16. In a community trial of the drug Ivermectin for the treatment of river blindness, villagers were randomized to receive Ivermectin or placebo tablets. Packed cell volume (PCV) was measured 6 months later. The mean and standard deviations in the two groups are as follows: Ivermectin Placebo n 16 14 mean 40.38 37.50 SD 5.04 4.74 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 .01321 .01287 .01255 .01222 .01191 .01017 .00990 .00964 .00939 .00914 .00776 .00755 .00734 .00714 .00695 .01160 .01130 .01101 .00889 .00866 .00842 .00676 .00657 .00639 2.5 .00621 .00604 .00587 .00570 2.6 .00466 .00453 .00440 2.7 .00347 .00336 .00326 2.8 .00256 .00248 .00240 2.9 .00187 .00181 .00175 .00554 .00539 .00523 .00427 .00415 .00402 .00391 1.00317 .00307 .00298 .00289 .00233 .00169 .00508 .00494 .00480 .00379 .00368 .00357 .00280 .00272 .00264 .00226 .00219 .00212 .00164 .00159 .00154 .00205 .00199 .00193 .00149 .00144 .00139 3.0 3.1 3.2 3.3 3.4 .00135 .00097 .00094 .00090 .00069 .00066. .00048 .00047 .00034 .00032 .00131 .00126 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 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 4.2067 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 4.0847 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 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 2.0970 2.0401 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 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
16. In a community trial of the drug Ivermectin for the treatment of river blindness, villagers were randomized to receive Ivermectin or placebo tablets. Packed cell volume (PCV) was measured 6 months later. The mean and standard deviations in the two groups are as follows: Ivermectin Placebo n 16 14 mean 40.38 37.50 SD 5.04 4.74 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 .01321 .01287 .01255 .01222 .01191 .01017 .00990 .00964 .00939 .00914 .00776 .00755 .00734 .00714 .00695 .01160 .01130 .01101 .00889 .00866 .00842 .00676 .00657 .00639 2.5 .00621 .00604 .00587 .00570 2.6 .00466 .00453 .00440 2.7 .00347 .00336 .00326 2.8 .00256 .00248 .00240 2.9 .00187 .00181 .00175 .00554 .00539 .00523 .00427 .00415 .00402 .00391 1.00317 .00307 .00298 .00289 .00233 .00169 .00508 .00494 .00480 .00379 .00368 .00357 .00280 .00272 .00264 .00226 .00219 .00212 .00164 .00159 .00154 .00205 .00199 .00193 .00149 .00144 .00139 3.0 3.1 3.2 3.3 3.4 .00135 .00097 .00094 .00090 .00069 .00066. .00048 .00047 .00034 .00032 .00131 .00126 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 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 4.2067 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 4.0847 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 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 2.0970 2.0401 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 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
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Question 16: Please use the approporate stats table attached. Do not use a software for this problem.
a. What was the observed difference between the
b.Assuming that the two groups have similar variances, estimate the standard error of the difference
between the sample means
c. Conduct an appropriate test to assess the difference between the two means. What do you conclude?
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