Determine the critical value of χ2 with 1 degree of freedom for α=0.005

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Determine the critical value of χ2 with 1 degree of freedom for α=0.005.

Round to three decimal places as​ needed.

Critical Values of x
For a particular number of degrees of freedom, entry represents the critical value of x
coresponding to the cumulative probability (1 - a) and a specified upper-tail area (a).
Cumulative Probabilities
0.005
0.01
0.025 0.05
0.10
0.25
0.75
0.90
0.95
0.975
0.99
0.995
Upper-Tail Areas (a)
Degrees of
Freedom
0.995
0.99
0.975
0.95
0.90
0.75
0.25
0.10
0.05
0.025
0.01
0.005
0.001
0.004
0.016
0.102
1.323
2.706
3.841
5.024
6.635
7.879
0.010
0.020
0.051
0.103
0.211
0.575
2.773
4.605
5.991
7.378
9.210
11.345
10.597
0.072
0.207
6251
7.779
3
0.115
0.216
0.352
0.584
1.213
4.108
7.815
9.348
12.838
0.297
0.484
0.711
1.064
1.923
5.385
9.488
11.143
13.277
14.860
0.412
0.554
0.831
1.145
1.610
2.675
6.626
9236
11.071
12.833
15.086
16.750
0.676
0.872
1.237
1.635
2.204
3.455
7.841
10.645
12.592
14.449
16.812
18.548
1.690
2.833
4.255
12.017
13.362
0.989
1.239
2.167
9.037
14.067
16.013
18.475
20.278
8.
1.344
1.646
2.180
2.733
3.490
5.071
10.219
15.507
17.535
20.090
21.955
1.735
2.088
2.700
3.325
4.168
5.899
11.389
14.684
16.919
19.023
21.666
23.589
10
2.156
2.558
3.247
3.940
4.865
6.737
12.549
15.987
18.307
20.483
23.209
25.188
2.603
3.053
4.575
7.584
13.701
14.845
3.816
5.578
17.275
19.675
21.920
24.725
26.757
12
3.074
3.571
4.404
5.226
6.304
8.438
18.549
21.026
23.337
26.217
28.299
13
3.565
4.107
5.009
5.892
7.042
9.299
15.984
19.812
22.362
24.736
27.688
29.819
14
4.075
4.660
5.629
6.571
7.790
10.165
17.117
21.064
23.685
26.119
29.141
31.319
15
4.601
5.229
6.262
7.261
8.547
11.037
18.245
22.307
24.996
27.488
30.578
32.801
7.962
19.369
23.542
24.769
16
5.142
5.812
6.908
9.312
11.912
26.296
28.845
32.000
34.267
12.792
13.675
14.562
17
5.697
6.408
7.564
8.672
10.085
20.489
27.587
30.191
33.409
35.718
18
6.265
7.015
8.231
9.390
10.865
21.605
25.989
28.869
31.526
34.805
37.156
19
6.844
7.633
8.907
10.117
11.651
22.718
27.204
30.144
32.852
36.191
38.582
Transcribed Image Text:Critical Values of x For a particular number of degrees of freedom, entry represents the critical value of x coresponding to the cumulative probability (1 - a) and a specified upper-tail area (a). Cumulative Probabilities 0.005 0.01 0.025 0.05 0.10 0.25 0.75 0.90 0.95 0.975 0.99 0.995 Upper-Tail Areas (a) Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.75 0.25 0.10 0.05 0.025 0.01 0.005 0.001 0.004 0.016 0.102 1.323 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 0.103 0.211 0.575 2.773 4.605 5.991 7.378 9.210 11.345 10.597 0.072 0.207 6251 7.779 3 0.115 0.216 0.352 0.584 1.213 4.108 7.815 9.348 12.838 0.297 0.484 0.711 1.064 1.923 5.385 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1.145 1.610 2.675 6.626 9236 11.071 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.204 3.455 7.841 10.645 12.592 14.449 16.812 18.548 1.690 2.833 4.255 12.017 13.362 0.989 1.239 2.167 9.037 14.067 16.013 18.475 20.278 8. 