322 18.245 19.311 22.307 24.996 27.488 28.259 30.578 32.801 37.697 18.418 19.369 20.465 23.542 26.296 28.845 29.633 32.000 34.267 39.252 19,511 20.489 24.769 21.615 27.587 30.191 30.995 33.409 35.718 20.601 21.605 22.760 25.989 28.869 31.526 32.346 34.805 37.156 40.790 42.312 21.689 22.718 23.900 27.204 30.144 32.852 33.687 36.191 38.582 43.820 22.775 23.828 25.038 28.412 31.410 34.170 35.020 37.566 39.997 45.315 23.858 24.935 26.171 29.615 32.671 35.479 36.343 38.932 41.401 46.797 24.939 26.039 27.301 30.813 33.924 36.781 37.659 40.289 42.796 48.268 26.018 27.141 28.429 32.007 35.172 38.076 38.968 41.638 44.181 49.728 27.096 28.241 29.553 33.196 36.415 39.364 40.270 42.980 45.558 28.172 29.339 30.675 34.382 37.652 40.646 41.566 44.314 46.928 51.179 52.620 29.246 31.795 30.434 35.563 38.885 41.923 42.856 45.642 48.290 54.052 30.319 31.528 32.912 36.741 40.113 43.194 44.140 46.963 49.645 55.476 31.391 32.620 34.027 37.916 41.337 44.461 45.419 48.278 50.993 56.893 32.461 33.711 35.139 39.087 42.557 45.722 46.693 49.588 52.336 58.302 33.530 34.800 36.250 40.256 43.773 46.979 47.962 50.892 53.672 59.703 44.165 45.616 47.269 51.805 55.759 59.342 60.436 63.691 66.766 73.402 54.723 56.334 58.164 63.167 67.505 71.420 72.613 76.154 79.490 86.661 65.227 66.981 68.972 74.397 79.082 83.298 84,580 88.379 91.952 99.607 75.689 77.577 79.715 85.527 90.531 95.023 96.388 100.425 86.120 88.130 90.405 96.578 101.880 106.629 96.524 98.650 101.054 106.906 109.141 111.667' 107.565 113.145 118.136 118.498 124.342 129.561 104.215 108.069 112.329 116.321 119.648 124.116 128.299 131.142 135.807 140.170 112.317 124.839 137.208 149.449 100 ± 298 220 22228 48822 28 14' 15 16 17 18 19 20 21 23 24 25 26 27 29 30 40 50 60 70 80 Table A4. Upper percentage points of the F distribution with V1, V2 df (a) 5% points V₁ df for the numerator V2 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 2 3 161.448 199.500 215.707 224.583 230.162 18.513 19.000 19.164 19.247 19.296 10.1280 9.5521 9.2766 9.1172 9.0135 4 7.7086 6.9443 6.5914 6.3882 506 6.6079 5.7861 5.1922 5.9874 4.2067 7 5.5914 4.7374 4.1203 3.9715 3.8660 8 CONNERO2222222222204828 3.8379 3.8625 3.6331 3.4817 3.6875 3.5806 3.3738 3.2927 3.1355 4.4513 3.5915 3.1968 2.8100 4.4139 3.5546 3.1599 2.9277 2.7729 4.3807 3.5219 3.1273 2.8951 2.7401 2.6283 2.5435 4.3512 3.4928 3.0984 2.8661 5.4095 5.1433 4.7571 4.5337 4.3468 5.3177 4.4590 4.0662 5.1174 4.2565 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.4630 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.4753 2.4034 2.3275 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756 2.9647 2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304 2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906 2.4768 2.4227 2.3080 2.2341 2.1555 2.4471 2.3928 2.2776 2.2033 233.986 236.768 238.883 240.543 241.882 19.330 19.353 19.371 19.385 8.9406 8.8867 8.8452 8.8123 6.2561 6.1631 6.0942 6.0410 5.9988 5.0503 4.9503 4.8759 4.8183 4.7725 4.3874 4.2839 4.0990 4.0600 3.9999 19.396 8.7855 5.9644 5.9117 5.8578 4.7351 4.6777 4.6188 243.906 245.950 248.013 19.413 19.429 19.446 8.7446 8.7029 8.6602 249.052 250.095 251.143 252.196 253.253 254.314 19.454 8.6385 19.462 8.6166 5.8025 5.7744 5.7459 19.471 19.479 8.5944 8.5720 5.7170 5.6877 5.6581 5.6281 19.487 8.5493 19.496 8.5265 4.5581 4.5272 4.4957 4.4638 4.4314 4.3985 4.3650 4.1468 3.9381 3.8742 3.8415 3.8082 3.7743 3.7398 3.7047 3.6689 3.7870 3.7257 3.6767 3.6365 3.5747 3.5107 3.4445 3.4105 3.3758 3.3404 3.3043 3.2674 3.2298 3.5005 3.4381 3.3881 3.3472 3.2839 3.2184 3.1503 3.1152 3.0794 3.0428 3.0053 2.9669 2.9276 3.2296 3.1789 3.1373 3.0729 3.0061 2.9365 2.9005 2.8637 2.8259 2.7872 2.7475 2.7067 3.0717 3.0204 2.9782 2.9130 2.8450 2.7740 2.7372 2.6996 2.6609 2.6211 2.5801 2.5379 2.7876 2.7186 2.7964 2.7534 2.6866 2.6169 2.6464 2.5436 2.5055 2.6090 2.5705 2.5309 2.4901 2.4480 2.4045 2.6710 2.6037 2.5331 2.6022 2.5437 2.5342 2.4663 2.4589 2.4202 2.3803 2.3879 2.3487 2.3082 2.2878 2.4259 2.3842 2.3410 2.3392 2.2966 2.2524 2.2664 2.2229 2.1778 2.2468 2.2043 2.1601 2.1141 2.2354 2.1938 2.1507 2.1058 2.0589 2.1898 2.1477 2.1040 2.0584 2.2962 2.2064 2.1307 2.0659 2.0096 2.0107 1.9604 4.3248 3.4668 3.0725 2.8401 2.6848 4.3009 3.4434 3.0491 2.8167 2.3965 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.2821 2.2365 2.1649 4.2252 4.2100 3.3690 2.9752 2.7426 3.3541 2.9604 2.7278 4.1960 3.3404 2.9467 2.7141 4.1830 3.3277 2.9340 4.1709 3.3158 2.9223 2.8387 3.9201 3.0718 3.8415 2.9957 2.5868 2.5719 2.4591 2.3732 2.3053 2.2501 2.2043 2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179 2.7014 2.5454 2.4324 2.3463 2.6896 2.5336 2.4205 2.3343 4.0847 3.2317 2.6060 2.4495 2.3359 2.2490 2.1802 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.6802 2.4472 2.2899 2.1750 2.0868 2.6049 