APPENDIX D STUDENT'S t CRITICAL VALUES This table shows the t-value that defines the area for the stated degrees of freedom (d.f.). Confidence Level Confidence Level .80 .90 .95 98 .99 80 .90 .95 .98 .99 Significance Level for Two-Tailed Test Significance Level for Two-Tailed Test .20 .10 .05 .02 .01 .20 .10 .05 .02 .01 Significance Level for One-Tailed Test Significance Level for One-Tailed Test d.f. .10 .05 .025 .01 .005 d.f. .10 .05 .025 .01 .005 1 3.078 6.314 12.706 31.821 63.657 36 1.306 1.688 2.028 2.434 2.719 2 1.886 2.920 4.303 6.965 9.925 37 1.305 1.687 2.026 2.431 2.715 3 1.638 2.353 3.182 4.541 5.841 38 1.304 1.686 2.024 2.429 2.712 4 1.533 2.132 2.776 3.747 4.604 39 1.304 1.685 2.023 2.426 2.708 5 1.476 2.015 2.571 3.365 4.032 40 1.303 1.684 2.021 2.423 2.704 6 1.440 1.943 2.447 3.143 3.707 41 1.303 1.683 2.020 2.421 2.701 7 1.415 1.895 2.365 2.998 3.499 42 1.302 1.682 2.018 2.418 2.698 8 1.397 1.860 2.306 2.896 3.355 43 1.302 1.681 2.017 2.416 2.695 9 1.383 1.833 2.262 2.821 3.250 44 1.301 1.680 2.015 2.414 2.692 10 1.372 1.812 2.228 2.764 3.169 45 1.301 1.679 2.014 2.412 2.690 11 1.363 1.796 2.201 2.718 3.106 46 1.300 1.679 2.013 2.410 2.687 12 1.356 1.782 2.179 2.681 3.055 47 1.300 1.678 2.012 2.408 2.685 13 1.350 1.771 2.160 2.650 3.012 48 1.299 1.677 2.011 2.407 2.682 14 1.345 1.761 2.145 2.624 2.977 49 1.299 1.677 2.010 2.405 2.680 15 1.341 1.753 2.131 2.602 2.947 50 1.299 1.676 2.009 2.403 2.678 16 1.337 1.746 2.120 2.583 2.921 55 1.297 1.673 2.004 2.396 2.668 17 1.333 1.740 2.110 2.567 2.898 60 1.296 1.671 2.000 2.390 2.660 18 1.330 1.734 2.101 2.552 2.878 65 1.295 1.669 1.997 2.385 2.654 19 1.328 1.729 2.093 2.539 2.861 70 1.294 1.667 1.994 2.381 2.648 20 1.325 1.725 2.086 2.528 2.845 75 1.293 1.665 1.992 2.377 2.643 21 1.323 1.721 2.080 2.518 2.831 80 1.292 1.664 1.990 2.374 2.639 22 1.321 1.717 2.074 2.508 2.819 85 1.292 1.663 1.988 2.371 2.635 23 1.319 1.714 2.069 2.500 2.807 90 1.291 1.662 1.987 2 2.368 2.632 24 1.318 1.711 2.064 2.492 2.797 95 1.291 1.661 1.985 2.366 2.629 25 1.316 1.708 2.060 2.485 2.787 100 1.290 1.660 1.984 2.364 2.626 26 1.315 1.706 2.056 2.479 2.779 110 1.289 1.659 1.982 2.361 2.621 27 1.314 1.703 2.052 2.473 2.771 120 1.289 1.658 1.980 2.358 2.617 28 1.313 1.701 2.048 2.467 2.763 130 1.288 1.657 1.978 2.355 2.614 29 1.311 1.699 2.045 2.462 2.756 140 1.288 1.656 1.977 2.353 2.611 30 1.310 1.697 2.042 2.457 2.750 150 1.287 1.655 1.976 2.351 2.609 31 1.309 1.696 2.040 2.453 2.744 00 1.282 1.645 1.960 2.326 2.576 32 1.309 1.694 2.037 2.449 2.738 33 1.308 1.692 2.035 2.445 2.733 34 1.307 1.691 2.032 2.441 2.728 35 1.306 1.690 2.030 2.438 2.724 Note: As n increases, critical values of Student's t approach the z-values in the last line of this table. A common rule of thumb is to use z when n > 30, but that is not conservative.Find the p-value as a range using Appendix D. (Round your left-tailed test answers to 3 decimal places and other values to 2 decimal places.) p-value (a) Right-tailed test t = 1.457, d.f. = 14 between and (b) Two-tailed test t = 2.601, d.f. = 8 between and (c) Left-tailed test t = -1.847, d.f. = 22 between and