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Posted on Jun 12, 2024

1.The human carcinogen dioxin can be produced by the burning of common trash. Curiously it is hypothesized that trash from homes that recycle will produce

1.The human carcinogen dioxin can be produced by the burning of common trash. Curiously it is hypothesized that trash from homes that recycle will produce more dioxins per kilogram of trash burned than homes that don't recycle. It is thought that a higher proportion of chlorine and metals in the recycler's trash is the cause of higher levels of dioxin per kilogram. The sample mean is 232.8667 picograms/kg of trash and the sample standard deviation is 39.8853 picograms/kg of trash from 15 families that are avid recyclers.

(a) Construct a 95% confidence interval for the average dioxin level for the avid recyclers.

(b) If a well-run municipal incinerator produces 200 picograms/kg of trash burned, do you feel the recylcers' trash produces significantly more dioxin per kilogram of trash?

2. In a population where the proportion of people who have the ability to taste umami is unknown, a random sample of 100 people were tested and 74 could clearly distinguish umami from saltiness.

(a) What is the sample proportion?

(b) make a 99% confidence interval for the true proportion of people in this region who can taste umami.

(c) Does this interval support the fact that more that 70% of the region can taste umami? Why or why not and explain using the values that make up the confi- dence interval.

874 APPENDIX Tables TABLE 3 The normal distribution f (x) = 1 @(-1/2)x2 f (x) = @(-1/2)x2 A(x) = 4(x) = Pr(X x) V2n B(x) = 1 - @(x) = Pr(X > x) 0 0 (a ) (b) C(x) = Pr(0 sXSx) D(x) = Pr(-xSXSx) f ( x ) = 1 @(-1/2)x2 f(x) = 1 (-1/2)x2 V2n V2n 0 X -X 0 X (c) (d) Bb C B C D 0.0 5000 5000 0.32 6255 .3745 1255 .2510 0.01 5040 4960 .0040 .0080 0.33 6293 .370' 1293 .2586 0.02 .5080 4920 0080 0160 0.34 633 3669 1331 .2661 0.03 5120 4880 .0120 .0239 0.35 6368 .3632 1368 .2737 ).04 5160 .4840 .0160 .0319 0.36 .6406 .3594 .1406 2812 0.0 .5199 4801 0199 0399 0.37 .6443 .3557 .1443 2886 0.06 .5239 4761 0239 0478 0.38 .6480 3520 1480 2961 0.07 5279 4721 0279 0558 0.39 6517 3483 . 1517 .3035 0.08 5319 468 0319 0638 0.40 6554 3446 1554 3108 0.09 5359 4641 0359 0717 0.41 6591 3409 .1591 .3182 0.10 .5398 4602 0398 0797 0.42 6628 3372 1628 3255 0.11 5438 4562 0438 .0876 0.43 6664 3336 .1664 .3328 0.12 .5478 4522 .0478 .0955 0.44 6700 .3300 .1700 .3401 0.13 5517 4483 .0517 .1034 0.45 6736 .3264 .1736 .3473 0.14 .5557 4443 0557 1113 0.46 6772 .3228 .1772 .3545 0.15 .5596 4404 0596 .1192 0.47 .6808 .3192 .1808 3616 0.16 .5636 4364 0636 1271 0.48 6844 .3156 1844 3688 0.17 4325 0675 .1350 0.49 6879 3121 .1879 3759 0.18 .5714 4286 0714 1428 0.50 6915 .3085 .1915 3829 0.19 .5753 4247 0753 1507 0.51 .6950 .3050 1950 .3899 0.20 .5793 4207 0793 .1585 0.52 .6985 3015 1985 3969 0.21 .5832 4168 0832 .1663 0.53 7019 2981 2019 4039 0.22 5871 4129 .0871 .1741 0.54 .7054 2946 2054 4108 0.23 . 