STATISTICAL TABLES.pdf

STATISTICAL TABLES This Tables may be used for all UG / PG Programmes B.E. / B.Tech. Probability and Statistics, Random Processes, Operations Research, Total Quality Management. M.E. / M.Tech. / MCA / MBA Theoretical Foundations of Computer Scien...

STATISTICAL TABLES This Tables may be used for all UG / PG Programmes B.E. / B.Tech. Probability and Statistics, Random Processes, Operations Research, Total Quality Management. M.E. / M.Tech. / MCA / MBA Theoretical Foundations of Computer Science, Probability and Statistics, Mathematical Foundation of Computer Applications, Statistical Methods for Business, Applied Operations Research. B.Sc. / M.Sc. Bio-Statistics and Mathematics, Optimization Techniques, Optimization Techniques and Numerical Methods. CONTENT Table No. Page No. Standard Normal Distribution Table 1 1 Critical values of the t - Distribution 2 2 Critical values of the F - Distribution 3 3 Critical values of the Chi-square Distribution 4 5 Table of Random Numbers 5 6 Kolmogorov – Smirnov Critical Values 6 7 Values for “Spearman’s Rank Correlation 7 8 for Combined Areas in both Tails” Table of Control Chart Constants 8 9 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 1 Area under Standard Normal Distribution P(0 z a) a 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 1 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 2 T distribution – critical values of t Level of significance for Two-tailed Test Degrees 20% 10% 5% 2% 1% 0.2% 0.1% of freedom Level of significance for One-tailed Test 10% 5% 2.5% 1% 0.5% 0.1% 0.05% 1 3.078 6.314 12.706 31.821 63.657 318.309 636.619 2 1.886 2.920 4.303 6.965 9.925 22.327 31.599 3 1.638 2.353 3.182 4.541 5.841 10.215 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 1.397 1.860 2.306 2.896 3.355 4.501 5.041 9 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.500 2.807 3.485 3.768 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 1.314 1.703 2.052 2.473 2.771 3.421 3.690 28 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 1.311 1.699 2.045 2.462 2.756 3.396 3.659 30 1.310 1.697 2.042 2.457 2.750 3.385 3.646 32 1.309 1.694 2.037 2.449 2.738 3.365 3.622 34 1.307 1.691 2.032 2.441 2.728 3.348 3.601 36 1.306 1.688 2.028 2.434 2.719 3.333 3.582 38 1.304 1.686 2.024 2.429 2.712 3.319 3.566 40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 42 1.302 1.682 2.018 2.418 2.698 3.296 3.538 44 1.301 1.680 2.015 2.414 2.692 3.286 3.526 46 1.300 1.679 2.013 2.410 2.687 3.277 3.515 48 1.299 1.677 2.011 2.407 2.682 3.269 3.505 50 1.299 1.676 2.009 2.403 2.678 3.261 3.496 60 1.296 1.671 2.000 2.390 2.660 3.232 3.460 70 1.294 1.667 1.994 2.381 2.648 3.211 3.435 80 1.292 1.664 1.990 2.374 2.639 3.195 3.416 90 1.291 1.662 1.987 2.368 2.632 3.183 3.402 100 1.290 1.660 1.984 2.364 2.626 3.174 3.390 1000 1.282 1.646 1.962 2.330 2.581 3.098 3.300 df … degrees of freedom 2 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 3 F DISTRIBUTION - Critical values of F – 5% POINTS Degrees of freedom for numerator (v1) 1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 60 100 1000 1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 245.95 248.01 249.26 250.10 251.14 252.20 253.04 254.19 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.43 19.45 19.46 19.46 19.47 19.48 19.49 19.49 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.70 8.66 8.63 8.62 8.59 8.57 8.55 8.53 4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.62 4.56 4.52 4.50 4.46 4.43 4.41 4.37 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 3.94 3.87 3.83 3.81 3.77 3.74 3.71 3.67 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.51 3.44 3.40 3.38 3.34 3.30 3.27 3.23 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.22 3.15 3.11 3.08 3.04 3.01 2.97 2.93 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.01 