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附表⚓︎

1. 1. 标准正态分布表⚓︎

本表列出了标准正态分布函数 \(\Phi(x)=(\sqrt{2 \pi})^{-1} \int_{-\infty}^{x} \mathrm{e}^{-t^{2} / 2} \mathrm{~d} t\)\(0 \leqslant x \leqslant 2.98\) 之值. 此范围内不能直接查出之值, 可用线性揷值 法. 对 \(x<0\) 可用 \(\Phi(x)=1-\Phi(-x)\) 化为 \(x>0\) 的情况.

\(x\) 0.00 0.02 0.04 0.06 0.08
0.0 0.5000 0.5030 0.5160 0.5239 0.5319
0.1 0.5398 0.5478 0.5557 \(0+5636\) 0.5714
0.2 0.5793 0.5871 0.5948 0.6026 0.6103
0.3 0.6179 0.6255 0.6331 0.6406 0.6480
0.4 0.6554 0.6628 0.6700 0.6772 0.6844
0.5 0.6915 0.6985 0.7054 0.7123 0.7190
0.6 0.7257 0.7324 0.7389 0.7454 0.7517
0.7 0.7580 0.7642 0.7703 0.7764 0.7823
0.8 0.7881 0.7939 0.7995 0.8051 0.8106
0.9 0.8159 0.8212 0.8264 0.8315 0.8365
1.0 0.8413 0.8461 0.8508 0.8554 0.8599
1,1 0.8643 0.8686 0.8729 0.8770 0.8810
1.2 0.8849 0.8888 0.8925 0.8962 0.8997
1.3 0.90320 0.90658 0.90988 0.91809 0.91621
1.4 0.91924 0.92220 0.92507 0.92785 0.93056
1.5 0.93319 0.93574 0.93822 0.94062 0.94295
1.6 0.94520 0.94738 0.94950 0.95154 0.95352
1.7 0.95543 0.95728 0.95907 0.96080 0.96246
1.8 0.96407 0.96562 0.96712 0.96856 0.96995

续表

\(x\) 0.00 0.02 0.04 0.06 0.08
1.9 0.97128 0.97257 0.97381 0.97500 0.97615
2.0 0.97725 0.97831 0.97932 0.98030 0.98124
2.1 0.98214 0.98300 0.98382 0.98461 0.98537
2.2 0.98610 0.98679 0.98745 0.98809 0.98870
2.3 0.98928 0.98988 0.99036 0.99086 0.99134
2.4 0.99180 0.99224 0.99266 0.99305 0.99343
2.5 0.99379 0.99413 0.99446 0.99477 0.99506
2.6 0.99534 0.99560 0.99586 0.99609 0.99632
2.7 0.99653 0.99674 0.99693 0.99711 0.99728
2.8 0.99745 0.99760 0.99774 0.99788 0.99801
2.9 0.99813 0.99825 0.99836 0.96846 0.99856

2. 2. 标准正态分布双侧上分位点 \(u_{\alpha / 2}\)⚓︎

本表列出满足条件 \(P\left(|X| \geqslant u_{\alpha / 2}\right)=a\)\(u_{\alpha / 2}\), 其中 \(X\) 服从 标准正态分布。

\(a\) 0.0 0.1 0.2 0.3 0.4
0.00 - 1.6449 1.2816 1.0364 0.8416
0.01 2.5758 1.5982 1.2536 1.0152 0.8239
0.02 2.3268 1.5548 1.2265 0.9945 0.8064
0.03 2.1701 1.5141 1.2004 0.9741 0.7892
0.04 2.0537 1.4758 1.1750 0.9542 0.7722
0.05 1.9600 1.4395 1.1503 0.9346 0.7554
0.06 1.8808 1.4051 1.1264 0.9154 0.7388
0.07 1.8119 1.3722 1.1031 0.8965 0.7225
0.08 1.7507 1.3408 1.0808 0.8779 0.7063
0.09 1.6954 1.3106 1.0581 0.8596 0.6903

3. 3. \(t\) 分布上侧分位点 \(t_{n}(\alpha)\)⚓︎

设随机变量 \(X\) 服从自由度为 \(n\)\(t\) 分布, 本表列出满足条件 \(P\left(X>t_{n}(\alpha)\right)=\alpha\) 的值 \(t_{n}(\alpha)\).