2.3719 2.2141 2.0986 2.0096 2.4741 2.3883 2.1497 2.1141 2.7109 2.5990 2.5140 2.0825 2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540 2.6613 2.5491 2.4638 2.3419 2.2967 2.2258 2.1508 2.0707 2.0283 2.3201 2.2747 2.2036 2.1282 2.0476 2.0050 2.3002 2.2547 2.1834 2.1077 2.0267 1.9838 2.0889 2.0075 1.9898 2.1071 2.0629 2.0166 1.9681 1.9168 2.3779 2.3479 2.0712 2.0264 1.9795 1.9302 1.8780 2.1242 2.0391 1.9938 1.9464 1.8963 1.8432 2.0102 1.9645 1.9165 1.8657 1.8117 1.9842 1.9380 1.8894 1.8380 1.7831 1.9605 1.9390 1.9139 1.8648 1.8128 1.7570 1.8920 1.8424 1.7896 1.7331 2.3205 2.2655 2.2197 2.1479 2.0716 1.9643 1.9192 1.8718 1.8217 1.7684 1.9464 1.9010 1.7110 1.8533 1.8027 1.7488 1.6906 2.1323 2.0558 1.9736 1.9299 1.8842 1.8361 1.7851 1.7306 1.6717 2.0411 1.9586 1.9147 1.8687 1.8203 1.7689 1.7138 1.6541 2.2783 2.2229 2.1768 2.1045 2.0275 1.9446 1.9005 1.8543 1.8055 1.7537 1.6981 1.6377 2.2662 2.2107 2.1646 2.0921 2.0148 1.9317 1.8874 1.8409 1.7918 1.7396 1.6835 1.6223 2.1240 2.0772 2.0035 1.9245 1.8389 1.7929 1.7444 1.6928 1.6373 1.5766 1.5089 2.0970 2.0401 1.9926 1.9174 1.8364 1.7480 2.0164 1.9588 1.9384 1.8799 1.9105 1.8307 1.7522 1.6664 1.7001 1.8337 1.7505 1.6587 1.6084 1.5543 1.6491 1.5943 1.5343 1.4673 1.3893 1.4952 1.4290 1.3519 1.2539 1.5705 1.5173 1.4591 1.3940 1.3180 1.2214 1.0033
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
To answer questions 19, please use the stats tables provided. Do not used a software.
Q19:
a. Death between those taking diuretic and those taking placebo?
b. Stroke between those taking beta-blocker and those taking placebo?
Transcribed Image Text:19. In a clinical trial involving 4,396 patients aged 65-74, patients were randomly assigned to initial
therapy with a diuretic or a beta-blocker or a matched placebo, and then followed up for an average of
5.8 years. The main objective was to see if a policy of anti-hypertensive treatment reduces the risk of
stroke, coronary heart disease and death. The main results are as follows:
Active treatment
Diuretic
No. of patients
Strokes
1081
45
Coronary events
48
Deaths
134
Beta-blocker
1102
56
80
167
Placebo
2213
134
159
315
Using 95% confidence intervals in both cases is there evidence for there being differences in the risk
(proportion) of:
![Table 3 Areas in Upper Tail of the Normal Distribution
The function tabulated is 1-(z) where (z) is the cumulative distribution function of a standardised Normal variable, z.
Thus 10(z):
°
1
-2212
12π
value of z
(-)
is the probability that a standardised Normal variate selected at random will be greater than a
0
x-1
.00
.01
.02
.03
.04
.05
.06
90
σ
1-0 (z)
.07
.08
.09
EUNES 8EPRE PR888
0.0
0.1
0.2
0.3
0.4
01234
.5000
.4960
.4920
.4880
.4840
.4801
.4761
.4721
.4681
.4641
.4602
.4562
.4522
.4483
.4443
.4404
.4364
.4325
.4286
.4247
.4207
.4168
.4129
.4090
.4052
.4013
.3974
..3936
.3897
.3859
.3821
.3783
.3745
.3707
.3669
.3632
.3594
.3557
.3520
.3483
.3446
.3409
.3372
.3336
.3300
.3264
.3228
.3192
.3156
.3121
0.5
.3085
.3050
.3015
.2981
.2946
.2912
.2877
.2843
.2810
.2776
0.6
.2743
.2709
.2676
.2643
.2611
.2578
.2546
.2514
.2483
.2451
0.7
.2420
.2389
.2358
.2327
.2296
.2266
.2236
.2206
.2177
.2148
0.8
.2119
.2090
.2061
.2033
.2005
.1977
.1949
.1922
.1894
.1867
0.9
.1841
.1814
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
1.0
.1587
.1562
.1539
.1515
.1492) .1469
.1446
.1423
.1401
.1379
1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
1.2
.1151
.1131
.1112
.1093
.1075
.1056
.1038
.1020
.1003
.0985
1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0838
.0823
1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0694
.0681
1.5
1.6
1.7
1.8
1.9
5678 a
.0668
.0655
.0643
.0630
.0618
.0606
.0594
.0582
.0571
.0559
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
.0446
.0436
.0427
.0418
.0409
.0401
.0392
.0384
.0375
.0367
.0359
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0294
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0239
.0233
2.0
.02275 .02222 .02169
.02118 .02068
.02018
.01970
.01923
.01876
.01831
2.1
.01786 .01743 .01700
.01659 .01618 .01578
.01539
.01500 .01463
.01426
2.2
.01390 .01355
2.3
.01072 .01044
2.4
.00820 .00798
2.5
.00621 .00604
2.6
.00466 .00453
.00440
2.7
.00347 .00336
.00326
2.8
.00256 .00248
.00240
2.9
.00187 .00181
.00175
.01321 .01287 .01255 .01222 .01191
.01017 .00990 .00964 .00939 .00914 .00889 .00866
.00776 .00755 .00734 .00714 .00695 .00676 .00657
.00587 .00570 .00554 .00539 .00523 .00508
.00427 .00415 .00402 .00391 .00379
1.00317 .00307 .00298 .00289 .00280
.00233 .00226 .00219 .00212
.00169 .00164 .00159 .00154
.01160 .01130
.01101
.00842
.00639
.00494 .00480
.00368 .00357
.00272 .00264
.00205
.00149
.00199 .00193
.00144 .00139
3.0
.00135
.00131 .00126
3.1
3.2
3.3
3.4
.00097 .00094 .00090
.00069 .00066.