2.94 2.89 2.86 2.83 2.79 2.76 2.71 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.85 2.77 2.73 2.70 2.66 2.62 2.59 2.54 Degrees of freedom for denominator ( v2) 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.72 2.65 2.60 2.57 2.53 2.49 2.46 2.41 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.62 2.54 2.50 2.47 2.43 2.38 2.35 2.30 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.53 2.46 2.41 2.38 2.34 2.30 2.26 2.21 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.46 2.39 2.34 2.31 2.27 2.22 2.19 2.14 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.40 2.33 2.28 2.25 2.20 2.16 2.12 2.07 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.35 2.28 2.23 2.19 2.15 2.11 2.07 2.02 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.31 2.23 2.18 2.15 2.10 2.06 2.02 1.97 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.27 2.19 2.14 2.11 2.06 2.02 1.98 1.92 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.23 2.16 2.11 2.07 2.03 1.98 1.94 1.88 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.20 2.12 2.07 2.04 1.99 1.95 1.91 1.85 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.18 2.10 2.05 2.01 1.96 1.92 1.88 1.82 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.15 2.07 2.02 1.98 1.94 1.89 1.85 1.79 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.13 2.05 2.00 1.96 1.91 1.86 1.82 1.76 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.11 2.03 1.97 1.94 1.89 1.84 1.80 1.74 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.09 2.01 1.96 1.92 1.87 1.82 1.78 1.72 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.07 1.99 1.94 1.90 1.85 1.80 1.76 1.70 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.06 1.97 1.92 1.88 1.84 1.79 1.74 1.68 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.04 1.96 1.91 1.87 1.82 1.77 1.73 1.66 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.03 1.94 1.89 1.85 1.81 1.75 1.71 1.65 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.01 1.93 1.88 1.84 1.79 1.74 1.70 1.63 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 1.92 1.84 1.78 1.74 1.69 1.64 1.59 1.52 60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.84 1.75 1.69 1.65 1.59 1.53 1.48 1.40 100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97 1.93 1.77 1.68 1.62 1.57 1.52 1.45 1.39 1.30 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE 3  Table – 3 (continued) F DISTRIBUTION - Critical values of F – 1% POINTS Degrees of freedom for numerator (v1) 1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 60 100 1000 1 4052 4999 5403 5625 5764 5859 5928 5981 6022 6056 6157 6209 6240 6261 6287 6313 6334 6363 2 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 26.87 26.69 26.58 26.50 26.41 26.32 26.24 26.14 4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.20 14.02 13.91 13.84 13.75 13.65 13.58 13.47 5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.72 9.55 9.45 9.38 9.29 9.20 9.13 9.03 6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.56 7.40 7.30 7.23 7.14 7.06 6.99 6.89 7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.31 6.16 6.06 5.99 5.91 5.82 5.75 5.66 8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.52 5.36 5.26 5.20 5.12 5.03 4.96 4.87 9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 4.96 4.81 4.71 4.65 4.57 4.48 4.41 4.32 10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.56 4.41 4.31 4.25 4.17 4.08 4.01 3.92 Degrees of freedom for denominator ( v2) 11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.25 4.10 4.01 3.94 3.86 3.78 3.71 3.61 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.01 3.86 3.76 3.70 3.62 3.54 3.47 3.37 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.82 3.66 3.57 3.51 3.43 3.34 3.27 3.18 14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.66 3.51 3.41 3.35 3.27 