\f-t -1 0 0 - 0 Confidence interval Left-tailed test Right-tailed test Two-tailed test Confidence Intervals, c Confidence Intervals, c 80% 90% 95% 98% 99% 99.99 80% 90% 95% 98% 99% 99.9% Level of Significance for One-Tailed Test, Level of Significance for One-Tailed Test, 0.10 0.05 0.025 0.01 0.005 0.0005 0.10 0.025 0.01 0.005 0.0005 Level of Significance for Two-Tailed Test, i Level of Significance for Two-Tailed Test, a 0.20 0.10 0.05 0.02 0.01 0.001 0.20 0.10 0.05 0.02 0.01 0.001 3.078 6.314 12.706 31.821 $3.657 636.619 1.306 1.688 2.028 2.434 2.719 3.582 1.8:86 2.920 4.303 6.965 9.925 31.599 1.305 1.687 2.026 2.431 2.715 3.574 1.638 2.352 3.182 4.541 5.841 12.924 38 1.304 1.686 2.024 2429 2.712 3.566 1.533 2.132 2.776 3.747 4 FO4 8.610 39 1.304 1.685 2.023 2.426 2.708 3.558 1.476 2.015 2.571 3.365 4.032 40 1.203 1.684 2.021 2.423 2.704 3.551 1.440 1.943 2.447 3.143 3.707 5.959 41 1.303 1.683 2.020 2.421 2.701 3.544 1.415 1.895 2.365 2.998 3.499 5.408 42 1.302 1.682 2.018 2.418 2.698 3.538 1.397 1.860 2.306 2.896 3.355 5.041 43 1.302 1.681 2.017 2.416 2.695 3.532 1.383 1.803 2.262 2.821 3.250 4.781 44 1.301 1.680 2.015 2414 2.692 3.526 1.372 1.812 2.228 2.764 3.169 4.587 45 1.301 1.679 2.014 2412 2.690 3.520 11 1.263 1.796 2.201 2.718 3.106 4.437 46 1.300 1.679 2.013 2.410 2.687 3.515 12 1.356 1.782 2.179 2.681 3.055 4.318 47 1.300 1.678 2.012 2.408 2.685 3.510 13 1.250 1.771 2.160 2.650 3.012 4.221 48 1.299 1.677 2.011 2.407 2.682 3.506 14 1.345 1.761 2145 2.624 2.977 4.140 1.299 1.677 2.010 2.405 2.680 3.500 15 1.341 1.75 2.131 2.602 2.947 4.073 1.299 1.676 2.009 2.403 2.678 3.496 16 1.237 1.746 2.120 2.583 2.921 4.015 51 1.298 1.675 2.008 2.402 2.676 3.492 17 1.333 1.740 2110 2.567 2.898 3.965 1.298 1.675 2.007 2400 2.674 1.488 18 1.330 1.734 2.101 2.552 2.878 3.922 53 1.298 1.674 2.00 2.399 2.672 3.48 19 1.328 1.729 2.093 2.539 2.861 3.883 54 1 1.297 1.674 2.005 2.397 2.670 3.480 1.325 1.725 2.086 2.528 2.845 3.85 55 1.297 1.673 2.004 2.396 2.668 3.476 1.323 1.721 2.080 2.518 2.831 3.819 56 1.297 1.673 2.003 2.395 2.667 3.473 1.321 1.717 2074 2.508 2.819 3.792 57 1.297 1.672 2.00 2.39 2.66 3.470 1.319 1.714 2.069 2.500 2.807 3.768 58 1.296 1.672 2.00 2.392 2.663 3.466 1.318 1.711 2.06 2.492 2.797 3.745 59 1.296 1.671 2.001 2.391 2.662 3.463 1.316 1.708 2.06 2.48 2.787 3.725 60 1.296 1.671 2.000 2.390 2.660 3.460 1.315 1.706 2.05 2.479 2.779 3.707 61 1.296 1.670 2.000 2.789 2.659 3.457 1.314 1.703 2.057 2.473 2.171 3.690 62 1.295 1.670 1.999 2.380 2.657 1.454 1.313 1.701 2048 2.467 2.763 3.674 63 1.295 1.669 1.998 2.38 2.656 3 452 1.311 1.699 2045 2.462 2.756 3.659 64 1.295 1.669 1.998 2.386 2.656 3.449 1.310 1.697 2.047 2.457 2.750 3.646 65 1.295 1.669 1.997 2.385 2.654 3.447 31 1.309 1.696 2.040 2.45 2.74 3.633 66 1.295 1.66 1.997 2.384 2.652 3.444 1.309 1.694 2.037 2.449 2.738 3.627 67 1.294 1.668 1.996 2.383 2.651 3.442 1.308 1.692 2.035 2.445 2.733 3.611 68 1.294 1.668 1.995 2.382 2.650 3.439 1.307 1.691 2.032 2.441 2.728 3.601 69 1.294 1.667 1.995 2.382 2.649 3.437 1.306 1.690 2030 2.724 3.59 70 1.294 1.667 1.994 2381 2.648 3.435 1.294 1.667 1.994 2.380 2.647 89 1.291 1.562 1.987 2 369 2.632 3.403 1.293 1.666 1.993 2.379 2.646 3.431 90 1.291 1.66 1.987 2 368 2.632 3.402 73 1.293 1.666 1.993 2.379 2.645 3.429 74 1.293 1.666 1.993 2.378 2.64 3.427 91 1.291 1.66 1.986 2 368 2.631 3.40 75 1.293 1.665 1.992 2.377 2.643 3.425 92 1.291 1.662 1.986 2.368 2.630 3.39 93 1.291 1.661 1.986 2 367 2.630 3.398 76 1.290 1.665 1.992 2.376 2.642 3.420 94 1.291 1.661 1.986 2 367 2.629 3.397 77 1.293 1.665 1.991 2.376 2.641 3.421 45 1.291 1.661 1.985 2 366 2.629 3.396 78 1.292 1.665 1.991 2.375 2.640 3.420 79 1.292 1.664 1.990 2.374 2.640 3.418 96 1.290 1.66 1989 2 366 2.628 8.39 1.292 1.664 1.590 2.374 2.639 3.416 97 1.290 1.661 1.985 2 365 2.627 3.39 98 1.290 1.661 1.984 2.365 2.627 3.39 1.292 1.664 1.990 2.373 2.638 3.415 99 1.290 1.660 1.984 2 365 2.626 3.39 828 89 82 1.292 1.664 1.989 2.373 2.637 3.413 100 1.290 1.660 1.984 2364 2.626 3.390 1.292 1.663 1.989 2.372 2.636 3.412 1.292 1.663 1.989 2.372 2.636 3.410 120 1.289 1.658 1980 2.61 3.373 1.292 1.663 1.988 2.371 2.635 340 140 1.288 1.656 1.977 2 353 2.611 3.361 160 1.287 1.654 1.975 2 350 2.607 3.352 86 1.291 1.663 1.988 2.370 2.634 3.407 180 1.286 1.653 1.973 2 347 2.603 3.345 1.291 1.663 1.988 2.370 2.634 3.406 200 1.286 1.653 1.972 2 345 2.601 3.340 1.291 1,662 1.987 2.369 2.633 3.405 1.282 1.645 1.960 2 326 2.576 3.29Example: If z = 1.96, then P(0 to z) = 0.4750. 0.4750 0 1.96 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0. 1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990