Determine the t-value in each of the cases. Click the icon to view the table of areas under the t-distribution. (a) Find the t-value such that the area in the right tail is 0.025 with 18 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.02 with 14 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.005 with 23 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 80% confidence. Assume 24 degrees of freedom. (Round to three decimal places as needed.) -Area in right tail Table VI t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1 1.000 1.376 1.963 2 0.816 1.061 1.386 3.078 6.314 1.886 2.920 12.706 15.894 31.821 4.303 4.849 6.965 63.657 127.321 318.309 9.925 14.089 636.619 22.327 31.599 3 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.215 12.924 4 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 5 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 6 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 7 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 8 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 19 0.688 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 21 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 22 23 0.686 0.858 1.061 0.685 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 0.685 0.857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 25 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 27 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 28 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 29 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 31 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 32 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 33 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356 3.611 34 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 35 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 36 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 37 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.326 3.574 38 39 0.681 0.851 1.050 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566 1.304 1.685 2.023 2.125 2.426 2.708 2.976 3.313 3.558 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 50 0.679 0.849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 0.679 0.848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 70 0.678 0.847 1.044 1.294 1.667 1.994 2.093 2.381 2.648 2.899 3.211 3.435 80 90 Z 0.678 0.846 1.043 1.292 1.664 0.677 0.846 1.042 1.291 1.662 100 0.677 0.845 1.042 1.290 1.660 1000 0.675 0.842 1.037 1.282 1.646 0.674 0.842 1.036 1.282 1.990 2.088 2.374 2.639 2.887 3.195 3.416 1.987 2.084 2.368 2.632 2.878 3.183 3.402 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1.962 2.056 2.330 2.581 2.813 3.098 3.300 1.645 1.960 2.054 2.326 2.576 2.807 3.090 3.291 df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 Area in Right Tail