# 11.1: A - Statistical Tables

## Standard Normal Probability Distribution: z Table

Numerical entries represent the one-tailed probability that a standard normal random variable exceeds |z| (image modified from z-table.com).

z Second decimal place of z
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641
0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247
0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859
0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483
0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121
0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776
0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451
0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148
0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867
0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611
1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379
1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170
1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985
1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823
1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681
1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110
2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084
2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
3.0 .00135
3.5 .000233
4.0 .0000317
4.5 .00000340
5.0 .000000287

## Student's t Distribution

The table shows the value of |t| that corresponds to the given one-tailed probabilities at varying degrees of freedom (df) (image modified from z-table.com).

df Confidence Level (Two-Tailed)
80% 90% 95% 98% 99% 99.8%
One-Tailed Probability
0.10 0.05 0.025 0.01 0.005 0.001
1 3.078 6.314 12.706 31.821 63.657 318.309
2 1.886 2.920 4.303 6.965 9.925 22.327
3 1.638 2.353 3.182 4.541 5.841 10.215
4 1.533 2.132 2.776 3.747 4.604 7.173
5 1.476 2.015 2.571 3.365 4.032 5.893
6 1.440 1.943 2.447 3.143 3.707 5.208
7 1.415 1.895 2.365 2.998 3.499 4.785
8 1.397 1.860 2.306 2.896 3.355 4.501
9 1.383 1.833 2.262 2.821 3.250 4.297
10 1.372 1.812 2.228 2.764 3.169 4.144
11 1.363 1.796 2.201 2.718 3.106 4.025
12 1.356 1.782 2.179 2.681 3.055 3.930
13 1.350 1.771 2.160 2.650 3.012 3.852
14 1.345 1.761 2.145 2.624 2.977 3.787
15 1.341 1.753 2.131 2.602 2.947 3.733
16 1.337 1.746 2.120 2.583 2.921 3.686
17 1.333 1.740 2.110 2.567 2.898 3.646
18 1.330 1.734 2.101 2.552 2.878 3.610
19 1.328 1.729 2.093 2.539 2.861 3.579
20 1.325 1.725 2.086 2.528 2.845 3.552
21 1.323 1.721 2.080 2.518 2.831 3.527
22 1.321 1.717 2.074 2.508 2.819 3.505
23 1.319 1.714 2.069 2.500 2.807 3.485
24 1.318 1.711 2.064 2.492 2.797 3.467
25 1.316 1.708 2.060 2.485 2.787 3.450
26 1.315 1.706 2.056 2.479 2.779 3.435
27 1.314 1.703 2.052 2.473 2.771 3.421
28 1.313 1.701 2.048 2.467 2.763 3.408
29 1.311 1.699 2.045 2.462 2.756 3.396
30 1.310 1.697 2.042 2.457 2.750 3.385
40 1.303 1.684 2.021 2.423 2.704 3.307
50 1.299 1.676 2.009 2.403 2.678 3.261
60 1.296 1.671 2.000 2.390 2.660 3.232
80 1.292 1.664 1.990 2.374 2.639 3.195
100 1.290 1.660 1.984 2.364 2.626 3.174
1.282 1.645 1.960 2.326 2.576 3.090

## F Distribution

The table shows the value of F that corresponds to the given right-tailed probabilities at varying degrees of freedom (df1df2) (image modified from z-table.com).