5910 4090 .0910 .1819 0.55 .7088 .2912 .2088 4177 0.24 5948 4052 0948 1897 0.56 .7123 2877 .2123 4245 0.25 5987 4013 0987 . 1974 0.57 7157 .2843 .2157 4313 0.26 .6026 .3974 1026 .2051 0.58 7190 .2810 2190 438 0.27 .6064 .3936 1064 2128 ).59 7224 2776 2224 .4448 .28 6103 3897 .1103 2205 0.60 .7257 .2743 2257 4515 0.29 6141 3859 .1141 2282 0.61 7291 .2709 229 4581 0.30 6179 3821 .1179 .2358 0.62 .7324 .2676 .2324 .4647 0.31 .6217 .3783 .1217 .2434 0.63 7357 2643 2357 4713 (continued on next page)TABLE 3 The normal distribution (continued) 876 APPENDIX Tables Bb Da B D 0.64 7389 2611 .2389 4778 1.23 8907 .1093 .3907 .7813 TABLE 3 The normal distribution (continued) 0.65 7422 2578 .2422 4843 1.24 8925 1075 .3925 .7850 0.66 .7454 2546 .2454 .4907 1.25 894 1056 .3944 7887 A Bb 0.67 .7486 2514 .2486 .4971 1.26 .8962 1038 .3962 .7923 0.68 7517 .2483 .2517 5035 1.27 8980 . 1020 3980 1.82 .9656 0344 .4656 .9312 2.39 .9916 0084 4916 9832 .7959 0.69 .7549 .2451 1.83 .9327 2.40 .9918 0082 .4918 .2549 .5098 1.28 .8997 1003 .7995 0336 4664 .9836 3997 .9664 1.84 .9671 .0329 4671 9342 241 0.70 .2420 .2580 5161 1.29 .0985 .8029 .9920 0080 4920 .9840 7580 9015 4015 4922 0.71 2.42 .7611 2389 9357 .0078 .2611 .5223 1.30 .9032 .0322 4678 .0968 4032 1.85 .9678 .9922 .9845 .8064 0.72 .4925 .7642 .9849 .2358 .2642 2.43 0075 .5285 1.31 .9049 1.86 0314 4686 .0951 9371 .9925 .4049 .9686 .8098 0,73 0307 .9385 2.44 .9927 .0073 7673 9853 .2327 .2673 5346 1.32 .9066 4927 .0934 .4066 8132 1.87 .9693 4693 030 2.45 .9929 4929 0.74 9857 .2297 .2703 .5407 .0071 7703 1.33 .9082 4082 1.88 9699 4699 9399 0918 8165 1.89 9412 0.75 .2734 .9099 .0294 4706 2.46 .2266 .5467 .0901 .9706 9931 .0069 4931 .9861 7734 1.34 4099 .8198 0.76 .7764 2236 .2764 5527 1.90 .9713 0287 4713 9426 2.47 .9932 .0068 4932 .9865 .9115 .0885 4115 .8230 .0066 4934 0.77 .7793 .2207 2793 .5587 1.36 .9131 1.91 0281 .4719 .9439 2.48 .9934 9869 .0869 .4131 .8262 .9719 0.78 7823 .2177 .2823 1.37 .9147 8293 1.92 .9726 .0274 4726 .9451 2.49 9936 .0064 4936 987 5646 0853 .4147 .2148 1.93 .9732 268 4732 946 2.50 .9938 4938 9876 0.79 .7852 .2852 .5705 9162 .0062 1.38 0838 416 .8324 9879 0.80 7881 .21 19 .2881 .5763 1.39 .0823 4177 1.94 .9738 .0262 4738 .9476 2.51 994 .0060 4940 .8355 0.81 .7910 2090 .2910 1.40 .9192 .0808 1.95 .9744 .0256 .4744 9488 2.52 994 .0059 4941 .9883 .5821 $192 .8385 0.82 .7939 .2061 1.96 .9750 .0250 750 9500 2.53 .9943 .0057 .4943 2939 5878 1.41 .9207 .0793 .4207 9886 .8415 9512 2.54 .9945 .0055 4945 9889 0.83 7967 2033 .2967 5935 1.42 .9222 .0778 4222 .8444 1.97 .9756 .0244 4756 0.84 7995 .2005 .2995 1.43 9236 .0764 .4236 1.98 .9761 .0239 4761 .9523 2.55 .9946 .0054 4946 9892 .5991 .8473 0.85 8023 1977 .3023 .6047 1.44 .9251 .0749 1.99 .9767 0233 .4767 9534 2.56 9948 .0052 4948 9895 .4251 8501 0.86 .1949 .3051 2.00 .9772 0228 .4772 9949 8051 2.57 .0051 4949 .6102 1.45 .9265 .0735 4265 8529 9545 9898 0.87 .8078 . 