Tabelas_Estatistica_Distribuição Normal_Tstudent

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TABELA DE PROBABILIDADES ACUMULADAS DA DISTRIBUIÇÃO NORMAL PADRÃO
A tabela ao lado fornece a probabilidade abaixo de um determinado valor padronizado (z). Lembre-se que o valor de z é encontrado na tabela da seguinte forma: busca-se na linha a parte inteira e a primeira casa decimal de z e, na coluna, obtém-se a segunda casa decimal.
Exemplo: A probabilidade abaixo do valor padronizado 1,96, como ilustrado na figura ao lado, é de 0,9750.
z
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0,0
0,5000
0,5040
0,5080
0,5120
0,5160
0,5199
0,5239
0,5279
0,5319
0,5359
0,1
0,5398
0,5438
0,5478
0,5517
0,5557
0,5596
0,5636
0,5675
0,5714
0,5753
0,2
0,5793
0,5832
0,5871
0,5910
0,5948
0,5987
0,6026
0,6064
0,6103
0,6141
0,3
0,6179
0,6217
0,6255
0,6293
0,6331
0,6368
0,6406
0,6443
0,6480
0,6517
0,4
0,6554
0,6591
0,6628
0,6664
0,6700
0,6736
0,6772
0,6808
0,6844
0,6879
0,5
0,6915
0,6950
0,6985
0,7019
0,7054
0,7088
0,7123
0,7157
0,7190
0,7224
0,6
0,7257
0,7291
0,7324
0,7357
0,7389
0,7422
0,7454
0,7486
0,7517
0,7549
0,7
0,7580
0,7611
0,7642
0,7673
0,7704
0,7734
0,7764
0,7794
0,7823
0,7852
0,8
0,7881
0,7910
0,7939
0,7967
0,7995
0,8023
0,8051
0,8078
0,8106
0,8133
0,9
0,8159
0,8186
0,8212
0,8238
0,8264
0,8289
0,8315
0,8340
0,8365
0,8389
1,0
0,8413
0,8438
0,8461
0,8485
0,8508
0,8531
0,8554
0,8577
0,8599
0,8621
1,1
0,8643
0,8665
0,8686
0,8708
0,8729
0,8749
0,8770
0,8790
0,8810
0,8830
1,2
0,8849
0,8869
0,8888
0,8907
0,8925
0,8944
0,8962
0,8980
0,8997
0,9015
1,3
0,9032
0,9049
0,9066
0,9082
0,9099
0,9115
0,9131
0,9147
0,9162
0,9177
1,4
0,9192
0,9207
0,9222
0,9236
0,9251
0,9265
0,9279
0,9292
0,9306
0,9319
1,5
0,9332
0,9345
0,9357
0,9370
0,9382
0,9394
0,9406
0,9418
0,9429
0,9441
1,6
0,9452
0,9463
0,9474
0,9484
0,9495
0,9505
0,9515
0,9525
0,9535
0,9545
1,7
0,9554
0,9564
0,9573
0,9582
0,9591
0,9599
0,9608
0,9616
0,9625
0,9633
1,8
0,9641
0,9649
0,9656
0,9664
0,9671
0,9678
0,9686
0,9693
0,9699
0,9706
1,9
0,9713
0,9719
0,9726
0,9732
0,9738
0,9744
0,9750
0,9756
0,9761
0,9767
2,0
0,9772
0,9778
0,9783
0,9788
0,9793
0,9798
0,9803
0,9808
0,9812
0,9817
2,1
0,9821
0,9826
0,9830
0,9834
0,9838
0,9842
0,9846
0,9850
0,9854
0,9857
2,2
0,9861
0,9864
0,9868
0,9871
0,9875
0,9878
0,9881
0,9884
0,9887
0,9890
2,3
0,9893
0,9896
0,9898
0,9901
0,9904
0,9906
0,9909
0,9911
0,9913
0,9916
2,4
0,9918
0,9920
0,9922
0,9925
0,9927
0,9929
0,9931
0,9932
0,9934
0,9936
2,5
0,9938
0,9940
0,9941
0,9943
0,9945
0,9946
0,9948
0,9949
0,9951
0,9952
2,6
0,9953
0,9955
0,9956
0,9957
0,9959
0,9960
0,9961
0,9962
0,9963
0,9964
2,7
0,9965
0,9966
0,9967
0,9968
0,9969
0,9970
0,9971
0,9972
0,9973
0,9974
2,8
0,9974
0,9975
0,9976
0,9977
0,9977
0,9978
0,9979
0,9979
0,9980
0,9981
2,9
0,9981
0,9982
0,9982
0,9983
0,9984
0,9984
0,9985
0,9985
0,9986
0,9986
3,0
0,9987
0,9987
0,9987
0,9988
0,9988
0,9989
0,9989
0,9989
0,9990
0,9990