3.18 3.11 3.02 15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.52 3.37 3.28 3.21 3.13 3.05 2.98 2.88 16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.41 3.26 3.16 3.10 3.02 2.93 2.86 2.76 17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.31 3.16 3.07 3.00 2.92 2.83 2.76 2.66 18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.23 3.08 2.98 2.92 2.84 2.75 2.68 2.58 19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.15 3.00 2.91 2.84 2.76 2.67 2.60 2.50 20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.09 2.94 2.84 2.78 2.69 2.61 2.54 2.43 21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.03 2.88 2.79 2.72 2.64 2.55 2.48 2.37 22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 2.98 2.83 2.73 2.67 2.58 2.50 2.42 2.32 23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 2.93 2.78 2.69 2.62 2.54 2.45 2.37 2.27 24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 2.89 2.74 2.64 2.58 2.49 2.40 2.33 2.22 25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.85 2.70 2.60 2.54 2.45 2.36 2.29 2.18 26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 2.81 2.66 2.57 2.50 2.42 2.33 2.25 2.14 27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.78 2.63 2.54 2.47 2.38 2.29 2.22 2.11 28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.75 2.60 2.51 2.44 2.35 2.26 2.19 2.08 29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.73 2.57 2.48 2.41 2.33 2.23 2.16 2.05 30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.70 2.55 2.45 2.39 2.30 2.21 2.13 2.02 40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.52 2.37 2.27 2.20 2.11 2.02 1.94 1.82 60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.35 2.20 2.10 2.03 1.94 1.84 1.75 1.62 100 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59 2.50 2.22 2.07 1.97 1.89 1.80 1.69 1.60 1.45 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE 4  Table – 4 Critical Values of Chi-Square Distribution The areas given across the top are the areas to the right of the critical value. To look up an area on the left, subtract it from one, and then look it up (ie: 0.05 on the left is 0.95 on the right) df 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 df 1 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 1 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 2 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 3 4 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 4 5 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.750 5 6 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 6 7 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 7 8 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 8 9 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 9 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188 10 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757 11 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300 12 13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819 13 14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319 14 15 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801 15 16 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.267 16 17 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.718 17 18 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.156 18 19 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582 19 20 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.997 20 21 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.401 21 22 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796 22 23 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181 23 24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.559 24 25 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.928 25 26 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.290 26 27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645 