10.3

t-Distribution Area in Right Tail Degrees of Freedom 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.657 127.321 318.309 636.619 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7453 10.215 12.924 0.741 0.941 1.190 1.533 2.132 2.776 2.990 3.747 4.604 5.598 2173 8.610 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 0,703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 0.688 0.862 1.067 1.330 1.734 2101 2.214 2.552 2.878 3.197 3.610 3.922 0.688 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 0.687 0.860 1.325 1.725 2 086 2.197 2.528 2.845 3.153 3.552 3.850 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 0.685 0.857 1.059 1.318 1,711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.07 3.450 3.725 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.06 3.43 3.707 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 0.683 0.855 1.056 1.313 1.701 2048 2.154 2.467 2.763 3.047 3.408 3.674 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 0.682 0.853 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356 3.611 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 0.682 0.852 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.326 3.57 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 2.976 3.313 3.558 0.681 0.851 1.050 1.303 1.684 2.02 2.123 2.423 2.704 2.971 3.307 3.55 0.679 0.849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 0.679 0.848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 0.678 0.847 1.044 1.294 1.667 1.994 2.093 2.381 2.648 2.899 3.211 3.435 0.678 0.846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 0.677 0.846 1.291 1.662 1.987 2.084 2.368 2.632 2.878 3.183 3.402 100 0.677 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1006 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 Z 0.674 0.842 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.090 3.291 (1) (2) O (3) O 0.01 0.10. 2. Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the o = 0.05 level of significance with 15 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the a = 0.05 level of significance based on a sample size of n = 20. c) Determine the critical value(s) for a two-tailed test of a population mean at the a = 0.01 level of significance based on a sample size of n = 11. Click here to view the t-Distribution Area in Right Tail. (a) torit = + 1.753 (Round to three decimal places as needed.) (b) tcrit = (1) (Round to three decimal places as needed.) (c) tcrit = (2) (Round to three decimal places as needed.) 4: t-Distribution Area in Right Tail 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 df 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.65 127.321 318.309 636.619 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.215 12.924 MANN 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 0.727 0.920 1.156 1476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.86 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 0.711 0.896 1.119 1.415 1.895 2.365 2517 2.998 3.499 4.029 4.785 5.408 0.706 0.889 1.108 1.397 1.860 2.306 2449 2.896 3.355 3.833 4.501 5.041 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.78 0.700 0.879 1.093 1.372 1.812 2.228 2.35 2.764 3.169 3.581 4.144 4.58 10 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 11 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 12 0.694 0.870 1.079 1.350 2. 160 2.282 2.650 3.012 3.372 3.85 4.221 13 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 14 0.69 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 15 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 16 0.689 17 0.863 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 18 0.68 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 19 0.687 0.860 1.064 325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 20 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 21 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 22 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 23 0.685 0.85 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 24 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 25 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 26 0.684 0.855 1.057 1.314 1.703 2052 2.158 2.473 2.771 3.057 3.421 3.690 27 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 28 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 29 30 0.68 0.85 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 31 0.68 0.853 1.054 1.309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 32 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356 3.611 33 0.68 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 34 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 35 0.68 0.852 1.052 1.306 1.688 2028 2.131 2.434 2.719 2.990 3.333 3.582 36 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.326 3.574 37 0.681 0.851 1.051 1.304 1.686 2024 2.127 2.429 2.712 2.980 3.319 3.566 38 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 2.976 3.313 3.558 39 0.68 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 40 0.679 0.849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 50 0.67 0.848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 60