Bảng Z-T - Toán Kinh Tế UEL

Appendix B: Tables TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Entries in the table give the area under the curve to the left of the z value. For example, for z = –.85, the cumulative probability is .1977. Cumulative probability 0 z z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 ⫺3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 ⫺2.9 ⫺2.8 ⫺2.7 ⫺2.6 ⫺2.5 .0019 .0026 .0035 .0047 .0062 .0018 .0025 .0034 .0045 .0060 .0018 .0024 .0033 .0044 .0059 .0017 .0023 .0032 .0043 .0057 .0016 .0023 .0031 .0041 .0055 .0016 .0022 .0030 .0040 .0054 .0015 .0021 .0029 .0039 .0052 .0015 .0021 .0028 .0038 .0051 .0014 .0020 .0027 .0037 .0049 .0014 .0019 .0026 .0036 .0048 ⫺2.4 ⫺2.3 ⫺2.2 ⫺2.1 ⫺2.0 .0082 .0107 .0139 .0179 .0228 .0080 .0104 .0136 .0174 .0222 .0078 .0102 .0132 .0170 .0217 .0075 .0099 .0129 .0166 .0212 .0073 .0096 .0125 .0162 .0207 .0071 .0094 .0122 .0158 .0202 .0069 .0091 .0119 .0154 .0197 .0068 .0089 .0116 .0150 .0192 .0066 .0087 .0113 .0146 .0188 .0064 .0084 .0110 .0143 .0183 ⫺1.9 ⫺1.8 ⫺1.7 ⫺1.6 ⫺1.5 .0287 .0359 .0446 .0548 .0668 .0281 .0351 .0436 .0537 .0655 .0274 .0344 .0427 .0526 .0643 .0268 .0336 .0418 .0516 .0630 .0262 .0329 .0409 .0505 .0618 .0256 .0322 .0401 .0495 .0606 .0250 .0314 .0392 .0485 .0594 .0244 .0307 .0384 .0475 .0582 .0239 .0301 .0375 .0465 .0571 .0233 .0294 .0367 .0455 .0559 ⫺1.4 ⫺1.3 ⫺1.2 ⫺1.1 ⫺1.0 .0808 .0968 .1151 .1357 .1587 .0793 .0951 .1131 .1335 .1562 .0778 .0934 .1112 .1314 .1539 .0764 .0918 .1093 .1292 .1515 .0749 .0901 .1075 .1271 .1492 .0735 .0885 .1056 .1251 .1469 .0721 .0869 .1038 .1230 .1446 .0708 .0853 .1020 .1210 .1423 .0694 .0838 .1003 .1190 .1401 .0681 .0823 .0985 .1170 .1379 ⫺.9 ⫺.8 ⫺.7 ⫺.6 ⫺.5 .1841 .2119 .2420 .2743 .3085 .1814 .2090 .2389 .2709 .3050 .1788 .2061 .2358 .2676 .3015 .1762 .2033 .2327 .2643 .2981 .1736 .2005 .2296 .2611 .2946 .1711 .1977 .2266 .2578 .2912 .1685 .1949 .2236 .2546 .2877 .1660 .1922 .2206 .2514 .2843 .1635 .1894 .2177 .2483 .2810 .1611 .1867 .2148 .2451 .2776 ⫺.4 ⫺.3 ⫺.2 ⫺.1 ⫺.0 .3446 .3821 .4207 .4602 .5000 .3409 .3783 .4168 .4562 .4960 .3372 .3745 .4129 .4522 .4920 .3336 .3707 .4090 .4483 .4880 .3300 .3669 .4052 .4443 .4840 .3264 .3632 .4013 .4404 .4801 .3228 .3594 .3974 .4364 .4761 .3192 .3557 .3936 .4325 .4721 .3156 .3520 .3897 .4286 .4681 .3121 .3483 .3859 .4247 .4641 Appendix B TABLE 1 979 Tables CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION (Continued ) Cumulative probability 0 Entries in the table give the area under the curve to the left of the z value. For example, for z = 1.25, the cumulative probability is .8944. z z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .1 .2 .3 .4 .5000 .5398 .5793 .6179 .6554 .5040 .5438 .5832 .6217 .6591 .5080 .5478 .5871 .6255 .6628 .5120 .5517 .5910 .6293 .6664 .5160 .5557 .5948 .6331 .6700 .5199 .5596 .5987 .6368 .6736 .5239 .5636 .6026 .6406 .6772 .5279 .5675 .6064 .6443 .6808 .5319 .5714 .6103 .6480 .6844 .5359 .5753 .6141 .6517 .6879 .5 .6 .7 .8 .9 .6915 .7257 .7580 .7881 .8159 .6950 .7291 .7611 .7910 .8186 .6985 .7324 .7642 .7939 .8212 .7019 .7357 .7673 .7967 .8238 .7054 .7389 .7704 .7995 .8264 .7088 .7422 .7734 .8023 .8289 .7123 .7454 .7764 .8051 .8315 .7157 .7486 .7794 .8078 .8340 .7190 .7517 .7823 .8106 .8365 .7224 .7549 .7852 .8133 .8389 1.0 1.1 1.2 1.3 1.4 .8413 .8643 .8849 .9032 .9192 .8438 .8665 .8869 .9049 .9207 .8461 .8686 .8888 .9066 .9222 .8485 .8708 .8907 .9082 .9236 .8508 .8729 .8925 .9099 .9251 .8531 .8749 .8944 .9115 .9265 .8554 .8770 .8962 .9131 .9279 .8577 .8790 .8980 .9147 .9292 .8599 .8810 .8997 .9162 .9306 .8621 .8830 .9015 .9177 .9319 1.5 1.6 1.7 1.8 1.9 .9332 .9452 .9554 .9641 .9713 .9345 .9463 .9564 .9649 .9719 .9357 .9474 .9573 .9656 .9726 .9370 .9484 .9582 .9664 .9732 .9382 .9495 .9591 .9671 .9738 .9394 .9505 .9599 .9678 .9744 .9406 .9515 .9608 .9686 .9750 .9418 .9525 .9616 .9693 .9756 .9429 .9535 .9625 .9699 .9761 .9441 .9545 .9633 .9706 .9767 2.0 2.1 2.2 2.3 2.4 .9772 .9821 .9861 .9893 .9918 .9778 .9826 .9864 .9896 .9920 .9783 .9830 .9868 .9898 .9922 .9788 .9834 .9871 .9901 .9925 .9793 .9838 .9875 .9904 .9927 .9798 .9842 .9878 .9906 .9929 .9803 .9846 .9881 .9909 .9931 .9808 .9850 .9884 .9911 .9932 .9812 .9854 .9887 .9913 .9934 .9817 .9857 .9890 .9916 .9936 2.5 2.6 2.7 2.8 2.9 .9938 .9953 .9965 .9974 .9981 .9940 .9955 .9966 .9975 .9982 .9941 .9956 .9967 .9976 .9982 .9943 .9957 .9968 .9977 .9983 .9945 .9959 .9969 .9977 .9984 .9946 .9960 .9970 .9978 .9984 .9948 .9961 .9971 .9979 .9985 .9949 .9962 .9972 .9979 .9985 .9951 .9963 .9973 .9980 .9986 .9952 .9964 .9974 .9981 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 980 Appendix B TABLE 2 Tables t DISTRIBUTION 0 t Area or probability Entries in the table give t values for an area or probability in the upper tail of the t distribution. For example, with 10 degrees of freedom and a .05 area in the upper tail, t.05 ⫽ 1.812. Area in Upper Tail Degrees of Freedom .20 .10 .05 .025 .01 .005 1 2 3 4 1.376 1.061 .978 .941 3.078 1.886 1.638 1.533 6.314 2.920 2.353 2.132 12.706 4.303 3.182 2.776 31.821 6.965 4.541 3.747 63.656 9.925 5.841 4.604 5 6 7 8 9 .920 .906 .896 .889 .883 1.476 1.440 1.415 1.397 1.383 2.015 1.943 1.895 1.860 1.833 2.571 2.447 2.365 2.306 2.262 3.365 3.143 2.998 2.896 2.821 4.032 3.707 3.499 3.355 3.250 10 11 12 13 14 .879 .876 .873 .870 .868 1.372 1.363 1.356 1.350 1.345 1.812 1.796 1.782 1.771 1.761 2.228 2.201 2.179 2.160 2.145 2.764 2.718 2.681 2.650 2.624 3.169 3.106 3.055 3.012 2.977 15 16 17 18 19 .866 .865 .863 .862 .861 1.341 1.337 1.333 1.330 1.328 1.753 1.746 1.740 1.734 1.729 2.131 2.120 2.110 2.101 2.093 2.602 2.583 2.567 2.552 2.539 2.947 2.921 2.898 2.878 2.861 20 21 22 23 24 .860 .859 .858 .858 .857 1.325 1.323 1.321 1.319 1.318 1.725 1.721 1.717 1.714 1.711 2.086 2.080 2.074 2.069 2.064 2.528 2.518 2.508 2.500 2.492 2.845 2.831 2.819 2.807 2.797 25 26 27 28 29 .856 .856 .855 .855 .854 1.316 1.315 1.314 1.313 1.311 1.708 1.706 1.703 1.701 1.699 2.060 2.056 2.052 2.048 2.045 2.485 2.479 2.473 2.467 2.462 2.787 