�
TABELA DE PONTOS CRÍTICOS DA DISTRIBUIÇÃO “t” de Student
Graus de Liberdade (gl)
Valores do nível de significância ( ( ) para os testes UNILATERAIS ( * )
0,005
0,01
0,015
0,02
0,025
0,03
0,04
0,05
0,06
0,08
0,10
0,12
1
63,657
31,821
21,205
15,895
12,706
10,579
7,916
6,314
5,242
3,895
3,078
2,526
2
9,925
6,965
5,643
4,849
4,303
3,896
3,320
2,920
2,620
2,189
1,886
1,654
3
5,841
4,541
3,896
3,482
3,182
2,951
2,605
2,353
2,156
1,859
1,638
1,462
4
4,604
3,747
3,298
2,999
2,776
2,601
2,333
2,132
1,971
1,723
1,533
1,379
5
4,032
3,365
3,003
2,757
2,571
2,422
2,191
2,015
1,873
1,649
1,476
1,333
6
3,707
3,143
2,829
2,612
2,447
2,313
2,104
1,943
1,812
1,603
1,440
1,304
7
3,499
2,998
2,715
2,517
2,365
2,241
2,046
1,895
1,770
1,572
1,415
1,284
8
3,355
2,896
2,634
2,449
2,306
2,189
2,004
1,860
1,740
1,549
1,397
1,269
9
3,250
2,821
2,574
2,398
2,262
2,150
1,973
1,833
1,718
1,532
1,383
1,258
10
3,169
2,764
2,527
2,359
2,228
2,120
1,948
1,812
1,700
1,518
1,372
1,249
11
3,106
2,718
2,491
2,328
2,201
2,096
1,928
1,796
1,686
1,507
1,363
1,242
12
3,055
2,681
2,461
2,303
2,179
2,076
1,912
1,782
1,674
1,498
1,356
1,236
13
3,012
2,650
2,436
2,282
2,160
2,060
1,899
1,771
1,664
1,490
1,350
1,231
14
2,977
2,624
2,415
2,264
2,145
2,046
1,887
1,761
1,656
1,484
1,345
1,227
15
2,947
2,602
2,397
2,249
2,131
2,034
1,878
1,753
1,649
1,478
1,341
1,224
16
2,921
2,583
2,382
2,235
2,120
2,024
1,869
1,746
1,642
1,474
1,337
1,220
17
2,898
2,567
2,368
2,224
2,110
2,015
1,862
1,740
1,637
1,469
1,333
1,218
18
2,878
2,552
2,356
2,214
2,101
2,007
1,855
1,734
1,632
1,466
1,330
1,215
19
2,861
2,539
2,346
2,205
2,093
2,000
1,850
1,729
1,628
1,462
1,328
1,213
20
2,845
2,528
2,336
2,197
2,086
1,994
1,844
1,725
1,624
1,459
1,325
1,211
21
2,831
2,518
2,328
2,189
2,080
1,988
1,840
1,721
1,621
1,457
1,323
1,209
22
2,819
2,508
2,320
2,183
2,074
1,983
1,835
1,717
1,618
1,454
1,321
1,208
23
2,807
2,500
2,313
2,177
2,069
1,978
1,832
1,714
1,615
1,452
1,319
1,206
24
2,797
2,492
2,307
2,172
2,064
1,974
1,828
1,711
1,612
1,450
1,318
1,205
25
2,787
2,485
2,301
2,167
2,060
1,970
1,825
1,708
1,610
1,448
1,316
1,204
26
2,779
2,479
2,296
2,162
2,056
1,967
1,822
1,706
1,608
1,446
1,315
1,203
27
2,771
2,473
2,291
2,158
2,052
1,963
1,819
1,703
1,606
1,445
1,314
1,201
28
2,763
2,467
2,286
2,154
2,048
1,960
1,817
1,701
1,604
1,443
1,313
1,201
29
2,756
2,462
2,282
2,150
2,045
1,957
1,814
1,699
1,602
1,442
1,311
1,200
30
2,750
2,457
2,278
2,147
2,042
1,955
1,812
1,697
1,600
1,441
1,310
1,199
31
2,744
2,453
2,275
2,144
2,040
1,952
1,810
1,696
1,599
1,440
1,309
1,198
32
2,738
2,449
2,271
2,141
2,037
1,950
1,808
1,694
1,597
1,439
1,309
1,197
33
2,733
2,445
2,268
2,138
2,035
1,948
1,806
1,692
1,596
1,437
1,308
1,197
34
2,728
2,441
2,265
2,136
2,032
1,946
1,805
1,691
1,595
1,436
1,307
1,196
35
2,724
2,438
2,262
2,133
2,030
1,944
1,803
1,690
1,594
1,436
1,306
1,195
36
2,719
2,434
2,260
2,131
2,028
1,942
1,802
1,688