27 28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.993 28 29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.336 29 30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672 30 40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766 40 50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.490 50 60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952 60 70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215 70 80 51.172 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 116.321 80 90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299 90 100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169 100 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE 5  Table – 5 Table of Random Numbers 15167 71241 61765 94133 44866 75008 78737 27153 64561 61221 77678 50572 67879 31873 48828 21386 33485 97506 20164 35794 89596 94806 58746 05906 02355 87542 88175 33432 60348 14438 69307 49349 18806 64312 57440 74956 68886 74961 77015 22397 29508 39923 62365 95225 97989 61499 43265 77541 59732 74525 45033 89290 07749 14689 29903 37011 06852 97012 30240 79035 74752 69851 62857 05265 57416 23804 90279 87132 47292 04275 17642 31333 96236 90542 04506 16822 77198 68435 64537 36210 30413 88371 81022 09274 35277 13114 80290 99221 12139 95500 75572 60516 42188 63638 48753 93636 49217 00465 14198 70979 24479 20396 85909 02813 46408 28206 15683 93391 77559 94706 66400 35051 87004 65488 12937 56566 28994 15644 41313 15019 64067 97774 08405 30392 11359 24720 82198 40374 02692 27607 01161 08421 98653 21195 19639 91513 41702 23843 70852 84560 25870 78298 15805 57841 66328 28033 90599 78424 33491 33690 88303 85043 50232 82119 63500 05578 10667 78315 52782 23535 80190 68593 50501 89798 16515 48144 35916 75347 03575 35968 12365 05634 21383 13340 65725 69483 88732 01069 88079 08376 82542 55817 40410 54662 86669 70355 01539 60885 15439 33613 12914 49978 32384 42908 88470 05743 17193 71410 43986 34745 07053 73153 39667 97373 08242 62131 47759 51956 42367 97705 24281 90997 40143 40702 67204 95908 41887 36373 24148 02215 69573 55611 91550 45250 19265 81848 77494 31154 27610 15701 71336 87819 55615 58546 88232 23661 48901 05171 83729 22168 06944 17084 46614 03256 35958 96730 62642 53431 85694 05682 25819 95256 41102 60073 14360 96401 26590 78478 37792 90048 19721 41248 94961 78460 74468 76027 78964 91421 74956 36105 41278 79837 85277 48649 51943 97035 83322 03039 57694 84017 82173 36388 86629 24321 20838 78573 90945 12742 37824 53136 52906 85039 90790 79145 30525 86368 84260 82326 04051 64700 55221 19182 06120 73224 27742 70797 20774 30477 62736 06516 29621 77285 37850 98946 01094 19139 50558 89571 91802 53446 15158 38633 01988 41206 38549 21363 43506 09601 74729 13033 47115 96401 27597 34135 14919 13123 57536 71311 20756 24982 19279 66879 53107 65696 16043 65225 15809 19541 86121 40588 40045 39410 06377 22861 00549 55686 03178 38851 12008 39204 52021 39057 23507 72331 94225 55701 87304 67426 17368 76879 18867 83126 22077 69014 20691 55295 68474 55330 46565 99786 53281 19695 87931 42307 03055 01875 02646 73236 35184 72356 74498 37226 80247 46223 94756 59742 63689 37583 12982 84195 82670 33152 88338 86036 39043 92270 27390 67981 51146 00409 23607 97325 14562 91272 82226 66997 06962 25333 57160 50914 98840 65967 42391 82802 56043 34577 66224 76106 40462 61185 86676 06373 35552 17263 81660 47941 99449 76235 73086 43267 43959 71937 32057 55336 02534 23124 26798 28969 88697 75733 26585 36074 12732 00124 98225 37674 51153 73732 66984 96123 88937 43149 54335 68890 09950 36683 93156 94464 30735 97045 32512 28495 55953 66475 09225 49087 80681 50937 12914 58207 58878 32849 11286 64104 03568 44433 01502 87235 78976 94700 18115 07411 20892 24566 69160 00415 25825 99078 03355 06043 6 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 6 Kolmogorov – Smirnov Critical Values Degrees of Freedom D0.10 D0.05 D0.01 1. 