0.05 0.025 0.01 0.005 0.05 0.025 0.01 0.005
1 6.314 12.706 31.821 63.657 16 1.746 2.120 2.583 2.921
2 2.970 4.303 6.965 9.925 17 1.740 2.110 2.567 2.898
3 2.353 3.182 4.541 5.841 18 1.734 2.101 2.552 2.878
4 2.132 2.776 3.747 4.604 19 1.729 2.093 2.539 2.861
5 2.015 2.571 3.365 4.032 20 1.725 2.086 2.528 2.845
6 1.943 2.447 3.143 3.701 21 1.721 2.080 2.518 2.831
7 1.895 2.365 2.998 3.499 22 1.717 2.074 2.508 2.819
8 1.860 2.306 2.896 3.355 23 1.714 2.069 2.500 2.807
9 1.833 2.262 2.821 3.250 24 \(\cdot 1.711\) 2.064 2.492 2.797
10 1.812 2.208 2.764 3.169 25 1.708 2.060 2.485 2.787
11 1.796 2.201 2.718 3.106 26 1.706 2.056 2.479 2.779
12 1.782 2.179 2.861 3.055 27 1.703 2.052 2.473 2.771
13 1.771 2.160 2.650 3.012 28 1.701 2.048 2.467 2.763
14 1.761 2.145 2.624 2.977 29 1.699 2.045 2.462 2.756
15 1.753 2.131 2.602 2.947 30 1.697 2.042 2.457 2.750
  1. 普阿松分布表 \(P(X=r)=\frac{\lambda^{r}}{r !} \mathrm{e}^{-\lambda}\)
\(r\) \(\lambda\)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 .90483 .81873 .74081 .67032 .60653 .54881 .49658 .44932
1 .09048 .16374 .22224 .26812 .30326 .32928 .34761 .35946
2 .00452 .01637 .03333 .05362 .07581 .09878 .12166 .14378
3 .00015 .00109 .00333 .00715 .01263 .01975 .02838 .03834
4 .00000 .00005 .00025 .00071 .00158 .00296 .00496 .00766
5 .00000 .00001 .00005 .00015 .00035 .00069 .00122
6 .00000 .00000 .00001 .00003 .00008 .00016
7 .00000 .00000 .00000 .00001
8 \(2+s^{2}\) .00001 .00000
\(r\) \(\lambda\)
0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 .40657 .36787 .22313 .13533 .08208 .04978 .03019 .01831
1 .36591 .36787 .33469 .27067 .20521 .14936 .10569 .07326
2 .16466 .18394 .25102 .27067 .25651 .22404 .18495 .14652
3 .04939 .06131 .12551 .18044 .21376 .22404 .21578 .19536
4 .01111 .01532 .04706 .09022 .13360 .16803 .18881 .19536
5 .00200 .00306 .01412 .03608 .06680 .10081 .13216 .15629
6 .00030 .00051 .00353 .01203 .02783 .05040 .07709 .10419
7 .00003 .00007 .00075 .00343 .00994 .02160 .03854 .05954
8 .00000 .00000 .00014 .00085 .00310 .00810 .01686 .02977
9 .00000 .00002 .00019 .00086 .00270 .00655 .01323
10 .00000 .00003 .00021 .00081 .00229 .00529
11 .00000 .00004 .00022 .00073 .00192
12 .00000 .00001 .00005 .00021 .00064
13 .00000 .00001 .00005 .00019
14 .00000 .00001 .00005
15 .00000 .00000 .00001
16 er .00000 .00000
17 .00000

4. 5. 卡方分布上侧分位点 \(\chi_{n}^{2}(\alpha)\)⚓︎

设随机变量 \(X\) 服从自由度为 \(n\) 的卡方分布, 本表列出满足条 件 \(P\left(X>\chi_{n}^{2}(\alpha)\right)=\alpha\) 的值 \(\chi_{n}^{2}(\alpha)\).

