Question: Appendix A APPENDIX A Statistical Tables 860 Table 1 Random Numbers 860 Table 2 Standard Normal Probabilities (Cumulative z Curve Areas) 862 Table 3 t

Appendix A APPENDIX A Statistical Tables 860 Table 1 Random Numbers 860 Table 2 Standard Normal Probabilities (Cumulative z Curve Areas) 862 Table 3 t Critical Values 864 Table 4 Tail Areas for t Curves 865 Table 5 Curves of b 5 P(Type II Error) for t Tests 868 Table 6 Values That Capture Specied Upper-Tail F Curve Areas 869 Table 7 Critical Values of q for the Studentized Range Distribution 873 Table 8 Upper-Tail Areas for Chi-Square Distributions 874 Table 9 Binomial Probabilities 876 859 54906-00-APPA-p859-878.indd 859 10/6/10 9:25 AM 860 Appendix A Statistical Tables Appendix A: Statistical Tables TA BLE 1 Random Numbers Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 4 4 8 8 5 0 4 6 8 9 6 0 6 2 0 6 9 9 2 5 1 9 1 6 1 1 1 7 1 2 0 8 7 4 9 0 7 9 0 0 3 6 9 5 1 4 7 2 54906-00-APPA-p859-878.indd 860 5 2 9 9 7 9 1 4 0 4 6 7 1 2 7 6 9 9 5 1 9 7 7 2 5 4 8 8 6 8 7 4 3 7 3 2 1 7 4 7 5 6 5 1 6 4 7 5 1 5 9 0 3 3 0 7 2 6 9 1 3 3 1 5 6 9 6 1 8 0 6 5 7 6 5 7 3 9 8 0 5 2 3 4 0 9 2 1 6 8 0 7 3 8 6 6 8 5 3 7 1 8 1 3 8 0 5 7 0 6 7 1 2 6 3 9 0 9 4 8 1 6 0 4 2 0 8 1 9 6 7 9 1 4 5 2 6 5 4 8 9 6 6 6 5 8 4 2 0 7 0 6 7 6 7 7 9 2 4 6 5 1 1 8 7 6 8 2 1 5 2 6 8 8 6 4 7 7 0 7 8 4 0 3 2 5 3 9 4 4 4 3 0 0 3 9 3 6 2 3 9 9 4 7 7 1 2 1 3 2 9 1 4 3 2 0 1 6 1 5 3 1 5 5 0 6 7 8 4 5 0 6 4 2 1 4 1 0 5 7 3 4 5 9 7 7 2 4 3 7 4 2 3 3 0 8 5 9 8 2 6 8 0 7 9 0 6 4 7 6 7 1 4 9 0 1 7 3 9 1 4 9 1 7 3 3 4 0 3 5 0 0 4 9 0 5 8 8 6 9 3 0 0 1 9 3 1 1 8 9 3 8 5 1 8 3 3 8 5 9 9 9 5 6 1 1 9 7 5 7 7 2 2 8 4 6 7 7 6 4 7 9 4 1 4 8 3 7 6 2 0 5 8 4 1 1 4 9 9 6 1 9 0 7 0 1 5 1 1 2 7 3 2 9 6 9 6 9 3 9 1 3 8 5 1 0 3 7 8 5 7 2 0 2 2 8 6 2 1 5 3 6 0 6 0 7 6 4 4 4 7 9 7 7 4 1 2 7 5 8 9 3 4 3 3 3 9 2 1 8 4 6 2 7 9 6 5 6 5 3 4 5 0 7 0 6 3 2 7 5 3 9 3 0 3 6 5 0 7 3 2 3 0 2 1 8 6 7 3 4 0 9 7 3 2 8 8 3 4 9 8 0 1 7 2 2 1 1 2 2 6 5 4 6 1 6 5 6 5 8 0 6 6 6 2 5 2 9 4 1 0 1 3 7 9 8 8 5 6 5 8 1 7 9 5 5 0 0 4 3 1 4 0 5 1 1 0 9 0 8 1 9 2 2 0 4 6 1 8 5 2 8 8 2 6 2 8 3 3 5 2 5 5 0 0 0 9 4 7 6 7 9 6 9 3 1 5 6 8 7 1 6 9 8 8 6 8 8 8 7 0 0 1 6 7 8 1 4 1 9 3 7 2 7 0 0 4 3 5 5 4 5 0 6 0 6 6 9 4 8 3 5 9 9 1 6 2 1 3 5 4 0 9 0 9 6 3 0 4 1 3 5 9 1 1 3 0 2 4 6 6 9 9 9 1 2 1 5 3 6 8 3 3 8 5 5 7 0 4 9 8 5 1 1 6 3 7 8 7 0 1 1 1 9 2 2 7 1 9 8 1 9 0 6 7 0 3 4 7 5 9 7 2 8 9 2 1 7 7 5 8 4 2 9 0 6 1 4 5 2 0 3 9 4 7 4 9 4 2 4 3 8 6 1 8 5 3 2 4 9 6 5 7 6 0 3 5 4 9 2 7 5 3 4 4 2 9 9 3 8 0 7 3 3 9 8 2 6 9 1 2 3 6 2 7 8 3 6 6 4 7 2 4 2 8 7 5 1 2 0 3 9 7 6 4 2 4 5 3 5 3 4 6 7 2 6 5 8 4 1 1 7 3 3 0 9 5 3 0 5 3 6 5 2 3 0 1 1 6 5 1 3 0 4 2 2 3 3 1 0 3 8 8 3 7 7 7 7 8 3 6 5 8 9 7 0 3 1 2 2 1 9 2 1 7 1 9 3 6 4 1 0 2 5 8 0 8 8 0 6 8 0 0 0 2 2 7 4 5 8 7 1 0 9 9 5 3 4 8 0 6 8 2 6 2 2 8 1 7 4 3 2 10/6/10 9:25 AM Appendix A TA B L E 1 861 Statistical Tables Random Numbers (Continued) Row 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 54906-00-APPA-p859-878.indd 861 9 7 7 3 0 8 5 5 0 3 9 5 9 6 8 3 1 5 8 6 2 2 4 1 1 5 1 2 3 0 8 5 0 9 5 5 3 3 5 3 9 9 9 8 6 0 5 2 7 1 2 4 4 3 5 3 2 5 4 0 2 8 1 3 6 3 5 8 4 9 7 7 3 9 8 5 8 7 8 6 6 7 3 3 9 4 5 3 3 0 0 6 0 5 4 1 9 0 3 5 4 9 4 1 0 1 8 6 9 9 7 3 6 1 5 5 6 0 8 2 4 9 1 2 2 5 9 6 1 7 6 6 6 8 6 6 3 7 4 0 0 5 8 4 4 2 5 1 4 6 3 6 3 0 8 7 4 5 2 0 6 6 6 6 3 6 6 6 4 6 3 4 1 5 7 3 8 7 8 5 1 0 0 7 4 0 0 9 7 4 1 0 9 7 6 7 4 6 7 8 7 8 9 2 7 8 0 8 7 6 8 9 9 2 1 4 7 3 0 3 5 7 5 9 1 3 5 1 7 8 3 7 7 9 5 9 5 1 5 0 7 0 7 5 3 1 0 8 9 9 0 0 8 8 3 7 9 8 2 6 5 6 8 1 8 9 0 1 5 8 6 9 7 9 2 0 7 7 2 4 0 4 2 7 2 5 4 4 7 2 7 6 2 0 8 4 2 9 8 2 1 3 3 5 3 7 8 6 6 0 5 7 3 5 8 1 9 6 0 9 1 1 5 5 7 5 0 9 4 2 5 9 9 7 7 5 8 5 8 2 8 1 7 3 8 0 6 8 9 5 1 3 6 9 4 4 3 2 4 0 8 1 2 1 2 0 7 0 3 8 1 8 1 4 6 4 6 5 6 2 6 5 6 2 7 9 6 4 5 6 3 2 3 1 9 8 6 3 4 0 4 8 6 5 8 6 6 2 9 4 9 3 6 2 7 1 8 3 6 3 8 2 0 4 6 5 6 7 1 4 6 6 3 1 8 1 1 0 9 3 5 8 4 8 0 3 1 7 4 5 2 7 0 0 2 7 5 5 4 8 1 4 1 8 2 2 0 5 7 5 4 2 1 1 4 4 6 2 3 3 5 6 0 2 6 7 7 7 1 3 1 4 8 6 5 7 2 4 5 5 3 4 3 4 5 0 0 9 2 1 2 5 2 7 9 1 8 2 5 8 2 3 1 7 5 2 6 1 0 9 6 6 4 2 0 9 5 1 9 0 1 6 9 3 9 8 3 4 8 2 8 9 2 6 2 7 5 4 8 8 8 8 5 3 5 6 1 4 3 7 9 9 7 7 1 8 3 4 1 2 5 4 2 6 4 2 6 5 6 1 9 8 2 9 8 8 9 2 5 3 4 1 8 5 9 6 9 6 4 5 6 5 9 8 4 3 0 6 7 4 8 5 6 4 4 2 0 2 9 7 4 0 8 2 3 7 8 8 0 1 5 0 1 6 8 2 6 1 9 2 8 4 6 6 4 9 4 2 8 2 8 3 5 2 0 7 8 3 1 0 8 2 4 6 6 8 9 8 2 0 9 0 1 2 1 5 0 5 0 4 6 9 5 7 3 7 2 0 9 8 6 6 7 9 7 9 9 7 8 6 4 1 7 0 4 7 7 8 6 0 2 3 4 6 2 5 1 9 3 6 3 5 7 6 5 5 2 7 0 0 6 4 3 1 7 1 9 8 9 6 5 9 2 0 7 6 2 3 5 4 2 2 6 1 5 3 0 6 5 2 1 1 3 4 5 8 2 5 5 8 9 2 1 3 0 8 0 1 3 3 0 1 5 0 0 9 7 0 6 9 1 0 2 9 0 5 7 1 1 3 7 2 9 3 3 2 7 0 7 9 7 0 1 1 0 7 2 3 0 7 8 3 6 4 9 4 7 3 9 8 3 2 1 5 7 0 1 0 0 9 4 9 0 6 4 4 1 5 8 9 4 5 2 5 9 6 8 1 5 2 2 0 2 4 9 4 1 5 2 6 7 8 7 0 5 1 3 8 7 4 6 1 6 3 8 6 6 9 7 8 3 2 9 4 6 2 9 4 6 1 5 4 5 4 2 6 6 1 3 2 3 7 9 2 5 4 1 4 1 6 5 3 0 7 9 9 5 8 6 9 1 6 5 2 1 1 5 7 3 9 0 3 5 8 3 7 7 6 9 1 6 8 7 3 2 0 7 2 9 1 0 6 8 6 1 4 1 7 8 8 2 8 4 2 5 2 7 0 6 7 0 8 6 1 5 1 3 8 9 3 0 8 5 3 8 8 0 4 7 8 9 1 7 7 0 9 3 4 6 9 9 4 5 9 8 7 0 9 8 9 8 3 5 2 4 8 3 6 5 7 10/6/10 9:25 AM 862 Appendix A Statistical Tables Tabulated area = probability z* TA BLE 2 Standard normal (z) curve 0 Standard Normal Probabilities (Cumulative z Curve Areas) z* .