.00048 .00047
.00034 .00032
3.5
.00023 .00022
.00122
.00087
.00064 .00062
.00045 .00043
.00031 .00030
.00022 .00021
3.6
3.7
3.8
3.9
4.0
.00118 .00114 .00111 .00107 .00104 .00100
.00084 .00082 .00079 .00076 .00074 .00071
.00060 .00058 .00056 .00054 .00052 .00050
.00042 .00040 .00039 .00038 .00036 .00035
.00029 .00028 .00027 .00026 .00025 .00024
.00020 .00019
.00019 .00018 .00017 .00017
.00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011
.000108 .000104 .000100 .000096 .000092 .000088 .000085 .000082 .000078 .000075
.000072 .000069 .000067 .000064 .000062 .000059 .000057 .000054 .000052 .000050
.000048 .000046 .000044 .000042 .000041 .000039 .000037 .000036 .000034 .000033
.000032
5.0 0.000 000 286 7
5.5 0.000 000 019 0
6.0 0.000 000 001 0
108
Table 7 Percentage Points of the t Distribution
The table gives the value of tay - the 100a percentage point of the distribution for v degrees of freedom.
The values of t are obtained by solution of the equation:
α = П[½(v+ 1)][¯¯(½v)]¯¹ (vπ)¯¹⁄2
-1/2
2
+
/v)-(v+1)/2
-(v+1)/2 doc
Note: The tabulation is for one tail only, that is, for positive values of 1.
the column headings for a should be doubled.
For
0
i a, v
απ
0.10
0.05
0.025
0,01
0.005
0.001
0.0005
v = 1
3.078
6.314
12.706
31.821
63.657
318.31
636.62
2
1.886
2.920
4.303
6.965
9.925
22.326
31.598
3
1.638
2.353
3.182
4.541
5.841
10.213
12.924
4
1.533
2.132
2.776
3.747
4.604
7.173
8.610
5
1.476
2.015
2.571
3.365
4.032
5.893
6.869
21
25
120
67890 =2D 67822 28220 22222 4828
1.440
1.943
2.447
3.143
3.707
5.208
5.959
1.415
1.895
2.365
2.998
3.499
4.785
5.408
1.397
1.860
2.306
2.896
3.355
4.501
5.041
1.383
1.833
2.262
2.821
3.250
4.297
4.781
1.372
1.812
2.228
2.764
3.169
4.144
4.587
1.363
1.796
2.201
2.718
3.106
4.025
4.437
12
1.356
1.782
2.179
2.681
3.055
3.930
4.318
13
1.350
1.771
2.160
2.650
3.012
3.852
4.221
14
1.345
1.761
2.145
2.624
2.977
3.787
4.140
15
1.341
1.753
2.131
2.602
2.947
3.733
4.073
16
1.337
1.746
2.120
2.583
2.921
3.686
4.015
17
1.333
1.740
2.110
2.567
2.898
3.646
3.965
18
1.330
1.734
2.101
2.552
2.878
3.610
3.922
19
1.328
1.729
2.093
2.539
2.861
3.579
3.883
20
1.325
1.725
2.086
2.528
2.845
3.552
3.850
1.323
1.721
2.080
2.518
2.831
3.527
3.819
1.321
1.717
2.074
2.508
2.819
3.505
3.792
23
1.319
1.714
2.069
2.500
2.807
3.485
3.767
24
1.318
1.711
2.064
2.492
2.797
3.467
3.745
1.316
1.708
2.060
2.485
2.787
3.450
3.725
1.315
1.706
2.056
2.479
2.779
3.435
3.707
1.314
1.703
2.052
2.473
2.771
3.421
3.690
1.313
1.701
2.048
2.467
2.763
3.408
3.674
1.311
1.699
2.045
2.462
2.756
3.396
3.659
1.310
1.697
2.042
2.457
2.750
3.385
3.646
40
1.303
1.684
2.021
2.423
2.704
3.307
3.551
60
1.296
1.671
2.000
2.390
2.660
3.232
3.460
1.289
1.658
1.980
2.358
2.617
3.160
3.373
1.282
1.645
1.960
2.326
2.576
3.090
3.291
Table 8 Percentage Points of the x² Distribution - continued
.30
.25
.20
.10
.05
.025
.02
.01
.005
.001
Ξα
1.074
1.323
1.642
2.706
3.841
5.024
5.412
6.635
7.879
10.827
y= 1
2.408
2.773
3.219
4.605
5.991
7.378
7.824
9.210
10.597
13.815
2
3.665
4.108
4.642
6.251
7.815
9.348
9.837
11.345
12.838
16.268
3
4.878
5.385
5.989
7.779
9.488
11.143
11.668
13.277
14.860
18.465
4
6.064
6.626
7.289
9.236
11.070
12.832
13.388
15.086
16.750
20.517
5
7.231
7.841
8.558
10.645
12.592
14.449
15.033
16.812
18.548
22.457
6
8.383
9.037
9.803
12,017
14.067
16.013
16.622
18.475
20.278
24.322
7
9.524
10.219
11.030
13.362
15.507
17.535
18.168
20.090
21.955
26.125
g
10.656
11.389
12.242
14.684
16.919
19.023
19.679
21.666
23.589
27.877
11.781
12.549
13.442
15.987
18.307
20.483
21.161
23.209
25.188
29.588
10
