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Critical Values for the Student’s t Distribution
Area
0
Degrees of
Freedom
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
50
60
80
100
200
z
tα
Area in Right Tail
0.025
0.01
0.005
0.40
0.25
0.10
0.05
0.0025
0.001
0.0005
0.325
0.289
0.277
0.271
0.267
0.265
0.263
0.262
0.261
0.260
0.260
0.259
0.259
0.258
0.258
0.258
0.257
0.257
0.257
0.257
0.257
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.255
0.255
0.255
0.255
0.255
0.255
0.255
0.255
0.255
0.255
0.254
0.254
0.254
0.254
0.253
20%
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.682
0.682
0.682
0.682
0.682
0.681
0.681
0.681
0.681
0.681
0.679
0.679
0.678
0.677
0.676
0.674
50%
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.309
1.308
1.307
1.306
1.306
1.305
1.304
1.304
1.303
1.299
1.296
1.292
1.290
1.286
1.282
80%
6.314 12.706 31.821 63.657 127.321 318.309 636.619
2.920 4.303 6.965 9.925 14.089 22.327 31.599
2.353 3.182 4.541 5.841
7.453 10.215 12.924
2.132 2.776 3.747 4.604
5.598
7.173
8.610
2.015 2.571 3.365 4.032
4.773
5.893
6.869
1.943 2.447 3.143 3.707
4.317
5.208
5.959
1.895 2.365 2.998 3.499
4.029
4.785
5.408
1.860 2.306 2.896 3.355
3.833
4.501
5.041
1.833 2.262 2.821 3.250
3.690
4.297
4.781
1.812 2.228 2.764 3.169
3.581
4.144
4.587
1.796 2.201 2.718 3.106
3.497
4.025
4.437
1.782 2.179 2.681 3.055
3.428
3.930
4.318
1.771 2.160 2.650 3.012
3.372
3.852
4.221
1.761 2.145 2.624 2.977
3.326
3.787
4.140
1.753 2.131 2.602 2.947
3.286
3.733
4.073
1.746 2.120 2.583 2.921
3.252
3.686
4.015
1.740 2.110 2.567 2.898
3.222
3.646
3.965
1.734 2.101 2.552 2.878
3.197
3.610
3.922
1.729 2.093 2.539 2.861
3.174
3.579
3.883
1.725 2.086 2.528 2.845
3.153
3.552
3.850
1.721 2.080 2.518 2.831
3.135
3.527
3.819
1.717 2.074 2.508 2.819
3.119
3.505
3.792
1.714 2.069 2.500 2.807
3.104
3.485
3.768
1.711 2.064 2.492 2.797
3.091
3.467
3.745
1.708 2.060 2.485 2.787
3.078
3.450
3.725
1.706 2.056 2.479 2.779
3.067
3.435
3.707
1.703 2.052 2.473 2.771
3.057
3.421
3.690
1.701 2.048 2.467 2.763
3.047
3.408
3.674
1.699 2.045 2.462 2.756
3.038
3.396
3.659
1.697 2.042 2.457 2.750
3.030
3.385
3.646
1.696 2.040 2.453 2.744
3.022
3.375
3.633
1.694 2.037 2.449 2.738
3.015
3.365
3.622
1.692 2.035 2.445 2.733
3.008
3.356
3.611
1.691 2.032 2.441 2.728
3.002
3.348
3.601
1.690 2.030 2.438 2.724
2.996
3.340
3.591
1.688 2.028 2.434 2.719
2.990
3.333
3.582
1.687 2.026 2.431 2.715
2.985
3.326
3.574
1.686 2.024 2.429 2.712
2.980
3.319
3.566
1.685 2.023 2.426 2.708
2.976
3.313
3.558
1.684 2.021 2.423 2.704
2.971
3.307
3.551
1.676 2.009 2.403 2.678
2.937
3.261
3.496
1.671 2.000 2.390 2.660
2.915
3.232
3.460
1.664 1.990 2.374 2.639
2.887
3.195
3.416
1.660 1.984 2.364 2.626
2.871
3.174
3.390
1.653 1.972 2.345 2.601
2.839
3.131
3.340
1.645 1.960 2.326 2.576
2.807
3.090
3.291
90%
95%
98%
99%
99.5%
99.8%
99.9%
Confidence Level
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