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 .0001 .0001 .0002 .0002 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 .0287 .0359 .0446 .0548 .0668 .0808 .0968 .1151 .1357 .1587 .1841 .2119 .2420 .2743 .3085 .3446 .3821 .4207 .4602 .5000 .0001 .0001 .0002 .0002 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 .0222 .0281 .0351 .0436 .0537 .0655 .0793 .0951 .1131 .1335 .1562 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 .4562 .4960 .0001 .0001 .0001 .0002 .0003 .0005 .0006 .0009 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 .0132 .0170 .0217 .0274 .0344 .0427 .0526 .0643 .0778 .0934 .1112 .1314 .1539 .1788 .2061 .2358 .2676 .3015 .3372 .3745 .4129 .4522 .4920 .0001 .0001 .0001 .0002 .0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 .0075 .0099 .0129 .0166 .0212 .0268 .0336 .0418 .0516 .0630 .0764 .0918 .1093 .1292 .1515 .1762 .2033 .2327 .2643 .2981 .3336 .3707 .4090 .4483 .4880 .0001 .0001 .0001 .0002 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 .0409 .0505 .0618 .0749 .0901 .1075 .1271 .1492 .1736 .2005 .2296 .2611 .2946 .3300 .3669 .4052 .4443 .4840 .0001 .0001 .0001 .0002 .0003 .0004 .0006 .0008 .0011 .0016 .0022 .0030 .0040 .0054 .0071 .0094 .0122 .0158 .0202 .0256 .0322 .0401 .0495 .0606 .0735 .0885 .1056 .1251 .1469 .1711 .1977 .2266 .2578 .2912 .3264 .3632 .4013 .4404 .4801 .0001 .0001 .0001 .0002 .0003 .0004 .0006 .0008 .0011 .0015 .0021 .0029 .0039 .0052 .0069 .0091 .0119 .0154 .0197 .0250 .0314 .0392 .0485 .0594 .0721 .0869 .1038 .1230 .1446 .1685 .1949 .2236 .2546 .2877 .3228 .3594 .3974 .4364 .4761 .0001 .0001 .0001 .0002 .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0244 .0307 .0384 .0475 .0582 .0708 .0853 .1020 .1210 .1423 .1660 .1922 .2206 .2514 .2843 .3192 .3557 .3936 .4325 .4721 .0001 .0001 .0001 .0002 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 .0571 .0694 .0838 .1003 .1190 .1401 .1635 .1894 .2177 .2483 .2810 .3156 .3520 .3897 .4286 .4681 .0000 .0001 .0001 .0002 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .0110 .0143 .0183 .0233 .0294 .0367 .0455 .0559 .0681 .0823 .0985 .1170 .1379 .1611 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 54906-00-APPA-p859-878.indd 862 10/6/10 9:25 AM Appendix A Tabulated area = probability z* 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 54906-00-APPA-p859-878.indd 863 863 Standard normal (z) curve 0 TA B L E 2 Statistical Tables z* Standard Normal Probabilities (Cumulative z Curve Areas) (Continued) .00 .01 .02 .03 .04 .05 .06 .07 .08 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8159 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9713 .9772 .9821 .9861 .9893 .9918 .9938 .9953 .9965 .9974 .9981 .9987 .9990 .9993 .9995 .9997 .9998 .9998 .9999 .9999 .5040 .5438 .5832 .6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 .9463 .9564 .9649 .9719 .9778 .9826 .9864 .9896 .9920 .9940 .9955 .9966 .9975 .9982 .9987 .9991 .9993 .9995 .9997 .9998 .9998 .9999 .9999 .5080 .5478 .5871 .6255 .6628 .6985 .7324 .7642 .7939 .8212 .8461 .8686 .8888 .9066 .9222 .9357 .9474 .9573 .9656 .9726 .9783 .9830 .9868 .9898 .9922 .9941 .9956 .9967 .9976 .9982 .9987 .9991 .9994 .9995 .9997 .9998 .9999 .9999 .9999 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 .9732 .9788 .9834 .9871 .9901 .9925 .9943 .9957 .9968 .9977 .9983 .9988 .9991 .9994 .9996 .9997 .9998 .9999 .9999 .9999 .5160 .5557 .5948 .6331 .6700 .7054 .7389 .7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 .9495 .9591 .9671 .9738 .9793 .9838 .9875 .9904 .9927 .9945 .9959 .9969 .9977 .9984 .9988 .9992 .9994 .9996 .9997 .9998 .9999 .9999 .9999 .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 .8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .9744 .9798 .9842 .9878 .9906 .9929 .9946 .9960 .9970 .9978 .9984 .9989 .9992 .9994 .9996 .9997 .9998 .9999 .9999 .9999 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 .9515 .9608 .9686 .9750 .9803 .9846 .9881 .9909 .9931 .9948 .9961 .9971 .9979 .9985 .9989 .9992 .9994 .9996 .9997 .9998 .9999 .9999 .9999 .5279 .5675 .6064 .6443 .6808 .7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 .9911 .9932 .9949 .9962 .9972 .9979 .9985 .9989 .9992 .9995 .9996 .9997 .9998 .9999 .9999 .9999 .5319 .5714 .6103 .6480 .6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 .9625 .9699 .9761 .9812 .9854 .9887 .9913 .9934 .9951 .9963 .9973 .9980 .9986 .9990 .9993 .9995 .9996 .9997 .9998 .9999 .9999 .9999 .09 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 .9441 .9545 .9633 .9706 .9767 .9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 .9981 .9986 .9990 .9993 .9995 .9997 .9998 .9998 .9999 .9999 1.0000 10/6/10 9:25 AM 864 Appendix A Statistical Tables t curve Central area 0 - t critical value TA BLE 3 t Critical Values