12.899
13.701
14.631
17.275
19.675
21,920
22.618
24.725
26.757
31.264
11
14.011
14.845
15.812
18.549
21.026
23.337
24.054
26.217
28.300
32.909
12
15.119
15.984
16.985
19.812
22.362
24.736
25.472
27.688
29.819
34.528
13
16.222
17.117
18.151
21.064
23.685
26.119
26.873
29.141
31.319
36.123
17.322
18.245
19.311
22.307
24.996
27.488
28.259
30.578
32.801
37.697
18.418
19.369
20.465
23.542
26.296
28.845
29.633
32.000
34.267
39.252
19,511
20.489
24.769
21.615
27.587
30.191
30.995
33.409
35.718
20.601
21.605
22.760
25.989
28.869
31.526
32.346
34.805
37.156
40.790
42.312
21.689
22.718
23.900 27.204
30.144
32.852
33.687
36.191
38.582
43.820
22.775
23.828
25.038
28.412
31.410
34.170
35.020
37.566
39.997
45.315
23.858
24.935
26.171
29.615
32.671
35.479
36.343
38.932
41.401
46.797
24.939
26.039
27.301
30.813
33.924
36.781
37.659
40.289
42.796
48.268
26.018
27.141 28.429
32.007
35.172
38.076
38.968
41.638
44.181
49.728
27.096
28.241
29.553 33.196
36.415
39.364
40.270
42.980
45.558
28.172
29.339
30.675
34.382
37.652
40.646
41.566
44.314
46.928
51.179
52.620
29.246
31.795
30.434
35.563
38.885
41.923
42.856
45.642
48.290
54.052
30.319
31.528
32.912
36.741
40.113
43.194
44.140
46.963
49.645
55.476
31.391
32.620
34.027
37.916
41.337
44.461
45.419
48.278
50.993
56.893
32.461
33.711
35.139
39.087
42.557
45.722
46.693
49.588
52.336
58.302
33.530 34.800
36.250
40.256
43.773
46.979
47.962
50.892
53.672
59.703
44.165
45.616 47.269
51.805
55.759
59.342
60.436
63.691
66.766
73.402
54.723
56.334 58.164
63.167
67.505
71.420
72.613
76.154
79.490
86.661
65.227 66.981
68.972
74.397
79.082
83.298
84,580
88.379
91.952
99.607
75.689
77.577
79.715
85.527
90.531
95.023
96.388 100.425
86.120
88.130
90.405
96.578 101.880
106.629
96.524
98.650
101.054
106.906
109.141
111.667'
107.565 113.145 118.136
118.498 124.342 129.561
104.215
108.069 112.329 116.321
119.648 124.116 128.299
131.142 135.807 140.170
112.317
124.839
137.208
149.449
100
± 298 220 22228 48822 28
14'
15
16
17
18
19
20
21
23
24
25
26
27
29
30
40
50
60
70
80
Table A4. Upper percentage points of the F distribution with V1, V2 df
(a) 5% points
V₁ df for the numerator
V2
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
∞
1
2
3
161.448 199.500 215.707 224.583 230.162
18.513 19.000 19.164 19.247 19.296
10.1280 9.5521 9.2766 9.1172 9.0135
4
7.7086
6.9443
6.5914 6.3882
506
6.6079
5.7861
5.1922
5.9874
4.2067
7
5.5914 4.7374
4.1203
3.9715
3.8660
8
CONNERO2222222222204828
3.8379
3.8625 3.6331 3.4817
3.6875
3.5806
3.3738
3.2927
3.1355
4.4513
3.5915
3.1968
2.8100
4.4139
3.5546
3.1599
2.9277
2.7729
4.3807
3.5219
3.1273
2.8951
2.7401 2.6283 2.5435
4.3512
3.4928
3.0984 2.8661
5.4095
5.1433 4.7571 4.5337
4.3468
5.3177 4.4590 4.0662
5.1174 4.2565
4.9646 4.1028 3.7083 3.4780 3.3258 3.2172
4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536
4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486
4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144
4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458
2.4630
4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876
2.4753 2.4034 2.3275
4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756
2.9647
2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304
2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906
2.4768 2.4227
2.3080 2.2341 2.1555
2.4471 2.3928
2.2776 2.2033
233.986 236.768 238.883 240.543 241.882
19.330 19.353 19.371 19.385
8.9406 8.8867 8.8452 8.8123
6.2561 6.1631 6.0942 6.0410 5.9988
5.0503 4.9503 4.8759 4.8183 4.7725
4.3874 4.2839
4.0990 4.0600 3.9999
19.396
8.7855
5.9644 5.9117 5.8578