0.995 0.99 0.975 0.95 0.90 0.75 0.50
1 - 0.0002 0.001 0.004 0.016 0.102 0.455
2 0.010 0.020 0.051 0.103 0.211 0.575 1.386
3 0.072 0.115 0.216 0.352 0.584 1.213 2.366
4 0.207 0.297 0.484 0.711 1.064 1.923 3.357
5 0.412 0.554 0.831 1.145 1.610 2.675 4.351
6 0.676 0.872 1.237 1.635 2.204 3.455 5.348
7 0.989 1.239 1.690 2.167 2.833 4.255 6.340
8 1.344 1.646 2.180 2.733 3.490 5.071 7.34
9 1.735 2.088 2.700 3.325 4.168 5.899 8.34
10 2.156 2.558 3.247 3.940 4.865 6.737 9.342
11 2.603 3.053 3.816 4.575 5.578 7.584 10.34
12 3.074 3.571 4.404 5.226 6.304 8.438 11.340
13 3.565 4.107 5.009 5.892 7.042 9.299 12.340
14 4.075 4.660 5.629 6.571 7.790 10.165 13.33
15 4.601 5.229 6.262 7.261 8.547 11.037 14.33
16 5.142 5.812 6.908 7.962 9.312 11.912 15.338
17 5.697 6.408 7.564 8.672 10.085 12.792 16.338
18 6.265 7.015 8.231 9.390 10.865 13.675 17.338
19 6.844 7.633 8.907 10.117 11.651 14.562 18.338
20 7.434 8.260 9.591 10.851 12.443 15.452 19.33
21 8.034 8.897 10.283 11.591 13.240 16.344 20.33
22 8.643 9.542 10.982 12.338 14.042 17.240 21.33
23 9.260 10.196 11.689 13.091 14.848 18.137 \(22.33^{\circ}\)
24 9.886 10.856 12.401 13.848 15.659 19.037 \(23.33^{\circ}\)
25 10.520 11.524 13.120 14.611 16.473 19.939 \(24.33^{\circ}\)
26 11.160 12.198 13.844 15.379 17.292 20.843 25.33
27 11.808 12.879 14.573 16.151 18.114 21.749 26.33
28 12.461 13.565 15.308 16.928 18.939 22.657 27.33
29 13.121 14.257 16.047 17.708 19.768 23.567 28.33
30 13.787 14.954 16.791 18.493 20.599 24.478 29.33
. 0.30 0.25 0.10 0.05 0.025 0.01 0.005
1 1.074 1.323 2.706 3.841 5.024 6.635 7.879
2 2.408 2.773 4.605 5.991 7.378 9.210 10.597
3 3.665 4.108 6.251 7.815 9.348 11.345 12.838
4 4.878 5.385 7.779 9.488 11.143 13.277 14.860
5 6.064 6.626 9.236 11.071 12.833 15.086 16.750
6 7.231 7.841 10.645 12.592 14.449 16.812 18.548
7 8.383 9.037 12.017 14.067 16.013 18.475 20.278
8 9.524 10.219 13.362 15.507 17.535 20.090 21.955
9 10.656 11.389 14.684 16.919 19.023 21.666 23.589
10 11.781 12.549 15.987 18.307 20.483 23.209 25.188
11 12.899 13.701 17.275 19.675 21.920 24.725 26.757
12 14.011 14.845 18.549 21.026 23.337 26.217 28.299
13 15.119 15.984 19.812 22.362 24.736 27.688 29.819
14 16.222 17.117 21.064 23.685 26.119 29.141 31.319
15 17.322 18.245 22.307 24.996 27.488 30.578 32.801
16 18.418 19.369 23.542 26.296 28.845 32.000 34.267
17 19.511 20.489 24.769 27.587 30.191 33.409 35.718
18 20.601 21.605 25.989 28.869 31.526 34.805 37.156
19 21.689 22.718 27.204 30.144 32.852 36.191 38.582
20 22.775 23.828 28.412 31.410 34.170 37.566 39.997
21 23.858 24.935 29.615 32.671 35.479 38.932 41.401
22 24.939 26.039 30.813 33.924 36.781 40.289 42.796
23 26.018 27.141 32.007 35.172 38.076 41.638 44.181
24 27.096 28.241 33.196 36.415 39.364 42.980 45.559
25 28.172 29.339 34.382 37.652 40.646 44.314 46.928
26 29.246 30.435 35.563 38.885 41.923 45.642 48.290
27 30.319 31.528 36.741 40.113 43.194 46.963 49.645
28 31.391 32.620 37.916 41.337 44.461 48.278 50.993
29 32.461 33.711 39.087 42.557 45.722 49.588 52.336
30 33.530 34.800 40.256 43.773 46.979 50.892 53.672

5. 6. \(\boldsymbol{F}\) 分布上侧分位数 \(F_{m, n}(\alpha)\)⚓︎

设随机变量 \(X\) 服从自由度为 \(m\)\(n\)\(F\) 分布, 本表列出满 足条件 \(P\left(X>F_{m, n}(\alpha)=\alpha\right.\) 的值 \(F_{m, n}(\alpha)\).

A. \(\alpha=0.05\)

\(n\) 1 2 3 4 \(5^{\circ}\) 6 7 8
1 161 200 216 225 230 234 237 239
2 18.5 19.0 19.2 19.2 19.3 19.3 19.4 19.4
3 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27

401006

\(n\) 1 2 7 8
1 405 500 540 563 576 586 593 598
2 98.5 99.0 99.2 99.2 99.3 3 99.4 99.4
3 34.1 30.8 29.5 28.7 . 9 27.7 27.5
4 21.2 18.0 16.7 16.0 15.5 15.2 15.0 14.8
5 16.3 13.3 12.1 11.4 11.0 10.7 10.5 10.3
6 13.7 10.9 9.78 9.15 8.75 8.47 8.26 8.10
7 12.2 9.55 8.45 7.85 7.46 7.19 6.99 6.84
8 11.3 8.65 7.59 7.01 6.63 6.37 6.18 6.03
9 10.6 8.02 6.99 6.42 6.06 5.80 5.61 5.47
10 10.0 7.56 6.55 5.99 5.64 5.39 5.20 5.06
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74
12 9.33 6.98 5.95 5.41 5.06 4.82 4.64 4.50
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30
14 8.86 6.51 5.56 5.04 4.70 4.46 4.23 4.14
15 8.68 6.36 5.42 4.89 4.56 4.32 \(4.14^{\circ}\) 4.00
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63
20 8.10 5.83 4.94 4.43 4.10 3.87 3.70 3.56
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36
25 7.77 5.57 4.68 4.18 3.86 3.63 3.46 3.32
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29
27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23
29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17

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