Central area captured: Condence level: Degrees of freedom z critical values 54906-00-APPA-p859-878.indd 864 t critical value .80 80% .90 90% .95 95% .98 98% .99 99% .998 99.8% .999 99.9% 1 3.08 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 1.89 1.64 1.53 1.48 1.44 1.42 1.40 1.38 1.37 1.36 1.36 1.35 1.35 1.34 1.34 1.33 1.33 1.33 1.33 1.32 1.32 1.32 1.32 1.32 1.32 1.31 1.31 1.31 1.31 1.30 1.30 1.29 6.31 2.92 2.35 2.13 2.02 1.94 1.90 1.86 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.75 1.74 1.73 1.73 1.73 1.72 1.72 1.71 1.71 1.71 1.71 1.70 1.70 1.70 1.70 1.68 1.67 1.66 12.71 4.30 3.18 2.78 2.57 2.45 2.37 2.31 2.26 2.23 2.20 2.18 2.16 2.15 2.13 2.12 2.11 2.10 2.09 2.09 2.08 2.07 2.07 2.06 2.06 2.06 2.05 2.05 2.05 2.04 2.02 2.00 1.98 31.82 6.97 4.54 3.75 3.37 3.14 3.00 2.90 2.82 2.76 2.72 2.68 2.65 2.62 2.60 2.58 2.57 2.55 2.54 2.53 2.52 2.51 2.50 2.49 2.49 2.48 2.47 2.47 2.46 2.46 2.42 2.39 2.36 63.66 9.93 5.84 4.60 4.03 3.71 3.50 3.36 3.25 3.17 3.11 3.06 3.01 2.98 2.95 2.92 2.90 2.88 2.86 2.85 2.83 2.82 2.81 2.80 2.79 2.78 2.77 2.76 2.76 2.75 2.70 2.66 2.62 318.31 23.33 10.21 7.17 5.89 5.21 4.79 4.50 4.30 4.14 4.03 3.93 3.85 3.79 3.73 3.69 3.65 3.61 3.58 3.55 3.53 3.51 3.49 3.47 3.45 3.44 3.42 3.41 3.40 3.39 3.31 3.23 3.16 636.62 31.60 12.92 8.61 6.86 5.96 5.41 5.04 4.78 4.59 4.44 4.32 4.22 4.14 4.07 4.02 3.97 3.92 3.88 3.85 3.82 3.79 3.77 3.75 3.73 3.71 3.69 3.67 3.66 3.65 3.55 3.46 3.37 1.28 1.645 1.96 2.33 2.58 3.09 3.29 10/6/10 9:25 AM Appendix A t curve Area to the right of t 0 TA B L E 4 865 Statistical Tables t Tail Areas for t Curves t df 1 2 3 4 5 6 7 8 9 10 11 12 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 .500 .468 .437 .407 .379 .352 .328 .306 .285 .267 .250 .235 .221 .209 .197 .187 .178 .169 .161 .154 .148 .141 .136 .131 .126 .121 .117 .113 .109 .106 .102 .099 .096 .094 .091 .089 .086 .084 .082 .080 .078 .500 .465 .430 .396 .364 .333 .305 .278 .254 .232 .211 .193 .177 .162 .148 .136 .125 .116 .107 .099 .092 .085 .079 .074 .069 .065 .061 .057 .054 .051 .048 .045 .043 .040 .038 .036 .035 .033 .031 .030 .029 .500 .463 .427 .392 .358 .326 .295 .267 .241 .217 .196 .176 .158 .142 .128 .115 .104 .094 .085 .077 .070 .063 .058 .052 .048 .044 .040 .037 .034 .031 .029 .027 .025 .023 .021 .020 .018 .017 .016 .015 .014 .500 .463 .426 .390 .355 .322 .290 .261 .234 .210 .187 .167 .148 .132 .117 .104 .092 .082 .073 .065 .058 .052 .046 .041 .037 .033 .030 .027 .024 .022 .020 .018 .016 .015 .014 .012 .011 .010 .010 .009 .008 .500 .462 .425 .388 .353 .319 .287 .258 .230 .205 .182 .162 .142 .125 .110 .097 .085 .075 .066 .058 .051 .045 .040 .035 .031 .027 .024 .021 .019 .017 .015 .013 .012 .011 .010 .009 .008 .007 .006 .006 .005 .500 .462 .424 .387 .352 .317 .285 .255 .227 .201 .178 .157 .138 .121 .106 .092 .080 .070 .061 .053 .046 .040 .035 .031 .027 .023 .020 .018 .016 .014 .012 .011 .009 .008 .007 .006 .006 .005 .004 .004 .004 .500 .462 .424 .386 .351 .316 .284 .253 .225 .199 .175 .154 .135 .117 .102 .089 .077 .066 .057 .050 .043 .037 .032 .027 .024 .020 .018 .015 .013 .011 .010 .009 .008 .007 .006 .005 .004 .004 .003 .003 .003 .500 .461 .423 .386 .350 .315 .283 .252 .223 .197 .173 .152 .132 .115 .100 .086 .074 .064 .055 .047 .040 .034 .029 .025 .022 .018 .016 .014 .012 .010 .009 .007 .006 .005 .005 .004 .004 .003 .003 .002 .002 .500 .461 .423 .386 .349 .315 .282 .251 .222 .196 .172 .150 .130 .113 .098 .084 .072 .062 .053 .045 .038 .033 .028 .023 .020 .017 .014 .012 .010 .009 .007 .006 .005 .005 .004 .003 .003 .002 .002 .002 .002 .500 .461 .423 .385 .349 .314 .281 .250 .221 .195 .170 .149 .129 .111 .096 .082 .070 .060 .051 .043 .037 .031 .026 .022 .019 .016 .013 .011 .009 .008 .007 .006 .005 .004 .003 .003 .002 .002 .002 .001 .001 .500 .461 .423 .385 .348 .313 .280 .249 .220 .194 .169 .147 .128 .110 .095 .081 .069 .059 .050 .042 .035 .030 .025 .021 .018 .015 .012 .010 .009 .007 .006 .005 .004 .004 .003 .002 .002 .002 .001 .001 .001 .500 .461 .422 .385 .348 .313 .280 .249 .220 .193 .169 .146 .127 .109 .093 .080 .068 .057 .049 .041 .034 .029 .024 .020 .017 .014 .012 .010 .008 .007 .006 .005 .004 .003 .003 .002 .002 .002 .001 .001 .001 (continued) 54906-00-APPA-p859-878.indd 865 10/6/10 9:25 AM 866 Appendix A Statistical Tables t curve Area to the right of t 0 TA BLE 4 t Tail Areas for t Curves (Continued) t df 13 14 15 16 17 18 19 20 21 22 23 24 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 .500 .461 .422 .384 .348 .313 .279 .248 .219 .192 .168 .146 .126 .108 .092 .079 .067 .056 .048 .040 .033 .028 .023 .019 .016 .013 .011 .009 .008 .006 .005 .004 .003 .003 .002 .002 .002 .001 .001 .001 .001 .500 .461 .422 .384 .347 .312 .279 .247 .218 .191 .167 .144 .124 .107 .091 .077 .065 .055 .046 .038 .032 .027 .022 .018 .015 .012 .010 .008 .007 .005 .004 .004 .003 .002 .002 .002 .001 .001 .001 .001 .001 .500 .461 .422 .384 .347 .312 .279 .247 .218 .191 .167 .144 .124 .107 .091 .077 .065 .055 .046 .038 .032 .027 .022 .018 .015 .012 .010 .008 .007 .005 .004 .004 .003 .002 .002 .002 .001 .001 .001 .001 .001 .500 .461 .422 .384 .347 .312 .278 .247 .218 .191 .166 .144 .124 .106 .090 .077 .065 .054 .045 .038 .031 .026 .021 .018 .014 .012 .010 .008 .006 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .001 .001 .500 .461 .422 .384 .347 .312 .278 .247 .217 .190 .166 .143 .123 .105 .090 .076 .064 .054 .045 .037 .031 .025 .021 .017 .014 .011 .009 .008 .006 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .001 .000 .500 .461 .422 .384 .347 .312 .278 .246 .217 .190 .165 .143 .123 .105 .089 .075 .064 .053 .044 .037 .030 .025 .021 .017 .014 .011 .009 .007 .006 .005 .004 .003 .002 .002 .002 .001 .001 .001 .001 .001 .000 .500 .461 .422 .384 .347 .311 .278 .246 .217 .190 .165 .143 .122 .105 .089 .075 .063 .053 .044 .036 .030 .025 .020 .016 .013 .011 .009 .007 .006 .005 .004 .003 .002 .002 .002 .001 .001 .001 .001 .000 .000 .500 .461 .422 .384 .347 .311 .278 .246 .217 .189 .165 .142 .122 .104 .089 .075 .063 .052 .043 .036 .030 .024 .020 .016 .013 .011 .009 .007 .006 .004 .004 .003 .002 .002 .001 .001 .001 .001 .001 .000 .000 .500 .461 .422 .384 .347 .311 .278 .246 .216 .189 .164 .142 .122 .104 .088 .074 .062 .052 .043 .036 .029 .024 .020 .016 .013 .010 .008 .007 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .001 .000 .000 .500 .461 .422 .383 .347 .311 .277 .246 .216 .189 .164 .142 .121 .104 .088 .074 .062 .052 .043 .035 .029 .024 .019 .016 .013 .010 .008 .007 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .500 .461 .422 .383 .346 .311 .277 .245 .216 .189 .164 .141 .121 .103 .087 .074 .062 .051 .042 .035 .029 .023 .019 .015 .012 .010 .008 .006 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .500 .461 .422 .383 .346 .311 .277 .245 .216 .189 .164 .141 .121 .103 .087 .073 .061 .051 .042 .035 .028 .023 .019 .015 .012 .010 .008 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .001 .000 .000 .000 54906-00-APPA-p859-878.indd 866 10/6/10 9:25 AM Appendix A t curve Area to the right of t 0 TA B L E 4 867 Statistical Tables t Tail Areas for t Curves (Continued) t df 25 26 27 28 29 30 35 40 60 120 (z) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 .500 .461 .422 .383 .346 .311 .277 .245 .216 .188 .163 .141 .121 .103 .087 .073 .061 .051 .042 .035 .028 .023 .019 .015 .012 .010 .008 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .001 .000 .000 .000 .500 .461 .422 .383 .346 .311 .277 .245 .215 .188 .163 .141 .120 .103 .087 .073 .061 .051 .042 .034 .028 .023 .018 .015 .012 .010 .008 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .001 .000 .000 .000 .500 .461 .421 .383 .346 .311 .277 .245 .215 .188 .163 .141 .120 .102 .086 .073 .061 .050 .042 .034 .028 .023 .018 .015 .012 .009 .007 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .500 .461 .421 .383 .346 .310 .277 .245 .215 .188 .163 .140 .120 .102 .086 .072 .060 .050 .041 .034 .028 .022 .018 .015 .012 .009 .007 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .500 .461 .421 .383 .346 .310 .277 .245 .215 .188 .163 .140 .120 .102 .086 .072 .060 .050 .041 .034 .027 .022 .018 .014 .012 .009 .007 .006 .005 .004 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .500 .461 .421 .383 .346 .310 .277 .245 .215 .188 .163 .140 .120 .102 .086 .072 .060 .050 .041 .034 .027 .022 .018 .014 .011 .009 .007 .006 .004 .003 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .500 .460 .421 .383 .346 .310 .276 .244 .215 .187 .162 .139 .119 .101 .085 .071 .059 .049 .040 .033 .027 .022 .017 .014 .011 .009 .007 .005 .004 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .000 .500 .460 .421 .383 .346 .310 .276 .244 .214 .187 .162 .139 .119 .101 .085 .071 .059 .048 .040 .032 .026 .021 .017 .013 .011 .008 .007 .005 .004 .003 .002 .002 .001 .001 .001 .001 .000 .000 .000 .000 .000 .500 .460 .421 .383 .345 .309 .275 .243 .213 .186 .161 .138 .117 .099 .083 .069 .057 .047 .038 .031 .025 .020 .016 .012 .010 .008 .006 .004 .003 .003 .002 .001 .001 .001 .001 .000 .000 .000 .000 .000 .000 .500 .460 .421 .382 .345 .309 .275 .243 .213 .185 .160 .137 .116 .098 .082 .068 .056 .046 .037 .030 .024 .019 .015 .012 .009 .007 .005 .004 .003 .002 .002 .001 .001 .001 .000 .000 .000 .000 .000 .000 .000 .500 .460 .421 .382 .345 .309 .274 .242 .212 .184 .159 .136 .115 .097 .081 .067 .055 .045 .036 .029 .023 .018 .014 .011 .008 .006 .005 .003 .003 .002 .001 .001 .001 .000 .000 .000 .000 .000 .000 .000 .000 54906-00-APPA-p859-878.indd 867 10/6/10 9:25 AM 868 Appendix A Statistical Tables Curves of b P(Type II Error) for t Tests TA BLE 5 1.0 99 .8 .6 1.0 = .05, one-tailed 74 49 39 29 = .05, two-tailed df = 1 .8 19 .6 .4 .4 14 9 6 0 0 0.4 0.8 1.2 4 3 1.6 2.0 2.4 3 4 df = 2 .2 2 29 39 74 2.8 3.2 d .2 49 6 19 14 9 99 0 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 d 1.0 1.0 = .01, one-tailed .8 .8 df = 2 39 49 74 .6 = .01, two-tailed df = 2 .6 3 .4 49 39 29 19 .4 4 74 .2 99 0 0 54906-00-APPA-p859-878.indd 868 0.4 29 14 9 .2 6 19 0.8 1.2 1.6 2.0 2.4 2.8 3.2 d 0 0 99 0.4 0.8 3 4 14 9 1.2 1.6 6 2.0 2.4 2.8 3.2 d 10/6/10 9:25 AM Appendix A 869 Statistical Tables