4.7351 4.6777 4.6188
243.906 245.950 248.013
19.413 19.429 19.446
8.7446 8.7029 8.6602
249.052 250.095 251.143
252.196 253.253 254.314
19.454
8.6385
19.462
8.6166
5.8025
5.7744
5.7459
19.471 19.479
8.5944 8.5720
5.7170 5.6877 5.6581 5.6281
19.487
8.5493
19.496
8.5265
4.5581
4.5272
4.4957
4.4638
4.4314 4.3985 4.3650
4.1468
3.9381
3.8742
3.8415
3.8082
3.7743
3.7398
3.7047
3.6689
3.7870
3.7257
3.6767
3.6365
3.5747
3.5107
3.4445
3.4105
3.3758
3.3404
3.3043
3.2674
3.2298
3.5005
3.4381
3.3881
3.3472
3.2839
3.2184
3.1503
3.1152
3.0794
3.0428
3.0053
2.9669
2.9276
3.2296
3.1789
3.1373 3.0729
3.0061
2.9365
2.9005
2.8637
2.8259 2.7872 2.7475 2.7067
3.0717 3.0204 2.9782
2.9130
2.8450
2.7740
2.7372 2.6996 2.6609 2.6211 2.5801 2.5379
2.7876
2.7186
2.7964
2.7534
2.6866
2.6169
2.6464
2.5436 2.5055
2.6090 2.5705 2.5309
2.4901
2.4480
2.4045
2.6710
2.6037
2.5331
2.6022
2.5437
2.5342
2.4663
2.4589 2.4202 2.3803
2.3879 2.3487 2.3082
2.2878
2.4259 2.3842 2.3410
2.3392 2.2966 2.2524
2.2664 2.2229 2.1778
2.2468 2.2043 2.1601 2.1141
2.2354 2.1938 2.1507 2.1058 2.0589
2.1898 2.1477 2.1040 2.0584
2.2962
2.2064
2.1307
2.0659
2.0096
2.0107 1.9604
4.3248
3.4668
3.0725
2.8401
2.6848
4.3009
3.4434
3.0491
2.8167
2.3965
4.2793
3.4221
3.0280
2.7955
2.6400
2.5277
2.4422
2.3748
4.2597
3.4028
3.0088
2.7763
2.6207
2.5082
2.4226
2.3551
4.2417 3.3852 2.9912
2.7587
2.6030
2.4904
2.4047 2.3371 2.2821 2.2365 2.1649
4.2252
4.2100
3.3690 2.9752 2.7426
3.3541 2.9604 2.7278
4.1960
3.3404 2.9467 2.7141
4.1830
3.3277 2.9340
4.1709
3.3158
2.9223
2.8387
3.9201 3.0718
3.8415
2.9957
2.5868
2.5719 2.4591 2.3732 2.3053 2.2501 2.2043
2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179
2.7014 2.5454 2.4324 2.3463
2.6896 2.5336 2.4205 2.3343
4.0847 3.2317
2.6060 2.4495 2.3359 2.2490 2.1802
4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665
2.6802 2.4472 2.2899 2.1750 2.0868
2.6049 2.3719 2.2141 2.0986 2.0096
2.4741
2.3883
2.1497
2.1141
2.7109 2.5990 2.5140
2.0825
2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540
2.6613 2.5491 2.4638
2.3419 2.2967 2.2258 2.1508 2.0707 2.0283
2.3201 2.2747 2.2036 2.1282 2.0476 2.0050
2.3002 2.2547 2.1834 2.1077 2.0267 1.9838
2.0889 2.0075
1.9898
2.1071
2.0629
2.0166
1.9681
1.9168
2.3779
2.3479
2.0712
2.0264
1.9795
1.9302
1.8780
2.1242
2.0391
1.9938
1.9464 1.8963 1.8432
2.0102
1.9645
1.9165 1.8657 1.8117
1.9842
1.9380
1.8894
1.8380
1.7831
1.9605
1.9390
1.9139
1.8648
1.8128
1.7570
1.8920
1.8424 1.7896
1.7331
2.3205 2.2655 2.2197 2.1479 2.0716
1.9643 1.9192 1.8718 1.8217 1.7684
1.9464 1.9010
1.7110
1.8533
1.8027
1.7488
1.6906
2.1323
2.0558
1.9736
1.9299
1.8842
1.8361
1.7851
1.7306
1.6717
2.0411
1.9586
1.9147 1.8687
1.8203 1.7689
1.7138
1.6541
2.2783
2.2229
2.1768
2.1045
2.0275
1.9446
1.9005
1.8543
1.8055
1.7537
1.6981
1.6377
2.2662
2.2107
2.1646
2.0921
2.0148
1.9317 1.8874
1.8409
1.7918
1.7396
1.6835
1.6223
2.1240
2.0772
2.0035
1.9245
1.8389
1.7929 1.7444
1.6928
1.6373
1.5766
1.5089
2.0970 2.0401
1.9926
1.9174
1.8364 1.7480
2.0164 1.9588
1.9384 1.8799
1.9105
1.8307 1.7522 1.6664
1.7001
1.8337 1.7505 1.6587 1.6084 1.5543
1.6491
1.5943
1.5343
1.4673 1.3893
1.4952
1.4290
1.3519
1.2539
1.5705 1.5173
1.4591
1.3940
1.3180
1.2214
1.0033](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe105e704-a79d-4550-8962-ee50fc655730%2Ffd3d8aa6-fe1b-4350-89fe-f945f9287fa0%2F7vs5pe6_processed.png&w=3840&q=75)
Transcribed Image Text:Table 3 Areas in Upper Tail of the Normal Distribution
The function tabulated is 1-(z) where (z) is the cumulative distribution function of a standardised Normal variable, z.