2.779 2.771 2.763 2.756 30 31 32 33 34 .854 .853 .853 .853 .852 1.310 1.309 1.309 1.308 1.307 1.697 1.696 1.694 1.692 1.691 2.042 2.040 2.037 2.035 2.032 2.457 2.453 2.449 2.445 2.441 2.750 2.744 2.738 2.733 2.728 Appendix B TABLE 2 981 Tables t DISTRIBUTION (Continued ) Area in Upper Tail Degrees of Freedom .20 .10 .05 .025 .01 .005 35 36 37 38 39 .852 .852 .851 .851 .851 1.306 1.306 1.305 1.304 1.304 1.690 1.688 1.687 1.686 1.685 2.030 2.028 2.026 2.024 2.023 2.438 2.434 2.431 2.429 2.426 2.724 2.719 2.715 2.712 2.708 40 41 42 43 44 .851 .850 .850 .850 .850 1.303 1.303 1.302 1.302 1.301 1.684 1.683 1.682 1.681 1.680 2.021 2.020 2.018 2.017 2.015 2.423 2.421 2.418 2.416 2.414 2.704 2.701 2.698 2.695 2.692 45 46 47 48 49 .850 .850 .849 .849 .849 1.301 1.300 1.300 1.299 1.299 1.679 1.679 1.678 1.677 1.677 2.014 2.013 2.012 2.011 2.010 2.412 2.410 2.408 2.407 2.405 2.690 2.687 2.685 2.682 2.680 50 51 52 53 54 .849 .849 .849 .848 .848 1.299 1.298 1.298 1.298 1.297 1.676 1.675 1.675 1.674 1.674 2.009 2.008 2.007 2.006 2.005 2.403 2.402 2.400 2.399 2.397 2.678 2.676 2.674 2.672 2.670 55 56 57 58 59 .848 .848 .848 .848 .848 1.297 1.297 1.297 1.296 1.296 1.673 1.673 1.672 1.672 1.671 2.004 2.003 2.002 2.002 2.001 2.396 2.395 2.394 2.392 2.391 2.668 2.667 2.665 2.663 2.662 60 61 62 63 64 .848 .848 .847 .847 .847 1.296 1.296 1.295 1.295 1.295 1.671 1.670 1.670 1.669 1.669 2.000 2.000 1.999 1.998 1.998 2.390 2.389 2.388 2.387 2.386 2.660 2.659 2.657 2.656 2.655 65 66 67 68 69 .847 .847 .847 .847 .847 1.295 1.295 1.294 1.294 1.294 1.669 1.668 1.668 1.668 1.667 1.997 1.997 1.996 1.995 1.995 2.385 2.384 2.383 2.382 2.382 2.654 2.652 2.651 2.650 2.649 70 71 72 73 74 .847 .847 .847 .847 .847 1.294 1.294 1.293 1.293 1.293 1.667 1.667 1.666 1.666 1.666 1.994 1.994 1.993 1.993 1.993 2.381 2.380 2.379 2.379 2.378 2.648 2.647 2.646 2.645 2.644 75 76 77 78 79 .846 .846 .846 .846 .846 1.293 1.293 1.293 1.292 1.292 1.665 1.665 1.665 1.665 1.664 1.992 1.992 1.991 1.991 1.990 2.377 2.376 2.376 2.375 2.374 2.643 2.642 2.641 2.640 2.639 982 Appendix B TABLE 2 Tables t DISTRIBUTION (Continued ) Area in Upper Tail Degrees of Freedom .20 .10 .05 .025 .01 .005 80 81 82 83 84 .846 .846 .846 .846 .846 1.292 1.292 1.292 1.292 1.292 1.664 1.664 1.664 1.663 1.663 1.990 1.990 1.989 1.989 1.989 2.374 2.373 2.373 2.372 2.372 2.639 2.638 2.637 2.636 2.636 85 86 87 88 89 .846 .846 .846 .846 .846 1.292 1.291 1.291 1.291 1.291 1.663 1.663 1.663 1.662 1.662 1.988 1.988 1.988 1.987 1.987 2.371 2.370 2.370 2.369 2.369 2.635 2.634 2.634 2.633 2.632 90 91 92 93 94 .846 .846 .846 .846 .845 1.291 1.291 1.291 1.291 1.291 1.662 1.662 1.662 1.661 1.661 1.987 1.986 1.986 1.986 1.986 2.368 2.368 2.368 2.367 2.367 2.632 2.631 2.630 2.630 2.629 95 96 97 98 99 100 ⬁ .845 .845 .845 .845 .845 .845 .842 1.291 1.290 1.290 1.290 1.290 1.290 1.282 1.661 1.661 1.661 1.661 1.660 1.660 1.645 1.985 1.985 1.985 1.984 1.984 1.984 1.960 2.366 2.366 2.365 2.365 2.364 2.364 2.326 2.629 2.628 2.627 2.627 2.626 2.626 2.576