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determine the level of confidence given the confidence coefficient z(a/2) = 1.96

determine the level of confidence given the confidence coefficient z(a/2) = 1.96

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t Table cum. prob 50 80 85 95 995 9995 one-tail 0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 two-tails 1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001 df 1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.31 636.62 2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599 3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 10.215 12.924 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.6047.173 8.610 5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5 7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 4.501 5.041 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 3.852 4.221 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015 14 17 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3 18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 0.000 0.685 0.858 1.060 1.319 1.7142.069 2.500 2.807 3.485 3.768 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 0.000 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 26 271 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.6 28 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.000 0.683 0.8541.055 1.311 1.699 2.045 2.462 2.756 3.3963 10ร 30 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 40 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.7043.307 3.551 3.460 2.374 2.639 3.195 3.416 2.364 2.626 3.174 3.390 9622.330 2.581 3.098 3.300 1.960 2.326 2.576 3.090 3.291 0% 50% 60% 70% 80% 909 95% % 99% 99.8% 99.9% 60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.232 80 0.000 0.678 0.846 1.043 1.292 1.664 19 100 0.000 0.677 0.845 1.042 1.290 1.660 10000.000 0.675 0.842 1.037 1.282 1.646 0.000 0.674 0.842 1.036 1.282 1.64 Confidence

look at the bottom row that starts with Z. In that row, you'll see 1.960. Right below it is 95%

So a 95% confidence level corresponds to z(α/2) = 1.96

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