Thus 10(z):
°
1
-2212
12π
value of z
(-)
is the probability that a standardised Normal variate selected at random will be greater than a
0
x-1
.00
.01
.02
.03
.04
.05
.06
90
σ
1-0 (z)
.07
.08
.09
EUNES 8EPRE PR888
0.0
0.1
0.2
0.3
0.4
01234
.5000
.4960
.4920
.4880
.4840
.4801
.4761
.4721
.4681
.4641
.4602
.4562
.4522
.4483
.4443
.4404
.4364
.4325
.4286
.4247
.4207
.4168
.4129
.4090
.4052
.4013
.3974
..3936
.3897
.3859
.3821
.3783
.3745
.3707
.3669
.3632
.3594
.3557
.3520
.3483
.3446
.3409
.3372
.3336
.3300
.3264
.3228
.3192
.3156
.3121
0.5
.3085
.3050
.3015
.2981
.2946
.2912
.2877
.2843
.2810
.2776
0.6
.2743
.2709
.2676
.2643
.2611
.2578
.2546
.2514
.2483
.2451
0.7
.2420
.2389
.2358
.2327
.2296
.2266
.2236
.2206
.2177
.2148
0.8
.2119
.2090
.2061
.2033
.2005
.1977
.1949
.1922
.1894
.1867
0.9
.1841
.1814
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
1.0
.1587
.1562
.1539
.1515
.1492) .1469
.1446
.1423
.1401
.1379
1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
1.2
.1151
.1131
.1112
.1093
.1075
.1056
.1038
.1020
.1003
.0985
1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0838
.0823
1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0694
.0681
1.5
1.6
1.7
1.8
1.9
5678 a
.0668
.0655
.0643
.0630
.0618
.0606
.0594
.0582
.0571
.0559
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
.0446
.0436
.0427
.0418
.0409
.0401
.0392
.0384
.0375
.0367
.0359
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0294
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0239
.0233
2.0
.02275 .02222 .02169
.02118 .02068
.02018
.01970
.01923
.01876
.01831
2.1
.01786 .01743 .01700
.01659 .01618 .01578
.01539
.01500 .01463
.01426
2.2
.01390 .01355
2.3
.01072 .01044
2.4
.00820 .00798
2.5
.00621 .00604
2.6
.00466 .00453
.00440
2.7
.00347 .00336
.00326
2.8
.00256 .00248
.00240
2.9
.00187 .00181
.00175
.01321 .01287 .01255 .01222 .01191
.01017 .00990 .00964 .00939 .00914 .00889 .00866
.00776 .00755 .00734 .00714 .00695 .00676 .00657
.00587 .00570 .00554 .00539 .00523 .00508
.00427 .00415 .00402 .00391 .00379
1.00317 .00307 .00298 .00289 .00280
.00233 .00226 .00219 .00212
.00169 .00164 .00159 .00154
.01160 .01130
.01101
.00842
.00639
.00494 .00480
.00368 .00357
.00272 .00264
.00205
.00149
.00199 .00193
.00144 .00139
3.0
.00135
.00131 .00126
3.1
3.2
3.3
3.4
.00097 .00094 .00090
.00069 .00066.
.00048 .00047
.00034 .00032
3.5
.00023 .00022
.00122
.00087
.00064 .00062
.00045 .00043
.00031 .00030
.00022 .00021
3.6
3.7
3.8
3.9
4.0
.00118 .00114 .00111 .00107 .00104 .00100
.00084 .00082 .00079 .00076 .00074 .00071
.00060 .00058 .00056 .00054 .00052 .00050
.00042 .00040 .00039 .00038 .00036 .00035
.00029 .00028 .00027 .00026 .00025 .00024
.00020 .00019
.00019 .00018 .00017 .00017
.00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011
.000108 .000104 .000100 .000096 .000092 .000088 .000085 .000082 .000078 .000075
.000072 .000069 .000067 .000064 .000062 .000059 .000057 .000054 .000052 .000050
.000048 .000046 .000044 .000042 .000041 .000039 .000037 .000036 .000034 .000033
.000032
5.0 0.000 000 286 7
5.5 0.000 000 019 0
6.0 0.000 000 001 0
108
Table 7 Percentage Points of the t Distribution
The table gives the value of tay - the 100a percentage point of the distribution for v degrees of freedom.
The values of t are obtained by solution of the equation:
α = П[½(v+ 1)][¯¯(½v)]¯¹ (vπ)¯¹⁄2
-1/2
2
+
/v)-(v+1)/2
-(v+1)/2 doc
Note: The tabulation is for one tail only, that is, for positive values of 1.
the column headings for a should be doubled.
For
0
i a, v
απ
0.10
0.05
0.025
0,01
0.005
0.001
0.0005
v = 1
3.078
6.314
12.706
31.821
63.657
318.31
636.62
2
1.886
2.920
4.303
6.965
9.925
22.326
31.598
3
1.638
2.353
3.182
4.541
5.841
10.213
12.924
4
1.533
2.132
2.776
3.747
4.604
7.173
8.610
5
1.476
2.015
2.571
3.365
4.032
5.893
6.869
21
25
120
67890 =2D 67822 28220 22222 4828
1.440
1.943
2.447
3.143
3.707
5.208
5.959
1.415
1.895
2.365
2.998
3.499
4.785
5.408
1.397
1.860
2.306
2.896
3.355
4.501
5.041
1.383
1.833
2.262
2.821
3.250
4.297
4.781
1.372
1.812
2.228
2.764
3.169
4.144
4.587
1.363
1.796
2.201
2.718
3.106
4.025
4.437
12
1.356
1.782
2.179
2.681
3.055
3.930
4.318
13
1.350
1.771
2.160
2.650
3.012
3.852
4.221
14
1.345
1.761
2.145
2.624
2.977
3.787
4.140
15