df2 α = .05
df1
1 2 3 4 5 6 8 12 24
1 161.45 199.50 215.71 224.58 230.16 233.99 238.88 243.91 249.05 254.31
2 18.51 19.00 19.16 19.25 19.30 19.33 19.37 19.41 19.45 19.50
3 10.13 9.55 9.28 9.12 9.01 8.94 8.85 8.74 8.64 8.53
4 7.71 6.94 6.59 6.39 6.26 6.16 6.04 5.91 5.77 5.63
5 6.61 5.79 5.41 5.19 5.05 4.95 4.82 4.68 4.53 4.37
6 5.99 5.14 4.76 4.53 4.39 4.28 4.15 4.00 3.84 3.67
7 5.59 4.74 4.35 4.12 3.97 3.87 3.73 3.57 3.41 3.23
8 5.32 4.46 4.07 3.84 3.69 3.58 3.44 3.28 3.12 2.93
9 5.12 4.26 3.86 3.63 3.48 3.37 3.23 3.07 2.90 2.71
10 4.96 4.10 3.71 3.48 3.33 3.22 3.07 2.91 2.74 2.54
11 4.84 3.98 3.59 3.36 3.20 3.09 2.95 2.79 2.61 2.40
12 4.75 3.89 3.49 3.26 3.11 3.00 2.85 2.69 2.51 2.30
13 4.67 3.81 3.41 3.18 3.03 2.92 2.77 2.60 2.42 2.21
14 4.60 3.74 3.34 3.11 2.96 2.85 2.70 2.53 2.35 2.13
15 4.54 3.68 3.29 3.06 2.90 2.79 2.64 2.48 2.29 2.07
16 4.49 3.63 3.24 3.01 2.85 2.74 2.59 2.42 2.24 2.01
17 4.45 3.59 3.20 2.96 2.81 2.70 2.55 2.38 2.19 1.96
18 4.41 3.55 3.16 2.93 2.77 2.66 2.51 2.34 2.15 1.92
19 4.38 3.52 3.13 2.90 2.74 2.63 2.48 2.31 2.11 1.88
20 4.35 3.49 3.10 2.87 2.71 2.60 2.45 2.28 2.08 1.84
21 4.32 3.47 3.07 2.84 2.68 2.57 2.42 2.25 2.05 1.81
22 4.30 3.44 3.05 2.82 2.66 2.55 2.40 2.23 2.03 1.78
23 4.28 3.42 3.03 2.80 2.64 2.53 2.37 2.20 2.01 1.76
24 4.26 3.40 3.01 2.78 2.62 2.51 2.36 2.18 1.98 1.73
25 4.24 3.39 2.99 2.76 2.60 2.49 2.34 2.16 1.96 1.71
26 4.23 3.37 2.98 2.74 2.59 2.47 2.32 2.15 1.95 1.69
27 4.21 3.35 2.96 2.73 2.57 2.46 2.31 2.13 1.93 1.67
28 4.20 3.34 2.95 2.71 2.56 2.45 2.29 2.12 1.91 1.65
29 4.18 3.33 2.93 2.70 2.55 2.43 2.28 2.10 1.90 1.64
30 4.17 3.32 2.92 2.69 2.53 2.42 2.27 2.09 1.89 1.62
40 4.08 3.23 2.84 2.61 2.45 2.34 2.18 2.00 1.79 1.51
60 4.00 3.15 2.76 2.53 2.37 2.25 2.10 1.92 1.70 1.39
120 3.92 3.07 2.68 2.45 2.29 2.18 2.02 1.83 1.61 1.25
3.84 3.00 2.60 2.37 2.21 2.10 1.94 1.75 1.52 1.00

df2 α = .01
df1
1 2 3 4 5 6 8 12 24
1 4052.2 4999.5 5403.4 5624.6 5763.7 5859.0 5981.1 6106.3 6234.6 6365.9
2 98.50 99.00 99.17 99.25 99.30 99.33 99.37 99.42 99.46 99.50
3 34.12 30.82 29.46 28.71 28.24 27.91 27.49 27.05 26.60 26.13
4 21.20 18.00 16.69 15.98 15.52 15.21 14.80 14.37 13.93 13.46
5 16.26 13.27 12.06 11.39 10.97 10.67 10.29 9.89 9.47 9.02
6 13.75 10.93 9.78 9.15 8.75 8.47 8.10 7.72 7.31 6.88
7 12.25 9.55 8.45 7.85 7.46 7.19 6.84 6.47 6.07 5.65
8 11.26 8.65 7.59 7.01 6.63 6.37 6.03 5.67 5.28 4.86
9 10.56 8.02 6.99 6.42 6.06 5.80 5.47 5.11 4.73 4.31
10 10.04 7.56 6.55 5.99 5.64 5.39 5.06 4.71 4.33 3.91
11 9.65 7.21 6.22 5.67 5.32 5.07 4.74 4.40 4.02 3.60
12 9.33 6.93 5.95 5.41 5.06 4.82 4.50 4.16 3.78 3.36
13 9.07 6.70 5.74 5.21 4.86 4.62 4.30 3.96 3.59 3.17
14 8.86 6.52 5.56 5.04 4.70 4.46 4.14 3.80 3.43 3.00
15 8.68 6.36 5.42 4.89 4.56 4.32 4.00 3.67 3.29 2.87
16 8.53 6.23 5.29 4.77 4.44 4.20 3.89 3.55 3.18 2.75
17 8.40 6.11 5.19 4.67 4.34 4.10 3.79 3.46 3.08 2.65
18 8.29 6.01 5.09 4.58 4.25 4.02 3.71 3.37 3.00 2.57
19 8.19 5.93 5.01 4.50 4.17 3.94 3.63 3.30 2.93 2.49
20 8.10 5.85 4.94 4.43 4.10 3.87 3.56 3.23 2.86 2.42
21 8.02 5.78 4.87 4.37 4.04 3.81 3.51 3.17 2.80 2.36
22 7.95 5.72 4.82 4.31 3.99 3.76 3.45 3.12 2.75 2.31
23 7.88 5.66 4.77 4.26 3.94 3.71 3.41 3.07 2.70 2.26
24 7.82 5.61 4.72 4.22 3.90 3.67 3.36 3.03 2.66 2.21
25 7.77 5.57 4.68 4.18 3.86 3.63 3.32 2.99 2.62 2.17
26 7.72 5.53 4.64 4.14 3.82 3.59 3.29 2.96 2.59 2.13
27 7.68 5.49 4.60 4.11 3.79 3.56 3.26 2.93 2.55 2.10
28 7.64 5.45 4.57 4.07 3.75 3.53 3.23 2.90 2.52 2.06
29 7.60 5.42 4.54 4.05 3.73 3.50 3.20 2.87 2.50 2.03
30 7.56 5.39 4.51 4.02 3.70 3.47 3.17 2.84 2.47 2.01
40 7.31 5.18 4.31 3.83 3.51 3.29 2.99 2.67 2.29 1.81
60 7.08 4.98 4.13 3.65 3.34 3.12 2.82 2.50 2.12 1.60
120 6.85 4.79 3.95 3.48 3.17 2.96 2.66 2.34 1.95 1.38
6.64 4.61 3.78 3.32 3.02 2.80 2.51 2.19 1.79 1.00