F curve Area Value TA B L E 6 Values That Capture Specied Upper-Tail F Curve Areas df1 df2 1 2 3 4 5 6 7 8 9 Area 1 2 3 4 5 6 7 8 9 10 .10 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 60.19 .05 161.40 199.50 215.70 224.60 230.20 234.00 236.80 238.90 240.50 241.90 .01 4052.00 5000.00 5403.00 5625.00 5764.00 5859.00 5928.00 5981.00 6022.00 6056.00 .10 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 .05 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 .01 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 .001 998.50 999.00 999.20 999.20 999.30 999.30 999.40 999.40 999.40 999.40 .10 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 .05 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 .01 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 .001 167.00 148.50 141.10 137.10 134.60 132.80 131.60 130.60 129.90 129.20 .10 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 .05 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 .01 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 .001 74.14 61.25 56.18 53.44 51.71 50.53 49.66 49.00 48.47 48.05 .10 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30 .05 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 .01 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 .001 47.18 37.12 33.20 31.09 29.75 28.83 28.16 27.65 27.24 26.92 .10 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94 .05 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 .01 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 .001 35.51 27.00 23.70 21.92 20.80 20.03 19.46 19.03 18.69 18.41 .10 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70 .05 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 .01 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 .001 29.25 21.69 18.77 17.20 16.21 15.52 15.02 14.63 14.33 14.08 .10 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54 .05 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 .01 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 .001 25.41 18.49 15.83 14.39 13.48 12.86 12.40 12.05 11.77 11.54 .10 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 .05 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 .01 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 .001 22.86 16.39 13.90 12.56 11.71 11.13 10.70 10.37 10.11 9.89 (continued) 54906-00-APPA-p859-878.indd 869 10/6/10 9:25 AM 870 Appendix A Statistical Tables TA BLE 6 Values That Capture Specied Upper-Tail F Curve Areas (Continued) df1 df2 10 11 12 13 14 15 16 17 18 19 Area .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 54906-00-APPA-p859-878.indd 870 1 3.29 4.96 10.04 21.04 3.23 4.84 9.65 19.69 3.18 4.75 9.33 18.64 3.14 4.67 9.07 17.82 3.10 4.60 8.86 17.14 3.07 4.54 8.68 16.59 3.05 4.49 8.53 16.12 3.03 4.45 8.40 15.72 3.01 4.41 8.29 15.38 2.99 4.38 8.18 15.08 2 2.92 4.10 7.56 14.91 2.86 3.98 7.21 13.81 2.81 3.89 6.93 12.97 2.76 3.81 6.70 12.31 2.73 3.74 6.51 11.78 2.70 3.68 6.36 11.34 2.67 3.63 6.23 10.97 2.64 3.59 6.11 10.66 2.62 3.55 6.01 10.39 2.61 3.52 5.93 10.16 3 2.73 3.71 6.55 12.55 2.66 3.59 6.22 11.56 2.61 3.49 5.95 10.80 2.56 3.41 5.74 10.21 2.52 3.34 5.56 9.73 2.49 3.29 5.42 9.34 2.46 3.24 5.29 9.01 2.44 3.20 5.18 8.73 2.42 3.16 5.09 8.49 2.40 3.13 5.01 8.28 4 2.61 3.48 5.99 11.28 2.54 3.36 5.67 10.35 2.48 3.26 5.41 9.63 2.43 3.18 5.21 9.07 2.39 3.11 5.04 8.62 2.36 3.06 4.89 8.25 2.33 3.01 4.77 7.94 2.31 2.96 4.67 7.68 2.29 2.93 4.58 7.46 2.27 2.90 4.50 7.27 5 2.52 3.33 5.64 10.48 2.45 3.20 5.32 9.58 2.39 3.11 5.06 8.89 2.35 3.03 4.86 8.35 2.31 2.96 4.69 7.92 2.27 2.90 4.56 7.57 2.24 2.85 4.44 7.27 2.22 2.81 4.34 7.02 2.20 2.77 4.25 6.81 2.18 2.74 4.17 6.62 6 7 8 9 10 2.46 3.22 5.39 9.93 2.39 3.09 5.07 9.05 2.33 3.00 4.82 8.38 2.28 2.92 4.62 7.86 2.24 2.85 4.46 7.44 2.21 2.79 4.32 7.09 2.18 2.74 4.20 6.80 2.15 2.70 4.10 6.56 2.13 2.66 4.01 6.35 2.11 2.63 3.94 6.18 2.41 3.14 5.20 9.52 2.34 3.01 4.89 8.66 2.28 2.91 4.64 8.00 2.23 2.83 4.44 7.49 2.19 2.76 4.28 7.08 2.16 2.71 4.14 6.74 2.13 2.66 4.03 6.46 2.10 2.61 3.93 6.22 2.08 2.58 3.84 6.02 2.06 2.54 3.77 5.85 2.38 3.07 5.06 9.20 2.30 2.95 4.74 8.35 2.24 2.85 4.50 7.71 2.20 2.77 4.30 7.21 2.15 2.70 4.14 6.80 2.12 2.64 4.00 6.47 2.09 2.59 3.89 6.19 2.06 2.55 3.79 5.96 2.04 2.51 3.71 5.76 2.02 2.48 3.63 5.59 2.35 3.02 4.94 8.96 2.27 2.90 4.63 8.12 2.21 2.80 4.39 7.48 2.16 2.71 4.19 6.98 2.12 2.65 4.03 6.58 2.09 2.59 3.89 6.26 2.06 2.54 3.78 5.98 2.03 2.49 3.68 5.75 2.00 2.46 3.60 5.56 1.98 2.42 3.52 5.39 2.32 2.98 4.85 8.75 2.25 2.85 4.54 7.92 2.19 2.75 4.30 7.29 2.14 2.67 4.10 6.80 2.10 2.60 3.94 6.40 2.06 2.54 3.80 6.08 2.03 2.49 3.69 5.81 2.00 2.45 3.59 5.58 1.98 2.41 3.51 5.39 1.96 2.38 3.43 5.22 10/6/10 9:25 AM Appendix A TA B L E 6 871 Statistical Tables Values That Capture Specied Upper-Tail F Curve Areas (Continued) df1 df2 Area 20 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 21 22 23 24 25 26 27 28 29 1 2.97 4.35 8.10 14.82 2.96 4.32 8.02 14.59 2.95 4.30 7.95 14.38 2.94 4.28 7.88 14.20 2.93 4.26 7.82 14.03 2.92 4.24 7.77 13.88 