tabella normale e TStudent (Statistica), Esercizi di Statistica

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Funzione di ripartizione Φ(z) = Pr(Z ≤ z) della variabile aleatoria Normale Standard z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.52790 0.53188 0.53586 0.1 0.53983 0.54380 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535 0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409 0.3 0.61791 0.62172 0.62552 0.62930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173 0.4 0.65542 0.65910 0.66276 0.66640 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793 0.5 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.71226 0.71566 0.71904 0.72240

0.6 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.75490 0.7 0.75804 0.76115 0.76424 0.76730 0.77035 0.77337 0.77637 0.77935 0.78230 0.78524 0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327 0.9 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891 1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214

1.1 0.86433 0.86650 0.86864 0.87076 0.87286 0.87493 0.87698 0.87900 0.88100 0.88298 1.2 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147 1.3 0.90320 0.90490 0.90658 0.90824 0.90988 0.91149 0.91309 0.91466 0.91621 0.91774 1.4 0.91924 0.92073 0.92220 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189 1.5 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408

1.6 0.94520 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.95254 0.95352 0.95449 1.7 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.96080 0.96164 0.96246 0.96327 1.8 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062 1.9 0.97128 0.97193 0.97257 0.97320 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670

2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.98030 0.98077 0.98124 0.98169 2.1 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98461 0.98500 0.98537 0.98574 2.2 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899 2.3 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158 2.4 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361 2.5 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.99492 0.99506 0.99520

2.6 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643 2.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.99720 0.99728 0.99736 2.8 0.99744 0.99752 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807 2.9 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861 3.0 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99896 0.99900

3.1 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.99929 3.2 0.99931 0.99934 0.99936 0.99938 0.99940 0.99942 0.99944 0.99946 0.99948 0.99950 3.3 0.99952 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.99965 3.4 0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99974 0.99975 0.99976 3.5 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.99982 0.99983 0.99983

3.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989 3.7 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992 0.99992 0.99992 3.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995 3.9 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997

α 0.5 0.25 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 zα 0.00000 0.67449 1.28155 1.64485 1.95996 2.32635 2.57583 3.09023 3.29053

Φ(zα) = 1− α 0.5 0.75 0.90 0.95 0.975 0.99 0.995 0.999 0.9995

Valori critici della distribuzione t di Student

Gradi di Area della coda destra della distribuzione t di Student Libertà 0.1 0.05 0.025 0.01 0.005 0.001 0.0005

1 3.0777 6.3138 12.7062 31.8205 63.6567 318.3088 636.6192 2 1.8856 2.9200 4.3027 6.9646 9.9248 22.3271 31.5991 3 1.6377 2.3534 3.1824 4.5407 5.8409 10.2145 12.9240 4 1.5332 2.1318 2.7764 3.7469 4.6041 7.1732 8.6103 5 1.4759 2.0150 2.5706 3.3649 4.0321 5.8934 6.8688 6 1.4398 1.9432 2.4469 3.1427 3.7074 5.2076 5.9588 7 1.4149 1.8946 2.3646 2.9980 3.4995 4.7853 5.4079 8 1.3968 1.8595 2.3060 2.8965 3.3554 4.5008 5.0413 9 1.3830 1.8331 2.2622 2.8214 3.2498 4.2968 4.7809 10 1.3722 1.8125 2.2281 2.7638 3.1693 4.1437 4.5869 11 1.3634 1.7959 2.2010 2.7181 3.1058 4.0247 4.4370 12 1.3562 1.7823 2.1788 2.6810 3.0545 3.9296 4.3178 13 1.3502 1.7709 2.1604 2.6503 3.0123 3.8520 4.2208 14 1.3450 1.7613 2.1448 2.6245 2.9768 3.7874 4.1405 15 1.3406 1.7531 2.1314 2.6025 2.9467 3.7328 4.0728 16 1.3368 1.7459 2.1199 2.5835 2.9208 3.6862 4.0150 17 1.3334 1.7396 2.1098 2.5669 2.8982 3.6458 3.9651 18 1.3304 1.7341 2.1009 2.5524 2.8784 3.6105 3.9216 19 1.3277 1.7291 2.0930 2.5395 2.8609 3.5794 3.8834 20 1.3253 1.7247 2.0860 2.5280 2.8453 3.5518 3.8495 21 1.3232 1.7207 2.0796 2.5176 2.8314 3.5272 3.8193 22 1.3212 1.7171 2.0739 2.5083 2.8188 3.5050 3.7921 23 1.3195 1.7139 2.0687 2.4999 2.8073 3.4850 3.7676 24 1.3178 1.7109 2.0639 2.4922 2.7969 3.4668 3.7454 25 1.3163 1.7081 2.0595 2.4851 2.7874 3.4502 3.7251 26 1.3150 1.7056 2.0555 2.4786 2.7787 3.4350 3.7066 27 1.3137 1.7033 2.0518 2.4727 2.7707 3.4210 3.6896 28 1.3125 1.7011 2.0484 2.4671 2.7633 3.4082 3.6739 29 1.3114 1.6991 2.0452 2.4620 2.7564 3.3962 3.6594 30 1.3104 1.6973 2.0423 2.4573 2.7500 3.3852 3.6460 31 1.3095 1.6955 2.0395 2.4528 2.7440 3.3749 3.6335 32 1.3086 1.6939 2.0369 2.4487 2.7385 3.3653 3.6218 33 1.3077 1.6924 2.0345 2.4448 2.7333 3.3563 3.6109 34 1.3070 1.6909 2.0322 2.4411 2.7284 3.3479 3.6007 35 1.3062 1.6896 2.0301 2.4377 2.7238 3.3400 3.5911 36 1.3055 1.6883 2.0281 2.4345 2.7195 3.3326 3.5821 37 1.3049 1.6871 2.0262 2.4314 2.7154 3.3256 3.5737 38 1.3042 1.6860 2.0244 2.4286 2.7116 3.3190 3.5657 39 1.3036 1.6849 2.0227 2.4258 2.7079 3.3128 3.5581 40 1.3031 1.6839 2.0211 2.4233 2.7045 3.3069 3.5510 41 1.3025 1.6829 2.0195 2.4208 2.7012 3.3013 3.5442 42 1.3020 1.6820 2.0181 2.4185 2.6981 3.2960 3.5377 43 1.3016 1.6811 2.0167 2.4163 2.6951 3.2909 3.5316 44 1.3011 1.6802 2.0154 2.4141 2.6923 3.2861 3.5258 45 1.3006 1.6794 2.0141 2.4121 2.6896 3.2815 3.5203 46 1.3002 1.6787 2.0129 2.4102 2.6870 3.2771 3.5150 47 1.2998 1.6779 2.0117 2.4083 2.6846 3.2729 3.5099 48 1.2994 1.6772 2.0106 2.4066 2.6822 3.2689 3.5051 49 1.2991 1.6766 2.0096 2.4049 2.6800 3.2651 3.5004 50 1.2987 1.6759 2.0086 2.4033 2.6778 3.2614 3.4960 60 1.2958 1.6706 2.0003 2.3901 2.6603 3.2317 3.4602 70 1.2938 1.6669 1.9944 2.3808 2.6479 3.2108 3.4350 80 1.2922 1.6641 1.9901 2.3739 2.6387 3.1953 3.4163 90 1.2910 1.6620 1.9867 2.3685 2.6316 3.1833 3.4019 100 1.2901 1.6602 1.9840 2.3642 2.6259 3.1737 3.3905 +∞ 1.2816 1.6449 1.9600 2.3263 2.5758 3.0902 3.2905

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