0.950 0.975 0.995 2. 0.776 0.842 0.929 3. 0.642 0.708 0.828 4. 0.564 0.624 0.733 5. 0.510 0.565 0.669 6. 0.470 0.521 0.618 7. 0.438 0.486 0.577 8. 0.411 0.457 0.543 9. 0.388 0.432 0.514 10. 0.368 0.410 0.490 11. 0.352 0.391 0.468 12. 0.338 0.375 0.450 13. 0.325 0.361 0.433 14. 0.314 0.349 0.418 15. 0.304 0.338 0.404 16. 0.295 0.328 0.392 17. 0.286 0.318 0.381 18. 0.278 0.309 0.371 19. 0.272 0.301 0.363 20. 0.264 0.294 0.356 25. 0.24 0.27 0.32 30. 0.22 0.24 0.29 35. 0.21 0.23 0.27 1.22 1.36 1.63 Over 35 N N N Source: F.J.Massey, “The Kolmogorov – Smirnov Test for Goodness of Fit, “The Journal of the American Statistical Association, [email protected], Adapted with permission of the American Statistical Association. 7 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 7 Values for Spearman’s Rank Correlation for Combined Areas in Both Tails.” EXAMPLE: For a two-tailed test of significance at the.20 level, with n = 12, the appropriate value for r s can be found by looking under the.20 column and proceeding down to the 12 row: there we find the appropriate r s value to be.3986. N.20.10.05.02.01.002 4.8000.8000 5.7000.8000.9000.9000 6.6000.7714.8286.8857.9429 7.5357.6786.7450.8571.8929.9643 8.5000.6190.7143.8095.8571.9286 9.4667.5833.6833.7667.8167.9000 10.4424.5515.6364.7333.7818.8667 11.4182.5273.6091.7000.7455.8364 12.3986.4965..5804.6713.7273.8182 13.3791.4780.5549.6429.6978.7012 14.3626.4593.5341.6220.6747.7670 15.3500.4429.5179.6000.6536.7464 16.3382.4265.5000.5824.6324.7265 17.3260.4118.4853.5637.6152.7083 18.3148.3994.4716.5480.5975.6904 19.3070.3895.4579.5333.5825.6737 20.2977.3789.4451.5203.5684.6586 21.2909.3688.4351.5078.5545.6455 22.2829.3597.4241.4963.5426.6318 23.2767.3518.4150.4852.5306.6186 24.2704.3435.4061.4748.5200.6070 25.2646.3362.3977.4654.5100.5962 26.2588.3299.3894.4564.5002.5856 27.2540.3236.3822.4481.4915.5757 28.2490.3175.3749.4401.4828.5660 29.2443.3113.3685.4320.4744.5567 30.2400.3059.3620.4251.4665.5479 8 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE  Table – 8 Table of Control Chart Constants Sample Factors for Chart Factors for s - chart Factors for R – chart size n A A1 A2 c2 B1 B2 B3 B4 d2 D1 D2 D3 D4 2. 2.121 3.670 1.880 0.5642 0 1.843 0 3.267 1.128 0 3.686 0 3.262 3. 1.732 2.394 1.023 0.7236 0 1.858 0 2.568 1.693 0 4.358 0 2.575 4. 1.500 1.880 0.729 0.7979 0 1.808 0 2.266 2.059 0 4.698 0 2.282 5. 1.342 1.596 0.577 0.8407 0 1.756 0 2.089 2.326 0 4.918 0 2.115 6. 1.225 1.410 0.483 0.8686 0.026 1.711 0.030 1.970 2.534 0 5.078 0 2.004 7. 1.134 1.277 0.419 0.8882 0.105 1.672 0.118 1.882 2.704 0.205 5.203 0.076 1.924 8. 1.061 1.175 0.373 0.9027 1.167 1.638 0.185 1.815 2.847 0.387 5.307 0.136 1.864 9. 1.000 1.094 0.337 0.9139 0.219 0.609 0.239 1.760 2.970 0.546 5.394 0.184 1.816 10. 0.949 1.028 0.308 0.9227 0.262 1.584 0.284 1.716 3.078 0.687 5.469 0.223 1.777 11. 0.905 0.793 0.285 0.9300 0.299 1.561 0.321 1.679 3.173 0.812 5.534 0.256 1.744 12. 0.866 0.925 0.266 0.9359 0.331 1.541 0.354 1.646 3.258 0.924 5.592 0.284 1.716 13. 0.832 0.884 0.249 0.9410 0.359 1.523 0.382 1.618 3.336 1.026 5.646 0.308 1.692 14. 0.802 0.848 0.235 0.9453 0.384 1.507 0.406 1.594 3.407 1.121 5.693 0.329 1.671 15. 0.775 0.816 0.223 0.9490 0.406 1.492 0.428 1.572 3.472 1.207 5.737 0.348 1.652 16. 0.750 0.788 0.212 0.9523 0.427 1.478 0.448 1.552 3.532 1.285 5.779 0.364 1.636 17. 0.728 0.762 0.203 0.9551 0.445 1.465 0.466 1.534 3.588 1.359 5.817 0.379 1.621 18. 0.707 0.738 0.194 0.9576 0.461 0.459 0.482 1.518 3.640 1.426 5.854 0.392 1.608 19. 0.688 0.717 0.184 0.9599 0.477 0.443 0.497 1.503 3.689 1.490 5.888 0.404 1.596 20. 0.671 0.697 0.110 0.9619 0.491 1.433 0.510 1.490 3.735 1.544 5.922 0.418 1.586 9 K.S.Rangasamy College of Technology, Tiruchengode – 637 215 COE