2.91 4.23 7.72 13.74 2.90 4.21 7.68 13.61 2.89 4.20 7.64 13.50 2.89 4.18 7.60 13.39 2 3 4 5 6 7 8 9 10 2.59 3.49 5.85 9.95 2.57 3.47 5.78 9.77 2.56 3.44 5.72 9.61 2.55 3.42 5.66 9.47 2.54 3.40 5.61 9.34 2.53 3.39 5.57 9.22 2.52 3.37 5.53 9.12 2.51 3.35 5.49 9.02 2.50 3.34 5.45 8.93 2.50 3.33 5.42 8.85 2.38 3.10 4.94 8.10 2.36 3.07 4.87 7.94 2.35 3.05 4.82 7.80 2.34 3.03 4.76 7.67 2.33 3.01 4.72 7.55 2.32 2.99 4.68 7.45 2.31 2.98 4.64 7.36 2.30 2.96 4.60 7.27 2.29 2.95 4.57 7.19 2.28 2.93 4.54 7.12 2.25 2.87 4.43 7.10 2.23 2.84 4.37 6.95 2.22 2.82 4.31 6.81 2.21 2.80 4.26 6.70 2.19 2.78 4.22 6.59 2.18 2.76 4.18 6.49 2.17 2.74 4.14 6.41 2.17 2.73 4.11 6.33 2.16 2.71 4.07 6.25 2.15 2.70 4.04 6.19 2.16 2.71 4.10 6.46 2.14 2.68 4.04 6.32 2.13 2.66 3.99 6.19 2.11 2.64 3.94 6.08 2.10 2.62 3.90 5.98 2.09 2.60 3.85 5.89 2.08 2.59 3.82 5.80 2.07 2.57 3.78 5.73 2.06 2.56 3.75 5.66 2.06 2.55 3.73 5.59 2.09 2.60 3.87 6.02 2.08 2.57 3.81 5.88 2.06 2.55 3.76 5.76 2.05 2.53 3.71 5.65 2.04 2.51 3.67 5.55 2.02 2.49 3.63 5.46 2.01 2.47 3.59 5.38 2.00 2.46 3.56 5.31 2.00 2.45 3.53 5.24 1.99 2.43 3.50 5.18 2.04 2.51 3.70 5.69 2.02 2.49 3.64 5.56 2.01 2.46 3.59 5.44 1.99 2.44 3.54 5.33 1.98 2.42 3.50 5.23 1.97 2.40 3.46 5.15 1.96 2.39 3.42 5.07 1.95 2.37 3.39 5.00 1.94 2.36 3.36 4.93 1.93 2.35 3.33 4.87 2.00 2.45 3.56 5.44 1.98 2.42 3.51 5.31 1.97 2.40 3.45 5.19 1.95 2.37 3.41 5.09 1.94 2.36 3.36 4.99 1.93 2.34 3.32 4.91 1.92 2.32 3.29 4.83 1.91 2.31 3.26 4.76 1.90 2.29 3.23 4.69 1.89 2.28 3.20 4.64 1.96 2.39 3.46 5.24 1.95 2.37 3.40 5.11 1.93 2.34 3.35 4.99 1.92 2.32 3.30 4.89 1.91 2.30 3.26 4.80 1.89 2.28 3.22 4.71 1.88 2.27 3.18 4.64 1.87 2.25 3.15 4.57 1.87 2.24 3.12 4.50 1.86 2.22 3.09 4.45 1.94 2.35 3.37 5.08 1.92 2.32 3.31 4.95 1.90 2.30 3.26 4.83 1.89 2.27 3.21 4.73 1.88 2.25 3.17 4.64 1.87 2.24 3.13 4.56 1.86 2.22 3.09 4.48 1.85 2.20 3.06 4.41 1.84 2.19 3.03 4.35 1.83 2.18 3.00 4.29 (continued) 54906-00-APPA-p859-878.indd 871 10/6/10 9:25 AM 872 Appendix A Statistical Tables TA BLE 6 Values That Capture Specied Upper-Tail F Curve Areas (Continued) df1 df2 Area 30 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 .10 .05 .01 .001 40 60 90 120 240 54906-00-APPA-p859-878.indd 872 1 2.88 4.17 7.56 13.29 2.84 4.08 7.31 12.61 2.79 4.00 7.08 11.97 2.76 3.95 6.93 11.57 2.75 3.92 6.85 11.38 2.73 3.88 6.74 11.10 2.71 3.84 6.63 10.83 2 3 4 5 6 7 8 9 10 2.49 3.32 5.39 8.77 2.44 3.23 5.18 8.25 2.39 3.15 4.98 7.77 2.36 3.10 4.85 7.47 2.35 3.07 4.79 7.32 2.32 3.03 4.69 7.11 2.30 3.00 4.61 6.91 2.28 2.92 4.51 7.05 2.23 2.84 4.31 6.59 2.18 2.76 4.13 6.17 2.15 2.71 4.01 5.91 2.13 2.68 3.95 5.78 2.10 2.64 3.86 5.60 2.08 2.60 3.78 5.42 2.14 2.69 4.02 6.12 2.09 2.61 3.83 5.70 2.04 2.53 3.65 5.31 2.01 2.47 3.53 5.06 1.99 2.45 3.48 4.95 1.97 2.41 3.40 4.78 1.94 2.37 3.32 4.62 2.05 2.53 3.70 5.53 2.00 2.45 3.51 5.13 1.95 2.37 3.34 4.76 1.91 2.32 3.23 4.53 1.90 2.29 3.17 4.42 1.87 2.25 3.09 4.25 1.85 2.21 3.02 4.10 1.98 2.42 3.47 5.12 1.93 2.34 3.29 4.73 1.87 2.25 3.12 4.37 1.84 2.20 3.01 4.15 1.82 2.18 2.96 4.04 1.80 2.14 2.88 3.89 1.77 2.10 2.80 3.74 1.93 2.33 3.30 4.82 1.87 2.25 3.12 4.44 1.82 2.17 2.95 4.09 1.78 2.11 2.84 3.87 1.77 2.09 2.79 3.77 1.74 2.04 2.71 3.62 1.72 2.01 2.64 3.47 1.88 2.27 3.17 4.58 1.83 2.18 2.99 4.21 1.77 2.10 2.82 3.86 1.74 2.04 2.72 3.65 1.72 2.02 2.66 3.55 1.70 1.98 2.59 3.41 1.67 1.94 2.51 3.27 1.85 2.21 3.07 4.39 1.79 2.12 2.89 4.02 1.74 2.04 2.72 3.69 1.70 1.99 2.61 3.48 1.68 1.96 2.56 3.38 1.65 1.92 2.48 3.24 1.63 1.88 2.41 3.10 1.82 2.16 2.98 4.24 1.76 2.08 2.80 3.87 1.71 1.99 2.63 3.54 1.67 1.94 2.52 3.34 1.65 1.91 2.47 3.24 1.63 1.87 2.40 3.09 1.60 1.83 2.32 2.96 10/6/10 9:25 AM Appendix A TA B L E 7 Error df 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 24 30 40 60 120 ` 54906-00-APPA-p859-878.indd 873 873 Statistical Tables Critical Values of q for the Studentized Range Distribution Condence level 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% 99% Number of populations, treatments, or levels being compared 3 4 5 6 7 8 9 10 4.60 6.98 4.34 6.33 4.16 5.92 4.04 5.64 3.95 5.43 3.88 5.27 3.82 5.15 3.77 5.05 3.73 4.96 3.70 4.89 3.67 4.84 3.65 4.79 3.63 4.74 3.61 4.70 3.59 4.67 3.58 4.64 3.53 4.55 3.49 4.45 3.44 4.37 3.40 4.28 3.36 4.20 3.31 4.12 5.22 7.80 4.90 7.03 4.68 6.54 4.53 6.20 4.41 5.96 4.33 5.77 4.26 5.62 4.20 5.50 4.15 5.40 4.11 5.32 4.08 5.25 4.05 5.19 4.02 5.14 4.00 5.09 3.98 5.05 3.96 5.02 3.90 4.91 3.85 4.80 3.79 4.70 3.74 4.59 3.68 4.50 3.63 4.40 5.67 8.42 5.30 7.56 5.06 7.01 4.89 6.62 4.76 6.35 4.65 6.14 4.57 5.97 4.51 5.84 4.45 5.73 4.41 5.63 4.37 5.56 4.33 5.49 4.30 5.43 4.28 5.38 4.25 5.33 4.23 5.29 4.17 5.17 4.10 5.05 4.04 4.93 3.98 4.82 3.92 4.71 3.86 4.60 6.03 8.91 5.63 7.97 5.36 7.37 5.17 6.96 5.02 6.66 4.91 6.43 4.82 6.25 4.75 6.10 4.69 5.98 4.64 5.88 4.59 5.80 4.56 5.72 4.52 5.66 4.49 5.60 4.47 5.55 4.45 5.51 4.37 5.37 4.30 5.24 4.23 5.11 4.16 4.99 4.10 4.87 4.03 4.76 6.33 9.32 5.90 8.32 5.61 7.68 5.40 7.24 5.24 6.91 5.12 6.67 5.03 6.48 4.95 6.32 4.88 6.19 4.83 