1922 .3078 .6157 1.46 .9279 .8557 2.01 9778 .0222 4778 9556 2.58 .9951 .0049 .4951 9901 .0721 4279 2.59 .0048 4952 9904 0.88 .8106 1894 .3106 6211 1.47 .9292 0708 .4292 8584 2.02 .9783 .0217 .4783 9566 .9952 0.89 8133 .1867 .3133 .6265 1.48 .9306 0694 4306 .8611 2.03 .9788 .0212 .4788 .9576 2.60 9953 .0047 .4953 9907 9955 .0045 0.90 8159 1841 .3159 .6319 2.04 .9793 .0207 4793 .9586 2.61 4955 .9909 1.49 .9319 .0681 4319 .8638 0.91 8186 . 1814 .3186 .6372 1.50 .9332 .4332 .8664 2.05 .9798 .0202 .4798 2.62 9956 .0044 4956 0668 .9596 9912 9915 0.92 .8212 .1788 9606 2.63 .9957 .0043 .3212 .6424 1.51 .9345 .0655 4345 .8690 2.06 9803 .0197 .4803 .4957 2.07 .9808 .0192 .4808 9615 2.64 .9959 .0041 4959 9917 0.93 .8238 .1762 .3238 6476 1.52 .9357 .0643 .4357 .8715 4960 9920 0.94 8264 .3264 2.08 .9812 0188 4812 .9625 2.65 9960 .0040 .1736 .6528 1.53 .9370 .0630 4370 8740 0.95 8289 .1711 .3289 .6579 .9382 2.09 .9817 .0183 .4817 9634 2.66 9961 .0039 .4961 .9922 .0618 4382 8764 0.96 3315 9962 1685 .6629 1.55 .9821 .0179 .4821 .9643 2.67 0038 .9394 2.10 .4962 9924 8315 0606 4394 .8789 0.97 .8340 1660 3340 .6680 1.56 .9406 0594 4406 8812 2.11 9826 .0174 .4826 9651 2.68 .9963 .0037 .4963 9926 0.98 8365 .6729 9660 .4964 9929 1635 .3365 1.57 .9418 .0582 .4418 2.12 8836 .9830 170 .4830 2.69 9964 .0036 3389 9834 .4834 .9668 2.70 0035 4965 .9931 0.99 8389 1611 .6778 1.58 .9429 2.13 .9965 0571 4429 8859 .0166 1.00 8413 .1587 3413 .6827 9838 1.59 .9441 .0559 4441 8882 2.14 0162 .4838 9676 2.71 9966 .0034 .4966 9933 1.01 8438 562 3438 6875 1.60 .9452 0548 .4452 .8904 2.15 .9842 0158 .4842 .9684 2.72 9967 .0033 .4967 9935 1.02 .8461 .1539 .3461 .9463 .4463 2.16 9846 .0154 .4846 2.73 .9968 1.61 9692 .0032 .4968 993 6923 0537 .8926 9939 1.03 .8485 1515 .3485 .6970 1.62 .9474 .0526 2.17 9850 .0150 .4850 9700 2.74 9969 .0031 .4969 .4474 .8948 1.04 8508 .1492 3508 .7017 1.63 .9484 2.18 9854 .0146 .4854 .9707 2.75 997 .0030 .4970 9940 0516 4484 8969 .8531 .1469 2.19 9715 2.76 .9971 002 9942 1.05 .3531 .7063 1.64 .9495 .0505 .4495 8990 9857 .0143 .4857 4971 220 1.06 .8554 .1446 3554 0495 9011 .9861 .0139 4861 9972 .0028 .4972 .9944 .7109 1.65 .9505 .9722 2.77 .4505 2.21 1.07 .8577 .1423 3577 .7154 1.66 .9515 0485 .4515 9031 .9864 .0136 .4864 .9729 2.78 .9973 .0027 .4973 .9946 1.08 .8599 .1401 .3599 .7199 1.67 .9525 .0475 2.22 .0132 9051 .9868 .4868 .4525 9736 279 9974 .0026 4974 9947 3621 2.23 .9743 2.80 0026 1974 .9949 1.09 862 .1379 .7243 1.68 .9535 0465 4535 9070 9871 .0129 .4871 .9974 9975 .0025 4975 .9950 1.10 .8643 .1357 2.24 .3643 .7287 1.69 9749 2.81 .9545 .0455 9090 9875 4545 .0125 .4875 2.25 .9878 .0122 .4878 9756 282 .8665 3665 9976 1335 .7330 .9554 .0446 .4554 .0024 .4976 .9952 1.11 1.70 .9109 2.83 1.12 .8686 .1314 3686 .7373 1.71 .9564 .0436 .9127 2.26 4564 .9881 .0119 .4881 9762 .9977 .0023 .4977 .9953 8708 1292 .3708 .7415 .9573 2.27 .9884 .0116 4884 .9768 2.84 9977 0023 1.13 .4977 .9955 1.72 .0427 4573 914 .7457 2.28 .9887 2.85 .8729 .9582 .4887 .9978 .0022 4978 .9956 1.14 1271 .3729 1.73 418 4582 9164 .0113 .9774 2.86 .9979 .0021 .9958 1.15 .8749 1251 .3749 .7499 1.74 2.29 9890 .0110 489 .9780 .4979 .9591 0409 4591 9181 287 4979 .9959 1.16 8770 1230 .3770 .7540 1.75 .9599 .0401 2.30 .9199 .0107 .4893 .9979 .0021 4599 .9893 .9786 2.88 1.17 .4896 4980 .9960 .8790 1210 .3790 1.76 9791 .0020 .7580 .9608 0392 9216 2.31 9896 .0104 .9980 4608 1.18 .8810 .1190 .3810 .7620 1.77 9616 4616 .9233 2.32 .9898 .0102 4898 .9797 2.89 .9981 0019 .4981 .9961 .0384 9901 2.90 .0019 .4981 9963 1.19 .8830 .1170 .3830 .7660 1.78 .9625 .0099 .4901 0375 4625 9249 2.33 .9802 1.20 234 .8849 1151 .3849 .7699 1.79 .9904 0367 .9265 .0096 4904 9807 2.91 .9982 .0018 .4982 .9964 .9633 4633 292 .9965 1.21 8869 .1131 3869 .0359 .4641 .9906 .9982 0018 .7737 9641 2.35 .4906 9812 .4982 1.80 928 .0094 1.22 .8888 .1112 .3888 2.36 .7775 1.81 .0351 .9297 9909 .0091 .9817 .9983 .0017 .4983 .9966 .9649 .4909 2.93 4649 2.37 .9911 .0089 .4911 .9822 2.94 9984 0016 .4984 9967 2.38 .9913 .0087 4913 9827 2.95 9984 0016 (continued on next page) .4984 .9968 (continued on next page)TABLE 3 The normal distribution (continued) A Bb C Da B C D 878 APPENDIX Tables 2.96 .9985 .0015 4985 .9969 3.49 .9998 .0002 4998 9995 2.97 9985 .0015 .4985 9970 3.50 .9998 .0002 4998 9995 TABLE 4 Table of 1000 random digits 2.98 9986 0014 4986 .9971 3.51 .9998 .0002 4998 999 .0002 32924 22324 18125 09077 26 96772 16443 39877 04653 2.99 9986 .0014 .4986 9972 3.52 .9998 4998 9996 01 3.00 .9987 0013 4987 9973 3.53 .9998 .0002 4998 9996 02 54632 90374 94143 49295 27 52167 21038 14338 01395 3.01 .9987 .0013 4987 9974 3.54 .9998 .0002 4998 9996 03 88720 43035 97081 83373 28 69644 37198 00028 98195 3.02 .9987 0013 4987 9975 3.5 .9998 .0002 4998 9996 21727 1 1904 41513 31653 29 71011 62004 81712 87536 3.03 9988 .0012 .4988 9976 3.56 .9998 .0002 4998 .9996 04 9996 05 80985 70799 57975 69282 30 31217 75877 85366 55500 3.04 9988 .0012 4988 9976 3.57 9998 .0002 4998 3.05 9989 .0011 .4989 .9977 3.58 .9998 .0002 4998 9997 06 40412 58826 94868 52632 31 64990 98735 02999 35521 3.06 9989 .0011 .4989 9978 3.59 9998 .0002 4998 9997 07 43918 56807 75218 46077 32 48417 23569 59307 46550 3.07 .9989 .0011 .4989 .9979 3.60 .9998 .0002 4998 .9997 08 26513 47480 77410 47741 33 07900 65059 48592 44087 3.08 9990 .0010 .4990 9979 3.61 9998 0002 4998 9997 44255 30124 34 74526 32601 24482 16981 3.09 .9990 .0010 .4990 .9980 .0001 09 18164 35784 3.62 .9999 4999 .9997 75264 51173 35 51056 04402 58353 37332 3.10 9990 .0010 .4990 .9981 3.63 .9999 .0001 4999 .9997 10 39446 01375 999 .0009 .4991 .9981 3.64 .9999 0001 4999 .9997 11 16638 04680 98617 90298 36 39005 93458 63143 21817 3.11 3.12 9991 .0009 4991 9982 3.65 .9999 0001 .4999 .9997 12 16872 94749 44012 48884 37 67883 76343 78155 67733 3.13 9991 .0009 4991 ,9983 3.66 .9999 .0001 4999 9997 13 65419 87092 78596 91512 38 06014 60999 87226 36071 3.14 .9992 .0008 4992 .9983 3.67 .9999 .0001 4999 .9998 14 05207 36702 56804 10498 39 93147 88766 04148 42471 3.15 .9992 .0008 4992 .9984 3.68 9999 0001 4999 9998 01099 95731 47622 13294 3.16 .9992 0008 4992 9984 3.69 .9999 .0001 4999 .9998 15 78807 79243 13729 81222 40 .9985 3.70 .9999 0001 4999 .9998 16 69341 79028 64253 80447 01201 58138 13809 3.17 9992 4992 41 89252 .0008 3.18 .0007 4993 9985 3.71 .9999 .0001 4999 .9998 17 41871 17566 61200 15994 42 41766 57239 50251 64675 .9993 3.19 .9993 .0007 4993 .9986 3.72 9999 0001 .4999 .9998 18 25758 04625 43226 32986 43 92736 77800 81996 45646 3.20 .9993 4993 9986 3.73 .9999 0001 .4999 .9998 19 06604 94486 40174 10742 44 451 18 36600 68977 68831 3.21 .9993 .0007 4993 9987 3.74 .9999 .0001 .4999 .9998 4994 .9987 3.75 .9999 0001 .4999 9998 20 82259 56512 48945 18183 45 73457 01579 00378 70197 3.22 .9994 0006 42914 17277 3.23 .9994 0006 4994 .9988 3.76 .9999 0001 .4999 9998 21 07895 37090 50627 71320 46 49465 85251 3.24 .9994 .0006 4994 .9988 3.77 .9999 0001 .4999 .9998 22 59836 71 148 42320 67816 47 15745 37285 23768 39302 3.25 .9994 .0006 4994 9988 3.78 .9999 0001 .4999 9998 23 57133 76610 89104 30481 48 28760 81331 78265 60690 3.26 .9994 .0006 4994 .9989 3.79 .9999 0001 .4999 9998 0001 .4999 .9999 24 76964 57126 87174 61025 49 82193 32787 70451 91141 3.27 .9995 0005 4995 9989 3.80 9999 .9999 25 27694 17145 32439 68245 50 50242 12382 .9995 000 9990 .4999 89664 39379 3.28 4995 3.81 .9999 .0001 3.29 .9995 0005 4995 .9990 3.82 9999 0001 .4999 .9999 3.30 .9995 .0005 4995 .9990 3.83 9999 .0001 .4999 9999 3.31 .9995 .0005 4995 .9991 3.84 .9999 .0001 .4999 .9999 3.32 .9995 .0005 .4995 9991 3.85 .9999 .0001 .4999 9999 3.3 9996 .0004 4996 9991 3.86 9999 .0001 .4999 .9999 3.34 .9996 .0004 4996 .9992 3.87 .9999 .0001 .4999 5666 3.3 .0004 4996 9992 3.88 9999 .0001 .4999 3.3 .9996 .0004 4996 .9992 3.89 9999 .0001 .4999 9999 3.37 999 .0004 4996 9992 3.90 1.0000 .0000 .5000 9999 3.38 .9996 .0004 4996 9993 3.91 1.0000 0000 .5000 99 3.39 999 .0003 4997 999 3.92 1.0000 .0000 .5000 9999 3.4 .9997 .0003 4997 .9993 3.93 1.0000 .0000 .5000 999 3.4 9997 .0003 4997 .9994 3.94 1.0000 0000 5000 9999 3.43 .9997 .0003 4997 .9994 3.95 1.0000 .0000 .5000 9999 3.45 .9997 .0003 .4997 .9994 3.96 1.0000 .0000 .5000 9999 3.46 .9997 .0003 4997 .9995 3.97 1.0000 0000 500 9999 3.47 .9997 0003 .4997 .9995 3.98 1.0000 .0000 .5000 9999 3.48 .9997 0003 .4997 .9995 3.99 1.0000 .0000 .5000 9999 "A(x) = (x) = PIX S x), where X is a standard normal distribution. "B(x) = 1 - (x) = Pr(X > x), where X is a standard normal distribution. "C(x) = Pr(0 S X S x), where X is a standard normal distribution. "D(x) = Pr(-x S X S x), where X is a standard normal distribution.TABLE 5 Percentage points of the t distribution (to ). U Degrees of freedom, d .75 80 85 90 .95 975 .99 .995 9995 1.000 1.376 1.963 3.078 6.314 12.706 31.821 63.657 636.619 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 31.598 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 12.924 OF A CON - 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 8.610 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 6.869 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.959 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 5.408 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 5.041 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.781 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 4.221 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 4.015 17 0.689 0.863 1.069 1.333 1.740 2.1 10 2.567 2.898 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.922 19 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.883 20 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.850 21 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.819 22 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.792 23 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.767 24 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.745 25 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.725 26 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.707 27 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.690 28 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.674 29 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.659 30 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.646 40 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.551 60 0.679 0.848 1.046 1.296 1.671 2.000 2.390 2.660 3.460 120 0.677 0.845 1.041 1.289 1.658 1.980 2.358 2.617 3.373 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.291 "The uth percentile of a t distribution with d degrees of freedom. Source: Table 5 is taken from Table Ill of Fisher and Yates: "Statistical Tables for Biological, Agricultural and Medical Research," published by Longman Group Lid., London (previously published by Oliver and Boyd Lid., Edinburgh)