TABLE A.7 Critical values of t (from the 3rd edition textbook) Upper tail area (shaded) 0 tcrit t Upper tail areas df t.10 t.05 t.025 t.01 t.005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.309 1.308 1.307 1.306 1.306 1.305 1.304 1.304 1.303 1.303 1.302 1.302 1.301 1.301 1.300 1.300 1.299 1.299 1.299 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.696 1.694 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.684 1.683 1.682 1.681 1.680 1.679 1.679 1.678 1.677 1.677 1.676 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2.024 2.023 2.021 2.020 2.018 2.017 2.015 2.014 2.013 2.012 2.011 2.010 2.009 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.453 2.449 2.445 2.441 2.438 2.434 2.431 2.429 2.426 2.423 2.421 2.418 2.416 2.414 2.412 2.410 2.408 2.407 2.405 2.403 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704 2.701 2.698 2.695 2.692 2.690 2.687 2.685 2.682 2.680 2.678 770 Appendix t.001 318.309 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.375 3.365 3.356 3.348 3.340 3.333 3.326 3.319 3.313 3.307 3.301 3.296 3.291 3.286 3.281 3.277 3.273 3.269 3.265 3.261 Upper tail area (shaded) 0 tcrit t Upper tail areas df t.10 t.05 t.025 t.01 t.005 t.001 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 150 200 1.298 1.298 1.298 1.297 1.297 1.297 1.297 1.296 1.296 1.296 1.296 1.295 1.295 1.295 1.295 1.295 1.294 1.294 1.294 1.294 1.294 1.293 1.293 1.293 1.293 1.293 1.293 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.290 1.290 1.290 1.290 1.290 1.287 1.286 1.282 1.675 1.675 1.674 1.674 1.673 1.673 1.672 1.672 1.671 1.671 1.670 1.670 1.669 1.669 1.669 1.668 1.668 1.668 1.667 1.667 1.667 1.666 1.666 1.666 1.665 1.665 1.665 1.665 1.664 1.664 1.664 1.664 1.663 1.663 1.663 1.663 1.663 1.662 1.662 1.662 1.662 1.662 1.661 1.661 1.661 1.661 1.661 1.661 1.660 1.660 1.655 1.653 1.645 2.008 2.007 2.006 2.005 2.004 2.003 2.002 2.002 2.001 2.000 2.000 1.999 1.998 1.998 1.997 1.997 1.996 1.995 1.995 1.994 1.994 1.993 1.993 1.993 1.992 1.992 1.991 1.991 1.990 1.990 1.990 1.989 1.989 1.989 1.988 1.988 1.988 1.987 1.987 1.987 1.986 1.986 1.986 1.986 1.985 1.985 1.985 1.984 1.984 1.984 1.976 1.972 1.960 2.402 2.400 2.399 2.397 2.396 2.395 2.394 2.392 2.391 2.390 2.389 2.388 2.387 2.386 2.385 2.384 2.383 2.382 2.382 2.381 2.380 2.379 2.379 2.378 2.377 2.376 2.376 2.375 2.374 2.374 2.373 2.373 2.372 2.372 2.371 2.370 2.370 2.369 2.369 2.368 2.368 2.368 2.367 2.367 2.366 2.366 2.365 2.365 2.365 2.364 2.351 2.345 2.326 2.676 2.674 2.672 2.670 2.668 2.667 2.665 2.663 2.662 2.660 2.659 2.657 2.656 2.655 2.654 2.652 2.651 2.650 2.649 2.648 2.647 2.646 2.645 2.644 2.643 2.642 2.641 2.640 2.640 2.639 2.638 2.637 2.636 2.636 2.635 2.634 2.634 2.633 2.632 2.632 2.631 2.630 2.630 2.629 2.629 2.628 2.627 2.627 2.626 2.626 2.609 2.601 2.576 3.258 3.255 3.251 3.248 3.245 3.242 