1.341
1.753
2.131
2.602
2.947
3.733
4.073
16
1.337
1.746
2.120
2.583
2.921
3.686
4.015
17
1.333
1.740
2.110
2.567
2.898
3.646
3.965
18
1.330
1.734
2.101
2.552
2.878
3.610
3.922
19
1.328
1.729
2.093
2.539
2.861
3.579
3.883
20
1.325
1.725
2.086
2.528
2.845
3.552
3.850
1.323
1.721
2.080
2.518
2.831
3.527
3.819
1.321
1.717
2.074
2.508
2.819
3.505
3.792
23
1.319
1.714
2.069
2.500
2.807
3.485
3.767
24
1.318
1.711
2.064
2.492
2.797
3.467
3.745
1.316
1.708
2.060
2.485
2.787
3.450
3.725
1.315
1.706
2.056
2.479
2.779
3.435
3.707
1.314
1.703
2.052
2.473
2.771
3.421
3.690
1.313
1.701
2.048
2.467
2.763
3.408
3.674
1.311
1.699
2.045
2.462
2.756
3.396
3.659
1.310
1.697
2.042
2.457
2.750
3.385
3.646
40
1.303
1.684
2.021
2.423
2.704
3.307
3.551
60
1.296
1.671
2.000
2.390
2.660
3.232
3.460
1.289
1.658
1.980
2.358
2.617
3.160
3.373
1.282
1.645
1.960
2.326
2.576
3.090
3.291
Table 8 Percentage Points of the x² Distribution - continued
.30
.25
.20
.10
.05
.025
.02
.01
.005
.001
Ξα
1.074
1.323
1.642
2.706
3.841
5.024
5.412
6.635
7.879
10.827
y= 1
2.408
2.773
3.219
4.605
5.991
7.378
7.824
9.210
10.597
13.815
2
3.665
4.108
4.642
6.251
7.815
9.348
9.837
11.345
12.838
16.268
3
4.878
5.385
5.989
7.779
9.488
11.143
11.668
13.277
14.860
18.465
4
6.064
6.626
7.289
9.236
11.070
12.832
13.388
15.086
16.750
20.517
5
7.231
7.841
8.558
10.645
12.592
14.449
15.033
16.812
18.548
22.457
6
8.383
9.037
9.803
12,017
14.067
16.013
16.622
18.475
20.278
24.322
7
9.524
10.219
11.030
13.362
15.507
17.535
18.168
20.090
21.955
26.125
g
10.656
11.389
12.242
14.684
16.919
19.023
19.679
21.666
23.589
27.877
11.781
12.549
13.442
15.987
18.307
20.483
21.161
23.209
25.188
29.588
10
12.899
13.701
14.631
17.275
19.675
21,920
22.618
24.725
26.757
31.264
11
14.011
14.845
15.812
18.549
21.026
23.337
24.054
26.217
28.300
32.909
12
15.119
15.984
16.985
19.812
22.362
24.736
25.472
27.688
29.819
34.528
13
16.222
17.117
18.151
21.064
23.685
26.119
26.873
29.141
31.319
36.123
17.322
18.245
19.311
22.307
24.996
27.488
28.259
30.578
32.801
37.697
18.418
19.369
20.465
23.542
26.296
28.845
29.633
32.000
34.267
39.252
19,511
20.489
24.769
21.615
27.587
30.191
30.995
33.409
35.718
20.601
21.605
22.760
25.989
28.869
31.526
32.346
34.805
37.156
40.790
42.312
21.689
22.718
23.900 27.204
30.144
32.852
33.687
36.191
38.582
43.820
22.775
23.828
25.038
28.412
31.410
34.170
35.020
37.566
39.997
45.315
23.858
24.935
26.171
29.615
32.671
35.479
36.343
38.932
41.401
46.797
24.939
26.039
27.301
30.813
33.924
36.781
37.659
40.289
42.796
48.268
26.018
27.141 28.429
32.007
35.172
38.076
38.968
41.638
44.181
49.728
27.096
28.241
29.553 33.196
36.415
39.364
40.270
42.980
45.558
28.172
29.339
30.675
34.382
37.652
40.646
41.566
44.314
46.928
51.179
52.620
29.246
31.795
30.434
35.563
38.885
41.923
42.856
45.642
48.290
54.052
30.319
31.528
32.912
36.741
40.113
43.194
44.140
46.963
49.645
55.476
31.391
32.620
34.027
37.916
41.337
44.461
45.419
48.278
50.993
56.893
32.461
33.711
35.139
39.087
42.557
45.722
46.693
49.588
52.336
58.302
33.530 34.800
36.250
40.256
43.773
46.979
47.962
50.892
53.672
59.703
44.165
45.616 47.269
51.805
55.759
59.342
60.436
63.691
66.766
73.402
54.723
56.334 58.164
63.167
67.505
71.420
72.613
76.154
79.490
86.661
65.227 66.981
68.972
74.397
79.082
83.298
84,580
88.379
91.952
99.607
75.689
77.577
79.715
85.527
90.531
95.023
96.388 100.425
86.120
88.130
90.405
96.578 101.880
106.629
96.524
98.650
101.054
106.906
109.141
111.667'
107.565 113.145 118.136
118.498 124.342 129.561
104.215
108.069 112.329 116.321
119.648 124.116 128.299
131.142 135.807 140.170
112.317
124.839
137.208
149.449
100
± 298 220 22228 48822 28
14'
15
16
17
18
19
20
21
23
24
25
26
27
29
30
40
50
60
70
80
Table A4. Upper percentage points of the F distribution with V1, V2 df
(a) 5% points
V₁ df for the numerator
V2
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
∞
1
2
3
161.448 199.500 215.707 224.583 230.162
18.513 19.000 19.164 19.247 19.296
10.1280 9.5521 9.2766 9.1172 9.0135
4
7.7086
6.9443
6.5914 6.3882
506
6.6079
5.7861
5.1922
5.9874
4.2067
7
5.5914 4.7374
4.1203
3.9715
3.8660
8
CONNERO2222222222204828
3.8379
3.8625 3.6331 3.4817
3.6875
3.5806
3.3738
3.2927
3.1355
4.4513
3.5915
3.1968
2.8100
4.4139
3.5546
3.1599
2.9277
2.7729