1.344 1.646 2.180 2.733 3.490 5.071 10.219 15.507 17.535 20.090 21.955 1.735 2.088 2.700 3.325 4.168 5.899 11.389 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 6.737 12.549 15.987 18.307 20.483 23.209 25.188 2.603 3.053 4.575 7.584 13.701 14.845 3.816 5.578 17.275 19.675 21.920 24.725 26.757 12 3.074 3.571 4.404 5.226 6.304 8.438 18.549 21.026 23.337 26.217 28.299 13 3.565 4.107 5.009 5.892 7.042 9.299 15.984 19.812 22.362 24.736 27.688 29.819 14 4.075 4.660 5.629 6.571 7.790 10.165 17.117 21.064 23.685 26.119 29.141 31.319 15 4.601 5.229 6.262 7.261 8.547 11.037 18.245 22.307 24.996 27.488 30.578 32.801 7.962 19.369 23.542 24.769 16 5.142 5.812 6.908 9.312 11.912 26.296 28.845 32.000 34.267 12.792 13.675 14.562 17 5.697 6.408 7.564 8.672 10.085 20.489 27.587 30.191 33.409 35.718 18 6.265 7.015 8.231 9.390 10.865 21.605 25.989 28.869 31.526 34.805 37.156 19 6.844 7.633 8.907 10.117 11.651 22.718 27.204 30.144 32.852 36.191 38.582
0.676
0.872
1.237
1.635
2.204
3.455
7.841
10.645
12.592
14.449
16.812
18.548
0.989
1.239
1.690
2.167
2.833
4.255
9.037
12.017
14.067
16.013
18.475
20.278
8.
1.344
1.646
2.180
2.733
3.490
5.071
10.219
13.362
15.507
17.535
20.090
21.955
9.
1.735
2.088
2.700
3.325
4.168
5.899
11.389
14.684
16.919
19.023
21.666
23.589
10
2.156
2.558
3.247
3.940
4.865
6.737
12.549
15.987
18.307
20.483
23.209
25.188
2.603
3.053
3.816
4.575
5.578
7.584
13.701
17.275
19.675
21.920
24.725
26.757
12
3.074
23.337
3.571
4.107
4.404
5.226
6.304
7.042
8.438
14.845
18.549
21.026
26.217
28.299
13
3.565
5.009
5.892
9.299
15.984
19.812
22.362
24.736
27.688
29.819
14
4.075
7.790
4.660
5.229
5.629
6.571
10.165
17.117
21.064
23.685
26.119
29.141
31.319
15
4.601
6.262
7.261
8.547
11.037
18.245
22.307
24.996
27.488
30.578
32.801
16
5.142
5.812
6.908
7.962
9.312
11.912
19.369
23.542
26.296
28.845
32.000
34.267
17
5.697
6.408
7.564
8.672
10.085
12.792
20.489
24.769
27.587
30.191
33.409
35.718
18
6.265
7.015
8.231
9.390
10.865
13.675
21.605
25.989
28.869
31.526
34.805
37.156
19
6.844
7.633
8.907
10.117
11.651
14.562
22.718
27.204
30.144
32.852
36.191
38.582
39.997
20
7.434
8.260
9.591
10.851
12.443
15.452
23.828
28.412
31.410
34.170
37.566
21
8.034
8.897
10.283
11.591
13.240
16.344
24.935
29.615
32.671
35.479
38.932
41.401
22
8.643
9.542
10.982
12.338
14.042
17.240
26.039
30.813
33.924
36.781
40.289
42.796
23
9.260
10.196
11.689
13.091
14.848
18.137
27.141
32.007
35.172
38.076
41.638
44.181
15.659
33.196
34.382
45.559
46.928
24
9.886
10.856
12.401
13.848
19.037
28.241
36.415
39.364
42.980
25
10.520
11.524
13.120
14.611
16.473
19.939
29.339
37.652
40.646
44.314
26
11.160
12.198
13.844
15.379
17.292
20.843
30.435
35.563
38.885
41.923
45.642
48.290