3.239 3.237 3.234 3.232 3.229 3.227 3.225 3.223 3.220 3.218 3.216 3.214 3.213 3.211 3.209 3.207 3.206 3.204 3.202 3.201 3.199 3.198 3.197 3.195 3.194 3.193 3.191 3.190 3.189 3.188 3.187 3.185 3.184 3.183 3.182 3.181 3.180 3.179 3.178 3.177 3.176 3.175 3.175 3.174 3.145 3.131 3.090 Appendix 771 TABLE A.5 Areas of the standard normal distribution = 0, = 1 The entries in this table are the probabilities that a standard normal random variable is between 0 and z1 (the shaded area). 0 z1 z z1 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 .0000 .0398 .0793 .1179 .1554 .0040 .0438 .0832 .1217 .1591 .0080 .0478 .0871 .1255 .1628 .0120 .0517 .0910 .1293 .1664 .0160 .0557 .0948 .1331 .1700 .0199 .0596 .0987 .1368 .1736 .0239 .0636 .1026 .1406 .1772 .0279 .0675 .1064 .1443 .1808 .0319 .0714 .1103 .1480 .1844 .0359 .0753 .1141 .1517 .1879 0.5 0.6 0.7 0.8 0.9 .1915 .2257 .2580 .2881 .3159 .1950 .2291 .2611 .2910 .3186 .1985 .2324 .2642 .2939 .3212 .2019 .2357 .2673 .2967 .3238 .2054 .2389 .2704 .2995 .3264 .2088 .2422 .2734 .3023 .3289 .2123 .2454 .2764 .3051 .3315 .2157 .2486 .2794 .3078 .3340 .2190 .2517 .2823 .3106 .3365 .2224 .2549 .2852 .3133 .3389 1.0 1.1 1.2 1.3 1.4 .3413 .3643 .3849 .4032 .4192 .3438 .3665 .3869 .4049 .4207 .3461 .3686 .3888 .4066 .4222 .3485 .3708 .3907 .4082 .4236 .3508 .3729 .3925 .4099 .4251 .3531 .3749 .3944 .4115 .4265 .3554 .3770 .3962 .4131 .4279 .3577 .3790 .3980 .4147 .4292 .3599 .3810 .3997 .4162 .4306 .3621 .3830 .4015 .4177 .4319 1.5 1.6 1.7 1.8 1.9 .4332 .4452 .4554 .4641 .4713 .4345 .4463 .4564 .4649 .4719 .4357 .4474 .4573 .4656 .4726 .4370 .4484 .4582 .4664 .4732 .4382 .4495 .4591 .4671 .4738 .4394 .4505 .4599 .4678 .4744 .4406 .4515 .4608 .4686 .4750 .4418 .4525 .4616 .4693 .4756 .4429 .4535 .4625 .4699 .4761 .4441 .4545 .4633 .4706 .4767 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 .4772 .4821 .4861 .4893 .4918 .4938 .4953 .4965 .4974 .4981 .4987 .4990 .4993 .4995 .4997 .4998 .49997 .499997 .4999997 .499999999 .4778 .4826 .4864 .4896 .4920 .4940 .4955 .4966 .4975 .4982 .4987 .4991 .4993 .4995 .4997 .4783 .4830 .4868 .4898 .4922 .4941 .4956 .4967 .4976 .4982 .4987 .4991 .4994 .4995 .4997 .4788 .4834 .4871 .4901 .4925 .4943 .4957 .4968 .4977 .4983 .4988 .4991 .4994 .4996 .4997 .4793 .4838 .4875 .4904 .4927 .4945 .4959 .4969 .4977 .4984 .4988 .4992 .4994 .4996 .4997 .4798 .4842 .4878 .4906 .4929 .4946 .4960 .4970 .4978 .4984 .4989 .4992 .4994 .4996 .4997 .4803 .4846 .4881 .4909 .4931 .4808 .4850 .4884 .4911 .4932 .4812 .4854 .4887 .4913 .4934 .4817 .4857 .4890 .4916 .4936 .4948 .4961 .4971 .4979 .4985 .4989 .4992 .4994 .4996 .4997 .4949 .4962 .4972 .4979 .4985 .4989 .4992 .4995 .4996 .4997 .4951 .4963 .4973 .4980 .4986 .4990 .4993 .4995 .4996 .4997 .4952 .4964 .4974 .4981 .4986 .4990 .4993 .4995 .4997 .4998 3.5 4.0 4.5 5.0 6.0 768 Appendix