4.3807
3.5219
3.1273
2.8951
2.7401 2.6283 2.5435
4.3512
3.4928
3.0984 2.8661
5.4095
5.1433 4.7571 4.5337
4.3468
5.3177 4.4590 4.0662
5.1174 4.2565
4.9646 4.1028 3.7083 3.4780 3.3258 3.2172
4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536
4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486
4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144
4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458
2.4630
4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876
2.4753 2.4034 2.3275
4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756
2.9647
2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304
2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906
2.4768 2.4227
2.3080 2.2341 2.1555
2.4471 2.3928
2.2776 2.2033
233.986 236.768 238.883 240.543 241.882
19.330 19.353 19.371 19.385
8.9406 8.8867 8.8452 8.8123
6.2561 6.1631 6.0942 6.0410 5.9988
5.0503 4.9503 4.8759 4.8183 4.7725
4.3874 4.2839
4.0990 4.0600 3.9999
19.396
8.7855
5.9644 5.9117 5.8578
4.7351 4.6777 4.6188
243.906 245.950 248.013
19.413 19.429 19.446
8.7446 8.7029 8.6602
249.052 250.095 251.143
252.196 253.253 254.314
19.454
8.6385
19.462
8.6166
5.8025
5.7744
5.7459
19.471 19.479
8.5944 8.5720
5.7170 5.6877 5.6581 5.6281
19.487
8.5493
19.496
8.5265
4.5581
4.5272
4.4957
4.4638
4.4314 4.3985 4.3650
4.1468
3.9381
3.8742
3.8415
3.8082
3.7743
3.7398
3.7047
3.6689
3.7870
3.7257
3.6767
3.6365
3.5747
3.5107
3.4445
3.4105
3.3758
3.3404
3.3043
3.2674
3.2298
3.5005
3.4381
3.3881
3.3472
3.2839
3.2184
3.1503
3.1152
3.0794
3.0428
3.0053
2.9669
2.9276
3.2296
3.1789
3.1373 3.0729
3.0061
2.9365
2.9005
2.8637
2.8259 2.7872 2.7475 2.7067
3.0717 3.0204 2.9782
2.9130
2.8450
2.7740
2.7372 2.6996 2.6609 2.6211 2.5801 2.5379
2.7876
2.7186
2.7964
2.7534
2.6866
2.6169
2.6464
2.5436 2.5055
2.6090 2.5705 2.5309
2.4901
2.4480
2.4045
2.6710
2.6037
2.5331
2.6022
2.5437
2.5342
2.4663
2.4589 2.4202 2.3803
2.3879 2.3487 2.3082
2.2878
2.4259 2.3842 2.3410
2.3392 2.2966 2.2524
2.2664 2.2229 2.1778
2.2468 2.2043 2.1601 2.1141
2.2354 2.1938 2.1507 2.1058 2.0589
2.1898 2.1477 2.1040 2.0584
2.2962
2.2064
2.1307
2.0659
2.0096
2.0107 1.9604
4.3248
3.4668
3.0725
2.8401
2.6848
4.3009
3.4434
3.0491
2.8167
2.3965
4.2793
3.4221
3.0280
2.7955
2.6400
2.5277
2.4422
2.3748
4.2597
3.4028
3.0088
2.7763
2.6207
2.5082
2.4226
2.3551
4.2417 3.3852 2.9912
2.7587
2.6030
2.4904
2.4047 2.3371 2.2821 2.2365 2.1649
4.2252
4.2100
3.3690 2.9752 2.7426
3.3541 2.9604 2.7278
4.1960
3.3404 2.9467 2.7141
4.1830
3.3277 2.9340
4.1709
3.3158
2.9223
2.8387
3.9201 3.0718
3.8415
2.9957
2.5868
2.5719 2.4591 2.3732 2.3053 2.2501 2.2043
2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179
2.7014 2.5454 2.4324 2.3463
2.6896 2.5336 2.4205 2.3343
4.0847 3.2317
2.6060 2.4495 2.3359 2.2490 2.1802
4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665
2.6802 2.4472 2.2899 2.1750 2.0868
2.6049 2.3719 2.2141 2.0986 2.0096
2.4741
2.3883
2.1497
2.1141
2.7109 2.5990 2.5140
2.0825
2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540
2.6613 2.5491 2.4638
2.3419 2.2967 2.2258 2.1508 2.0707 2.0283
2.3201 2.2747 2.2036 2.1282 2.0476 2.0050
2.3002 2.2547 2.1834 2.1077 2.0267 1.9838
2.0889 2.0075
1.9898
2.1071
2.0629
2.0166
1.9681
1.9168
2.3779
2.3479
2.0712
2.0264
1.9795
1.9302
1.8780
2.1242
2.0391
1.9938
1.9464 1.8963 1.8432
2.0102
1.9645
1.9165 1.8657 1.8117
1.9842
1.9380
1.8894
1.8380
1.7831
1.9605
1.9390
1.9139
1.8648
1.8128
1.7570
1.8920
1.8424 1.7896
1.7331
2.3205 2.2655 2.2197 2.1479 2.0716
1.9643 1.9192 1.8718 1.8217 1.7684
1.9464 1.9010
1.7110
1.8533
1.8027
1.7488
1.6906
2.1323
2.0558
1.9736
1.9299
1.8842
1.8361
1.7851
1.7306
1.6717
2.0411
1.9586
1.9147 1.8687
1.8203 1.7689
1.7138
1.6541
2.2783
2.2229
2.1768
2.1045
2.0275
1.9446
1.9005
1.8543
1.8055
1.7537
1.6981
1.6377
2.2662
2.2107
2.1646
2.0921
2.0148
1.9317 1.8874
1.8409
1.7918
1.7396
1.6835
1.6223
2.1240
2.0772
2.0035
1.9245
1.8389
1.7929 1.7444
1.6928
1.6373
1.5766
1.5089
2.0970 2.0401
1.9926
1.9174
1.8364 1.7480
2.0164 1.9588
1.9384 1.8799
1.9105
1.8307 1.7522 1.6664
1.7001
1.8337 1.7505 1.6587 1.6084 1.5543
1.6491
1.5943
1.5343
1.4673 1.3893
1.4952
1.4290
1.3519
1.2539
1.5705 1.5173
1.4591
1.3940
1.3180
1.2214
1.0033
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