1,593
1,435
1,306
1,195
37
2,715
2,431
2,257
2,129
2,026
1,940
1,800
1,687
1,592
1,434
1,305
1,194
38
2,712
2,429
2,255
2,127
2,024
1,939
1,799
1,686
1,591
1,433
1,304
1,194
39
2,708
2,426
2,252
2,125
2,023
1,937
1,798
1,685
1,590
1,432
1,304
1,193
40
2,704
2,423
2,250
2,123
2,021
1,936
1,796
1,684
1,589
1,432
1,303
1,193
41
2,701
2,421
2,248
2,121
2,020
1,934
1,795
1,683
1,588
1,431
1,303
1,192
42
2,698
2,418
2,246
2,120
2,018
1,933
1,794
1,682
1,587
1,430
1,302
1,192
43
2,695
2,416
2,244
2,118
2,017
1,932
1,793
1,681
1,586
1,430
1,302
1,191
44
2,692
2,414
2,243
2,116
2,015
1,931
1,792
1,680
1,586
1,429
1,301
1,191
45
2,690
2,412
2,241
2,115
2,014
1,929
1,791
1,679
1,585
1,429
1,301
1,191
46
2,687
2,410
2,239
2,114
2,013
1,928
1,790
1,679
1,584
1,428
1,300
1,190
47
2,685
2,408
2,238
2,112
2,012
1,927
1,789
1,678
1,584
1,428
1,300
1,190
48
2,682
2,407
2,237
2,111
2,011
1,926
1,789
1,677
1,583
1,427
1,299
1,190
49
2,680
2,405
2,235
2,110
2,010
1,925
1,788
1,677
1,582
1,427
1,299
1,189
50
2,678
2,403
2,234
2,109
2,009
1,924
1,787
1,676
1,582
1,426
1,299
1,189
( * ) Para testes BILATERAIS, a coluna do nível de significância escolhida deve ser
aquela que é a metade do valor do ( dado no problema
�
TABELA DE PONTOS CRÍTICOS DA DISTRIBUIÇÃO DE QUI-QUADRADO ((2) 
Graus de Liberdade (gl)
Valores do nível de significância ( ( ) para os testes UNILATERAIS
0,005
0,01
0,015
0,02
0,025
0,03
0,04
0,05
0,06
0,08
0,10
0,12
1
7,879
6,635
5,916
5,412
5,024
4,709
4,218
3,841
3,537
3,065
2,706
2,417
2
10,597
9,210
8,399
7,824
7,378
7,013
6,438
5,991
5,627
5,051
4,605
4,241
3
12,838
11,345
10,465
9,837
9,348
8,947
8,311
7,815
7,407
6,759
6,251
5,833
4
14,860
13,277
12,339
11,668
11,143
10,712
10,026
9,488
9,044
8,337
7,779
7,318
5
16,750
15,086
14,098
13,388
12,833
12,375
11,644
11,070
10,596
9,837
9,236
8,738
6
18,548
16,812
15,777
15,033
14,449
13,968
13,198
12,592
12,090
11,283
10,645
10,112
7
20,278
18,475
17,398
16,622
16,013
15,509
14,703
14,067
13,540
12,691
12,017
11,454
8
21,955
20,090
18,974
18,168
17,535
17,010
16,171
15,507
14,956
14,068
13,362
12,770
9
23,589
21,666
20,513
19,679
19,023
18,480
17,608
16,919
16,346
15,421
14,684
14,066
10
25,188
23,209
22,021
21,161
20,483
19,922
19,021
18,307
17,713
16,753
15,987
15,344
11
26,757
24,725
23,503
22,618
21,920
21,342
20,412
19,675
19,061
18,069
17,275
16,609
12
28,300
26,217
24,963
24,054
23,337
22,742
21,785
21,026
20,393
19,369
18,549
17,860
13
29,819
27,688
26,403
25,472
24,736
24,125
23,142
22,362
21,711
20,657
19,812
19,101
14
31,319
29,141
27,827
26,873
26,119
25,493
24,485
23,685
23,017
21,933
21,064
20,333
15
32,801
30,578
29,235
28,259
27,488
26,848
25,816
24,996
24,311
23,199
22,307
21,555
16
34,267
32,000
30,629
29,633
28,845
28,191
27,136
26,296
25,595
24,456
23,542
22,771
17
35,718
33,409
32,011
30,995
30,191
29,523
28,445
27,587
26,870
25,705
24,769
23,979
18
37,156
34,805
33,382
32,346
