Question

4. Draw the appropriate picture and use the t-table, to find each of the following: a. The area to the left of 2.571 in the t distribution with 5 degrees of freedom. b. The area to the right of - 1.314 in the t distribution with 27 degrees of freedom. c. The area between -2.390 and 1.671 in the t distribution with 60 degrees of freedom.

Answer 1

4. The table gives upper tailed (right tailed) t values for different probability cut-offs. Area to the left of 2.571 in t distribution with df = 5 P(t5 < 2.571) = 1 - P(t5 > 2.571) P(t< a) = 1 - P(t> a) Probability p Table entry for p and C is the critical value tº with probability p lying to its right and probability C lying between -t" and t. TABLE D t distribution critical values Upper-tail probability p df 25 20 15 10 .05 .025 .02 .01 .005 .0025 .001 .0005 1.000 0.816 0.765 0.741 1.376 1.963 3.078 1.061 1.3861.886 0.978 1.250 1.638 0.941 1.190 1.533 non 1155 0.906 1.134 1.440 0.896 1.119 1.415 0.889 1.108 1.397 0.883 1.100 1.383 0.8791.093 1.372 0.718 0.711 0.706 0.703 0.700 6.314 2.920 2.353 2.132 2 1.943 1.895 1.860 1.833 1.812 1217 4.3 3.32 216 2.571 22447 2.365 2.306 2.262 2.228 2 15.89 31.82 63.66 127.3 4.8496.9659.925 14.09 3.482 4.541 5.841 7.453 2.999 3.747 4.604 5.598 2.757 3.365 4.032 4.773 .612 3.143 3.707 4.317 2.517 2.998 3.499 4.029 2.449 2.896 3.355 3.833 2.398 2.821 3.250 3.690 2.764 3.1693.581 318.3 636.6 22.3331.60 10.21 12.92 7.173 8.610 5.893 6.869 5.208 5.959 4.785 5.408 4.501 5.041 4.297 4.781 4.144 4.587 From t table for df = 5, P(t5 > 2.571) = 0.025, hence P(t < 2.571) = 1 – 0.025 = 0.975 Distribution Plot T, df=5 0.9750 Density 0 2.571 b. Area to the right of -1.314 in t distribution with df = 27 P(t27 > -1.314) = P(t27 < 1.314) as we do not negative t values in table T distribution is symmetric around 0 And Plt > -a) = P(t <a) = 1 – P(t27 > 1.314)

TABLE D t distribution critical values Upper-tail probability p .025 .02 .01 df | 25 20 15 10 .05 .005 .0025 .001 .0005 3. 1.886 1.33 1.476 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 S. 0.683 0.683 0.683 1.415 1.197 1.183 1.72 1.163 1.56 1. 150 1.145 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 SO 0.855 0.854 0.854 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1. 137 1.33 1.30 1.128 1125 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 .697 12.71 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 15.89 4.849 3.482 2.999 2.757 2.612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.205 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 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 63.66 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 2.750 127.3 14.09 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 318.3 22.33 10.21 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 3.611 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 636.6 31.60 12.92 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 11.123 1.121 1.119 is 16 115 (1.314 1.313 1.311 1.310 1.056 1.055 1.055 29 30 1 From t table P(t27 > 1.314) = 0.1, hence P(t27 > -1.314) = 1 – 0.1 = 0.9 Distribution Plot T, df=27 0.9000 Density 0.04 -1.314 ох c. The area between -2.390 and 1.671 in the t distribution with df = 60 P(-2.390 < too < 1.671) = P(t60 < 1.671) – P(t60 < -2.390) Pla<t<b) = P(t < b) – P(t < a) = [1 – P(+60 > 1.671)] - P(60 > 2.390)

TABLE D t distribution critical values Upper-tail probability p .025 .02 .01 df 25 20 15 10 .05 .005 .0025 .001 .0005 m 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.849 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.047 es 1.043 1.042 1.037 3.0786.34 1.886 2.920 1.638 2.33 1.533 2.152 1.476 2.0.5 1.440 1.913 1.415 1.815 1.397 1.850 1.383 1.8653 1.372 1.82 1.363 1.76 1.356 1.712 1.350 1.71 1.345 1.71 1.341 1.73 1.337 1.746 1.333 1.710 1.330 1.784 1.328 1.79 1.325 1.75 1.323 1. 71 1.321 1.77 1.319 1.74 1.318 1.7.1 1.316 1.78 1.315 1.76 1.314 1.73 1.313 1.751 1.311 1.699 1.310 1.67 1.303 1.04 1.299 1.CFO (1.671 1.292 1.664 1.290 1.660 1.282 1.646 12.71 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 2.021 2.009 000 1.990 1.984 1.962 15.89 4.849 3.482 2.999 2.757 2.612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.205 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.123 2.109 minicidiciciririricininioinicininiai iniciricinininin 3118263.66 9.925 5.841 4.604 3.165 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 2.704 2.678 2.390 2.680 2.374 2.639 2364 2.626 2.330 2.581 127. 3 14.09 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 2.971 2.937 2.915 2.882 2.871 2.813 318.3 22.33 10.21 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 3.611 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.261 3.232 3.195 3.174 3.098 636.6 31.60 12.92 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.490 3.460 3.416 3.390 3.300 60 80 100 1000 0.678 0.677 0.675 0.846 0.845 0.842 2.088 2.081 2.056 From t table P(160 > 1.671) = 0.05 and P(t60 > 2.390) = 0.01, hence P(-2.390 < 160 < 1.671) = [1 – 0.05] – 0.01 = 0.94 Distribution Plot T, df=60 0.4 0.9400 Density 0.0 -2.39 1.671 хо Please rate the question if it was helpful, happy HomeworkLibing! ☺