27
11.808
12.879
14.573
16.151
18.114
21.749
31.528
36.741
40.113
43.194
49.645
46.963
48.278
13.565
22.657
41.337
44.461
45.722
28
12.461
15.308
16.928
18.939
32.620
37.916
50.993
29
13.121
14.257
16.047
17.708
19.768
23.567
33.711
39.087
42.557
49.588
52.336
30
13.787
14.954
16.791
18.493
20.599
24.478
34.800
40.256
43.773
46.979
50.892
53.672
0.995
0.99
0.975
0.95
0.90
0.75
0.25
0.10
0.05
0.025
0.01
0.005
Degrees of
Freedom
Upper-Tail Areas (a)
0.005
0.01
0.025
0.05
0.10
0.25
0.75
0.90
0.95
0.975
0.99
0.995
Cumulative Probabilities
679
Transcribed Image Text:0.676 0.872 1.237 1.635 2.204 3.455 7.841 10.645 12.592 14.449 16.812 18.548 0.989 1.239 1.690 2.167 2.833 4.255 9.037 12.017 14.067 16.013 18.475 20.278 8. 1.344 1.646 2.180 2.733 3.490 5.071 10.219 13.362 15.507 17.535 20.090 21.955 9. 1.735 2.088 2.700 3.325 4.168 5.899 11.389 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 6.737 12.549 15.987 18.307 20.483 23.209 25.188 2.603 3.053 3.816 4.575 5.578 7.584 13.701 17.275 19.675 21.920 24.725 26.757 12 3.074 23.337 3.571 4.107 4.404 5.226 6.304 7.042 8.438 14.845 18.549 21.026 26.217 28.299 13 3.565 5.009 5.892 9.299 15.984 19.812 22.362 24.736 27.688 29.819 14 4.075 7.790 4.660 5.229 5.629 6.571 10.165 17.117 21.064 23.685 26.119 29.141 31.319 15 4.601 6.262 7.261 8.547 11.037 18.245 22.307 24.996 27.488 30.578 32.801 16 5.142 5.812 6.908 7.962 9.312 11.912 19.369 23.542 26.296 28.845 32.000 34.267 17 5.697 6.408 7.564 8.672 10.085 12.792 20.489 24.769 27.587 30.191 33.409 35.718 18 6.265 7.015 8.231 9.390 10.865 13.675 21.605 25.989 28.869 31.526 34.805 37.156 19 6.844 7.633 8.907 10.117 11.651 14.562 22.718 27.204 30.144 32.852 36.191 38.582 39.997 20 7.434 8.260 9.591 10.851 12.443 15.452 23.828 28.412 31.410 34.170 37.566 21 8.034 8.897 10.283 11.591 13.240 16.344 24.935 29.615 32.671 35.479 38.932 41.401 22 8.643 9.542 10.982 12.338 14.042 17.240 26.039 30.813 33.924 36.781 40.289 42.796 23 9.260 10.196 11.689 13.091 14.848 18.137 27.141 32.007 35.172 38.076 41.638 44.181 15.659 33.196 34.382 45.559 46.928 24 9.886 10.856 12.401 13.848 19.037 28.241 36.415 39.364 42.980 25 10.520 11.524 13.120 14.611 16.473 19.939 29.339 37.652 40.646 44.314 26 11.160 12.198 13.844 15.379 17.292 20.843 30.435 35.563 38.885 41.923 45.642 48.290 27 11.808 12.879 14.573 16.151 18.114 21.749 31.528 36.741 40.113 43.194 49.645 46.963 48.278 13.565 22.657 41.337 44.461 45.722 28 12.461 15.308 16.928 18.939 32.620 37.916 50.993 29 13.121 14.257 16.047 17.708 19.768 23.567 33.711 39.087 42.557 49.588 52.336 30 13.787 14.954 16.791 18.493 20.599 24.478 34.800 40.256 43.773 46.979 50.892 53.672 0.995 0.99 0.975 0.95 0.90 0.75 0.25 0.10 0.05 0.025 0.01 0.005 Degrees of Freedom Upper-Tail Areas (a) 0.005 0.01 0.025 0.05 0.10 0.25 0.75 0.90 0.95 0.975 0.99 0.995 Cumulative Probabilities 679
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