To find the approximate P-value for any z statistic, compare z (ignoring its sign) with the critical value z* at the bottom of Table C. If z falls between two values of z*, the P-value falls between the two corresponding values of P in the "One-sided P" or the "Two-sided P" row of Table C. Example: "Is it statistically Significant?" The z-statistic for a one-sided test is z=2.13. How statistically significant is this result? Compare z=2.13 with the z* row in Table C z* 2.054 2.326 One-sided P 0.02 0.01 It lies between z* = 2.054 and z* = 2.326. So the P-value lies between the corresponding entries in the "One-sided P" row, which are P=0.02 and P=0.01. This z is statistically significant at the a=0.02 level and is not statistically significant at the a=0.01 level. Using the information above, answer the following question: 4 6-a) A test of Ho:µ = 0 against Ha: µ > 0 has test statistic z=1.65. Is this test statistically significant at the 5% level (a=0.05)? Is it statistically significant at the 1% (a=0.01)? 6-b) A test of Ho:µ = 0 against Ha:µ # 0 has test statistic z=1.65. Is this test statistically significant at the 5% level (a=0.05)? Is it statistically significant at the 1% (a=0.01)? TABLE C t distribution critical values degrees of Confidence level C freedom 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1.000 1.376 1.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 3 0.765 0.978 1.250 1.638 2.853 3.182 3.482 4.541 5.841 7.453 10.21 12.92 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 6 0.718 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 0.906 1.184 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 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 0.873 1.083 0.870 1.079 12 0.695 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 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 3.611 3.922 0.688 0.861 1.066 0.860 19 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 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 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 1.714 0.858 0,857 23 0.685 1.060 1.319 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 0.685 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 0.854 0.851 30 0.683 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 40 0.681 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.849 0.679 0.848 0.846 0:677-0.845-1.0421.290" 50 0.679 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 80 0.678 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 100 1.660 1.984 2.081-2.364 2.626 2.871 3.174 3.390 0.842 1.037 1.282 1.646 1.645 1000 0.675 1.962 2.056 2.330 2.581 2.813 3.098 3.300 0.674 0.841 1.036 .15 1.282 1.960 2.054 2.326 2,576 2.807 3.091 3.291 One-sided P 25 20 10 .05 .025 .02 .01 .005 .0025 .001 .0005 Two-sided P 50 40 .30 20 .10 .05 .04 .02 .01 .005 .002 .001

To find the approximate P-value for any z statistic, compare z (ignoring its sign) with the critical value z* at the bottom of Table C. If z falls between two values of z, the P-value falls between the two corresponding values of P in the "One-sided P" or the "Two-sided P" row of Table C. Example: "Is it statistically Significant?" The z-statistic for a one-sided test is z=2.13. How statistically significant is this result? Compare z=2.13 with the z row in Table C z* 2.054 2.326 One-sided P 0.02 0.01 It lies between z* = 2.054 and z* = 2.326. So the P-value lies between the corresponding entries in the "One-sided P" row, which are P=0.02 and P=0.01. This z is statistically significant at the a=0.02 level and is not statistically significant at the a=0.01 level. Using the information above, answer the following question: 4 6-a) A test of Ho:µ = 0 against Ha: µ > 0 has test statistic z=1.65. Is this test statistically significant at the 5% level (a=0.05)? Is it statistically significant at the 1% (a=0.01)? 6-b) A test of Ho:µ = 0 against Ha:µ # 0 has test statistic z=1.65. Is this test statistically significant at the 5% level (a=0.05)? Is it statistically significant at the 1% (a=0.01)? TABLE C t distribution critical values degrees of Confidence level C freedom 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1.000 1.376 1.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 3 0.765 0.978 1.250 1.638 2.853 3.182 3.482 4.541 5.841 7.453 10.21 12.92 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 6 0.718 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 0.906 1.184 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 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 0.873 1.083 0.870 1.079 12 0.695 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 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 3.611 3.922 0.688 0.861 1.066 0.860 19 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 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 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 1.714 0.858 0,857 23 0.685 1.060 1.319 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 0.685 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 0.854 0.851 30 0.683 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 40 0.681 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.849 0.679 0.848 0.846 0:677-0.845-1.0421.290" 50 0.679 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 80 0.678 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 100 1.660 1.984 2.081-2.364 2.626 2.871 3.174 3.390 0.842 1.037 1.282 1.646 1.645 1000 0.675 1.962 2.056 2.330 2.581 2.813 3.098 3.300 0.674 0.841 1.036 .15 1.282 1.960 2.054 2.326 2,576 2.807 3.091 3.291 One-sided P 25 20 10 .05 .025 .02 .01 .005 .0025 .001 .0005 Two-sided P 50 40 .30 20 .10 .05 .04 .02 .01 .005 .002 .001

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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