6.08 4.78 5.99 4.74 5.92 4.70 5.85 4.67 5.79 4.65 5.73 4.62 5.69 4.54 5.54 4.46 5.40 4.39 5.26 4.31 5.13 4.24 5.01 4.17 4.88 6.58 9.67 6.12 8.61 5.82 7.94 5.60 7.47 5.43 7.13 5.30 6.87 5.20 6.67 5.12 6.51 5.05 6.37 4.99 6.26 4.94 6.16 4.90 6.08 4.86 6.01 4.82 5.94 4.79 5.89 4.77 5.84 4.68 5.69 4.60 5.54 4.52 5.39 4.44 5.25 4.36 5.12 4.29 4.99 6.80 9.97 6.32 8.87 6.00 8.17 5.77 7.68 5.59 7.33 5.46 7.05 5.35 6.84 5.27 6.67 5.19 6.53 5.13 6.41 5.08 6.31 5.03 6.22 4.99 6.15 4.96 6.08 4.92 6.02 4.90 5.97 4.81 5.81 4.72 5.65 4.63 5.50 4.55 5.36 4.47 5.21 4.39 5.08 6.99 10.24 6.49 9.10 6.16 8.37 5.92 7.86 5.74 7.49 5.60 7.21 5.49 6.99 5.39 6.81 5.32 6.67 5.25 6.54 5.20 6.44 5.15 6.35 5.11 6.27 5.07 6.20 5.04 6.14 5.01 6.09 4.92 5.92 4.82 5.76 4.73 5.60 4.65 5.45 4.56 5.30 4.47 5.16 10/6/10 9:25 AM 874 Appendix A Statistical Tables TABLE 8 54906-00-APPA-p859-878.indd 874 Upper-Tail Areas for Chi-Square Distributions Right-tail area df 5 1 df 5 2 df 5 3 df 5 4 df 5 5 0.100 0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.001 0.001 , 2.70 2.70 2.78 2.87 2.96 3.06 3.17 3.28 3.40 3.53 3.68 3.84 4.01 4.21 4.44 4.70 5.02 5.41 5.91 6.63 7.87 10.82 10.82 , 4.60 4.60 4.70 4.81 4.93 5.05 5.18 5.31 5.46 5.62 5.80 5.99 6.20 6.43 6.70 7.01 7.37 7.82 8.39 9.21 10.59 13.81 13.81 , 6.25 6.25 6.36 6.49 6.62 6.75 6.90 7.06 7.22 7.40 7.60 7.81 8.04 8.31 8.60 8.94 9.34 9.83 10.46 11.34 12.83 16.26 16.26 , 7.77 7.77 7.90 8.04 8.18 8.33 8.49 8.66 8.84 9.04 9.25 9.48 9.74 10.02 10.34 10.71 11.14 11.66 12.33 13.27 14.86 18.46 18.46 , 9.23 9.23 9.37 9.52 9.67 9.83 10.00 10.19 10.38 10.59 10.82 11.07 11.34 11.64 11.98 12.37 12.83 13.38 14.09 15.08 16.74 20.51 20.51 Right-tail area df 5 6 df 5 7 df 58 df 5 9 df 5 10 0.100 0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.001 0.001 10.64 10.64 10.79 10.94 11.11 11.28 11.46 11.65 11.86 12.08 12.33 12.59 12.87 13.19 13.55 13.96 14.44 15.03 15.77 16.81 18.54 22.45 22.45 12.01 12.01 12.17 12.33 12.50 12.69 12.88 13.08 13.30 13.53 13.79 14.06 14.36 14.70 15.07 15.50 16.01 16.62 17.39 18.47 20.27 24.32 24.32 13.36 13.36 13.52 13.69 13.87 14.06 14.26 14.48 14.71 14.95 15.22 15.50 15.82 16.17 16.56 17.01 17.53 18.16 18.97 20.09 21.95 26.12 26.12 14.68 14.68 14.85 15.03 15.22 15.42 15.63 15.85 16.09 16.34 16.62 16.91 17.24 17.60 18.01 18.47 19.02 19.67 20.51 21.66 23.58 27.87 27.87 15.98 15.98 16.16 16.35 16.54 16.75 16.97 17.20 17.44 17.71 17.99 18.30 18.64 19.02 19.44 19.92 20.48 21.16 22.02 23.20 25.18 29.58 29.58 10/6/10 9:25 AM Appendix A TABLE 8 54906-00-APPA-p859-878.indd 875 Statistical Tables 875 Upper-Tail Areas for Chi-Square Distributions (Continued) Right-tail area df 5 11 df 5 12 df 5 13 df 5 14 df 5 15 0.100 0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.001 0.001 17.27 17.27 17.45 17.65 17.85 18.06 18.29 18.53 18.78 19.06 19.35 19.67 20.02 20.41 20.84 21.34 21.92 22.61 23.50 24.72 26.75 31.26 31.26 18.54 18.54 18.74 18.93 19.14 19.36 19.60 19.84 20.11 20.39 20.69 21.02 21.38 21.78 22.23 22.74 23.33 24.05 24.96 26.21 28.29 32.90 32.90 19.81 19.81 20.00 20.21 20.42 20.65 20.89 21.15 21.42 21.71 22.02 22.36 22.73 23.14 23.60 24.12 24.73 25.47 26.40 27.68 29.81 34.52 34.52 21.06 21.06 21.26 21.47 21.69 21.93 22.17 22.44 22.71 23.01 23.33 23.68 24.06 24.48 24.95 25.49 26.11 26.87 27.82 29.14 31.31 36.12 36.12 22.30 22.30 22.51 22.73 22.95 23.19 23.45 23.72 24.00 24.31 24.63 24.99 25.38 25.81 26.29 26.84 27.48 28.25 29.23 30.57 32.80 37.69 37.69 Right-tail area df 5 16 df 5 17 df 5 18 df 5 19 df 5 20 0.100 0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.001 0.001 23.54 23.54 23.75 23.97 24.21 24.45 24.71 24.99 25.28 25.59 25.93 26.29 26.69 27.13 27.62 28.19 28.84 29.63 30.62 32.00 34.26 39.25 39.25 24.77 24.76 24.98 25.21 25.45 25.70 25.97 26.25 26.55 26.87 27.21 27.58 27.99 28.44 28.94 29.52 30.19 30.99 32.01 33.40 35.71 40.78 40.78 25.98 25.98 26.21 26.44 26.68 26.94 27.21 27.50 27.81 28.13 28.48 28.86 29.28 29.74 30.25 30.84 31.52 32.34 33.38 34.80 37.15 42.31 42.31 27.20 27.20 27.43 27.66 27.91 28.18 28.45 28.75 29.06 29.39 29.75 30.14 30.56 31.03 31.56 32.15 32.85 33.68 34.74 36.19 38.58 43.81 43.81 28.41 28.41 28.64 28.88 29.14 29.40 29.69 29.99 30.30 30.64 31.01 31.41 31.84 32.32 32.85 33.46 34.16 35.01 36.09 37.56 39.99 45.31 45.31 10/6/10 9:25 AM 876 Appendix A Statistical Tables TA BLE 9 Binomial Probabilities n5 x 0.05 0.1 0.2 0.25 0.3 0.4 p 0.5 0 1 2 3 4 5 .774 .204 .021 .001 .000 .000 .590 .328 .073 .008 .000 .000 .328 .410 .205 .051 .006 .000 .237 .396 .264 .088 .015 .001 .168 .360 .309 .132 .028 .002 .078 .259 .346 .230 .077 .010 .031 .156 .313 .313 .156 .031 .010 .077 .230 .346 .259 .078 .002 .028 .132 .309 .360 .168 .001 .015 .088 .264 .396 .237 .000 .006 .051 .205 .410 .328 .000 .000 .008 .073 .328 .590 .000 .000 .001 .021 .204 .774 0.6 0.7 0.75 0.8 0.9 0.95 .000 .002 .011 .042 .111 .201 .251 .215 .121 .040 .006 .000 .000 .001 .009 .037 .103 .200 .267 .233 .121 .028 .000 .000 .000 .003 .016 .058 .146 .250 .282 .188 .056 .000 .000 .000 .001 .006 .026 .088 .201 .302 .268 .107 .000 .000 .000 .000 .000 .001 .011 .057 .194 .387 .349 .000 .000 .000 .000 .000 .000 .001 .010 .075 .315 .599 0.6 0.7 0.75 0.8 0.9 0.95 n 10 x 0.05 0.1 0.2 0.25 0.3 0.4 p 0.5 0 1 2 3 4 5 6 7 8 9 10 .599 .315 .075 .010 .001 .000 .000 .000 .000 .000 .000 .349 .387 .194 .057 .011 .001 .000 .000 .000 .000 .000 .107 .268 .302 .201 .088 .026 .006 .001 .000 .000 .000 .056 .188 .282 .250 .146 .058 .016 .003 .000 .000 .000 .028 .121 .233 .267 .200 .103 .037 .009 .001 .000 .000 .006 .040 .121 .215 .251 .201 .111 .042 .011 .002 .000 .001 .010 .044 .117 .205 .246 .205 .117 .044 .010 .001 54906-00-APPA-p859-878.indd 876 10/6/10 9:25 AM Appendix A TA B L E 9 Statistical Tables 877 Binomial Probabilities (Continued) n 15 x 0.05 0.1 0.2 0.25 0.3 0.4 p 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 .463 .366 .135 .031 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .206 .343 .267 .129 .043 .010 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .035 .132 .231 .250 .188 .103 .043 .014 .003 .001 .000 .000 .000 .000 .000 .000 .013 .067 .156 .225 .225 .165 .092 .039 .013 .003 .001 .000 .000 .000 .000 .000 .005 .031 .092 .170 .219 .206 .147 .081 .035 .012 .003 .001 .000 .000 .000 .000 .000 .005 .022 .063 .127 .186 .207 .177 .118 .061 .024 .007 .002 .000 .000 .000 .000 .000 .003 .014 .042 .092 .153 .196 .196 .153 .092 .042 .014 .003 .000 .000 .000 .000 .000 .002 .007 .024 .061 .118 .177 .207 .186 .127 .063 .022 .005 .000 .000 .000 .000 .000 .001 .003 .012 .035 .081 .147 .206 .219 .170 .092 .031 .005 .000 .000 .000 .000 .000 .001 .003 .013 .039 .092 .165 .225 .225 .156 .067 .013 .000 .000 .000 .000 .000 .000 .001 .003 .014 .043 .103 .188 .250 .231 .132 .035 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .010 .043 .129 .267 .343 .206 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .031 .135 .366 .463 0.6 0.7 0.75 0.8 0.9 0.95 .000 .000 .000 .000 .000 .001 .005 .015 .035 .071 .117 .160 .180 .166 .124 .075 .035 .012 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .004 .012 .031 .065 .114 .164 .192 .179 .130 .072 .028 .007 .001 .000 .000 .000 .000 .000 .000 .000 .000 .001 .003 .010 .027 .061 .112 .169 .202 .190 .134 .067 .021 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .007 .022 .055 .109 .175 .218 .205 .137 .058 .012 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .009 .032 .090 .190 .285 .270 .122 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .013 .060 .189 .377 .358 0.6 0.7 0.75 0.8 0.9 0.95 n 20 x 0.05 0.1 0.2 0.25 0.3 0.4 p 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .358 .377 .189 .060 .013 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .122 .270 .285 .190 .090 .032 .009 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .012 .058 .137 .205 .218 .175 .109 .055 .022 .007 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 .021 .067 .134 .190 .202 .169 .112 .061 .027 .010 .003 .001 .000 .000 .000 .000 .000 .000 .000 .000 .001 .007 .028 .072 .130 .179 .192 .164 .114 .065 .031 .012 .004 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 .012 .035 .075 .124 .166 .180 .160 .117 .071 .035 .015 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .015 .037 .074 .120 .160 .176 .160 .120 .074 .037 .015 .005 .001 .000 .000 .000 (continued) 54906-00-APPA-p859-878.indd 877 10/6/10 9:25 AM 878 Appendix A Statistical Tables TA BLE 9 Binomial Probabilities (Continued) n 25 x 0.05 0.1 0.2 0.25 0.3 0.4 p 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 .277 .365 .231 .093 .027 .006 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .072 .199 .266 .226 .138 .065 .024 .007 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .004 .024 .071 .136 .187 .196 .163 .111 .062 .029 .012 .004 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .006 .025 .064 .118 .165 .183 .165 .124 .078 .042 .019 .007 .002 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .007 .024 .057 .103 .147 .171 .165 .134 .092 .054 .027 .011 .004 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .007 .020 .044 .080 .120 .151 .161 .147 .114 .076 .043 .021 .009 .003 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .005 .014 .032 .061 .097 .133 .155 .155 .133 .097 .061 .032 .014 .005 .002 .000 .000 .000 .000 .000 54906-00-APPA-p859-878.indd 878 0.6 0.7 0.75 0.8 0.9 0.95 .000 .000 .000 .000 .000 .000 .000 .001 .003 .009 .021 .043 .076 .114 .147 .161 .151 .120 .080 .044 .020 .007 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .004 .011 .027 .054 .092 .134 .165 .171 .147 .103 .057 .024 .007 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .002 .007 .019 .042 .078 .124 .165 .183 .165 .118 .064 .025 .006 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .004 .012 .029 .062 .111 .163 .196 .187 .136 .071 .024 .004 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .007 .024 .065 .138 .226 .266 .199 .072 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .006 .027 .093 .231 .365 .277 10/6/10 9:25 AM

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