df2 α = .001
df1
1 2 3 4 5 6 8 12 24
1 405284 500000 540379 562500 576405 585937 598144 610668 623497 636619
2 998.50 999.00 999.17 999.25 999.30 999.33 999.37 999.42 999.46 999.50
3 167.03 148.50 141.11 137.10 134.58 132.85 130.62 128.32 125.93 123.50
4 74.14 61.25 56.18 53.44 51.71 50.53 49.00 47.41 45.77 44.05
5 47.18 37.12 33.20 31.09 29.75 28.83 27.65 26.42 25.13 23.78
6 35.51 27.00 23.70 21.92 20.80 20.03 19.03 17.99 16.90 15.75
7 29.25 21.69 18.77 17.20 16.21 15.52 14.63 13.71 12.73 11.69
8 25.41 18.49 15.83 14.39 13.48 12.86 12.05 11.19 10.30 9.34
9 22.86 16.39 13.90 12.56 11.71 11.13 10.37 9.57 8.72 7.81
10 21.04 14.91 12.55 11.28 10.48 9.93 9.20 8.45 7.64 6.76
11 19.69 13.81 11.56 10.35 9.58 9.05 8.35 7.63 6.85 6.00
12 18.64 12.97 10.80 9.63 8.89 8.38 7.71 7.00 6.25 5.42
13 17.82 12.31 10.21 9.07 8.35 7.86 7.21 6.52 5.78 4.97
14 17.14 11.78 9.73 8.62 7.92 7.44 6.80 6.13 5.41 4.60
15 16.59 11.34 9.34 8.25 7.57 7.09 6.47 5.81 5.10 4.31
16 16.12 10.97 9.01 7.94 7.27 6.80 6.19 5.55 4.85 4.06
17 15.72 10.66 8.73 7.68 7.02 6.56 5.96 5.32 4.63 3.85
18 15.38 10.39 8.49 7.46 6.81 6.35 5.76 5.13 4.45 3.67
19 15.08 10.16 8.28 7.27 6.62 6.18 5.59 4.97 4.29 3.52
20 14.82 9.95 8.10 7.10 6.46 6.02 5.44 4.82 4.15 3.38
21 14.59 9.77 7.94 6.95 6.32 5.88 5.31 4.70 4.03 3.26
22 14.38 9.61 7.80 6.81 6.19 5.76 5.19 4.58 3.92 3.15
23 14.20 9.47 7.67 6.70 6.08 5.65 5.09 4.48 3.82 3.05
24 14.03 9.34 7.55 6.59 5.98 5.55 4.99 4.39 3.74 2.97
25 13.88 9.22 7.45 6.49 5.89 5.46 4.91 4.31 3.66 2.89
26 13.74 9.12 7.36 6.41 5.80 5.38 4.83 4.24 3.59 2.82
27 13.61 9.02 7.27 6.33 5.73 5.31 4.76 4.17 3.52 2.75
28 13.50 8.93 7.19 6.25 5.66 5.24 4.69 4.11 3.46 2.70
29 13.39 8.85 7.12 6.19 5.59 5.18 4.64 4.05 3.41 2.64
30 13.29 8.77 7.05 6.12 5.53 5.12 4.58 4.00 3.36 2.59
40 12.61 8.25 6.59 5.70 5.13 4.73 4.21 3.64 3.01 2.23
60 11.97 7.77 6.17 5.31 4.76 4.37 3.86 3.32 2.69 1.90
120 11.38 7.32 5.78 4.95 4.42 4.04 3.55 3.02 2.40 1.56
10.83 6.91 5.42 4.62 4.10 3.74 3.27 2.74 2.13 1.00