31,526
30,845
29,745
28,869
28,137
26,947
25,989
25,181
19
38,582
36,191
34,742
33,687
32,852
32,158
31,037
30,144
29,396
28,181
27,204
26,378
20
39,997
37,566
36,093
35,020
34,170
33,462
32,321
31,410
30,649
29,410
28,412
27,569
21
41,401
38,932
37,434
36,343
35,479
34,759
33,597
32,671
31,895
30,632
29,615
28,755
22
42,796
40,289
38,768
37,659
36,781
36,049
34,867
33,924
33,135
31,849
30,813
29,937
23
44,181
41,638
40,094
38,968
38,076
37,332
36,131
35,172
34,370
33,062
32,007
31,115
24
45,559
42,980
41,413
40,270
39,364
38,609
37,389
36,415
35,599
34,269
33,196
32,288
25
46,928
44,314
42,725
41,566
40,646
39,880
38,642
37,652
36,824
35,472
34,382
33,458
26
48,290
45,642
44,031
42,856
41,923
41,146
39,889
38,885
38,044
36,671
35,563
34,625
27
49,645
46,963
45,331
44,140
43,195
42,407
41,132
40,113
39,259
37,866
36,741
35,788
28
50,993
48,278
46,626
45,419
44,461
43,662
42,370
41,337
40,471
39,058
37,916
36,949
29
52,336
49,588
47,915
46,693
45,722
44,913
43,604
42,557
41,679
40,246
39,087
38,106
30
53,672
50,892
49,199
47,962
46,979
46,160
44,834
43,773
42,883
41,430
40,256
39,260
31
55,003
52,191
50,478
49,226
48,232
47,402
46,059
44,985
44,084
42,612
41,422
40,412
32
56,328
53,486
51,753
50,487
49,480
48,641
47,282
46,194
45,282
43,791
42,585
41,562
33
57,648
54,776
53,024
51,743
50,725
49,876
48,500
47,400
46,476
44,966
43,745
42,709
34
58,964
56,061
54,290
52,995
51,966
51,107
49,716
48,602
47,667
46,140
44,903
43,854
35
60,275
57,342
55,553
54,244
53,203
52,335
50,928
49,802
48,856
47,310
46,059
44,997
36
61,581
58,619
56,811
55,489
54,437
53,560
52,137
50,998
50,042
48,478
47,212
46,137
37
62,883
59,893
58,067
56,730
55,668
54,781
53,344
52,192
51,225
49,644
48,363
47,276
38
64,181
61,162
59,318
57,969
56,896
56,000
54,547
53,384
52,406
50,807
49,513
48,413
39
65,476
62,428
60,567
59,204
58,120
57,215
55,748
54,572
53,584
51,969
50,660
49,548
40
66,766
63,691
61,812
60,436
59,342
58,428
56,946
55,758
54,761
53,128
51,805
50,681
41
68,053
64,950
63,054
61,665
60,561
59,638
58,142
56,942
55,934
54,285
52,949
51,813
42
69,336
66,206
64,293
62,892
61,777
60,845
59,335
58,124
57,106
55,441
54,090
52,943
43
70,616
67,459
65,529
64,116
62,990
62,050
60,526
59,304
58,276
56,594
55,230
54,071
44
71,893
68,710
66,763
65,337
64,201
63,253
61,714
60,481
59,444
57,746
56,369
55,198
45
73,166
69,957
67,994
66,555
65,410
64,453
62,901
61,656
60,609
58,895
57,505
56,323
46
74,437
71,201
69,222
67,771
66,617
65,652
64,085
62,830
61,773
60,044
58,641
57,447
47
75,704
72,443
70,448
68,985
67,821
66,847
65,268
64,001
62,936
61,190
59,774
58,570
48
76,969
73,683
71,671
70,197
69,023
68,041
66,448
65,171
64,096
62,335
60,907
59,691
49
78,231
74,919
72,892
71,406
70,222
69,233
67,627
66,339
65,255
63,479
62,038
60,811
50
79,490
76,154
74,111
72,613
71,420
70,423
68,804
67,505
66,412
64,621
63,167
61,930
ESTATÍSTICA E PROBABILIDADE – JOAB DE OLIVEIRA LIMA