1. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 90%,
qué tpo de disribución siguen los daos. i 0-2 2. -4 4. 4.-6
Oi 23 26 17
Ei 10 10 10
((Ei-Oi)^2)/Ei 16.9 25.6 4 .9
6. -8
14
10
1 .6
8. -10
6
10
1 .6
10. - 12
5
10
2 .5
# $
12. -14
3
10
4 .9
14 -16
2
10
6 .4
% 1&
16 -18
3
10
4 .9
1 8 - 20
1
10
8 .1
1&&
1&&
##.
0.022 0.119 0.154 0.202 0.433 0.569 0.818 0.843 0.877 1.182 1.264 1.29
1 2 3 ! "
1.392 1.395
Viendo en tablas
1.422 1.453 1.453
Conc Conclu lusi sion on como como:: 77.4 77.4<1 <16. 6.9 9 no se acep acepta tan n los los i como como uni! uni!o ome mess
1.486 1.495 1.53 1.578 1.611 1.781 1.816 2.007 2.052 2.072 2.103 2.155 2.333 2.381 2.44 2.498 2.547 2.63 2.637 2.717 2.945 3.032 3.043 3.078 3.151 3.28
'isribucion ognoral
3.384 3.461 3.528 3.69 3.708 3.791 3.957 4.078 4.214 4.301 4.313 4.661 4.714 4.767 4.772 4.793 4.891 5.244 5.285 5.3 5.901 5.924 5.959 5.977 6.001 6.412 6.443 6.72 6.966 7.088 7.094 7.281 7.378 7.489 7.552 7.728 7.766 7.822 8.11 8.115 8.121 8.281 8.477 9.269 10.177
3.384 3.461 3.528 3.69 3.708 3.791 3.957 4.078 4.214 4.301 4.313 4.661 4.714 4.767 4.772 4.793 4.891 5.244 5.285 5.3 5.901 5.924 5.959 5.977 6.001 6.412 6.443 6.72 6.966 7.088 7.094 7.281 7.378 7.489 7.552 7.728 7.766 7.822 8.11 8.115 8.121 8.281 8.477 9.269 10.177
10.369 10.451 10.87 11.094 12.171 12.877 13.602 14.344 15.733 16.677 17.066 17.392 19.867
2. A partir de la prueba Chi-cuadrada determine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo dato.
i 0-3 3. -6
Oi 0 0
Ei 10 10
((Ei-Oi)^2)/Ei 10 10
6.-9
0
10
10
9. -12
3
10
4.9
12. -15
11
10
0.1
" #
15. - 18
20
10
10
18 -21
27
10
28.9
$ % 1&
21 -24
21
10
12.1
24 -27
11
10
0.1
27- 30
6
10
1.6
%%
1&&
$#.#
9.69
1
11.266
2 3 !
11.528 12.612 12.901 13.03 13.238 13.55 13.764 13.914 14.223
14.513 14.881 14.889 15.195
Viendo en tablas
15.537 15.653
Conclusion como: 87.7<16.9 no se aceptan los i como uni!o
15.781 15.892 16.089 16.241 16.307 16.356 16.611 16.64 16.715 16.905 17.054 17.239 17.38 17.386 17.454 17.728 17.905 17.947 18.187 18.284 18.384 18.475 18.519
'isribucion ognoral
18.538 18.548 18.692 18.709 18.755 18.799 19.036 19.063 19.255 19.659 19.662 19.87 19.898 20.008 20.112 20.289 20.452 20.526 20.539 20.555 20.854 20.977 21.291 21.777 21.815 21.867 21.949 22.156 22.231 22.383 22.472 22.554 22.701 22.776 22.845 23.03 23.031 23.313 23.319 23.448 23.463 23.498 23.609 24.38 24.445
24.793 24.953 25.106 25.216 25.371 25.775 25.791 26.646 26.933 27.539 27.676 27.889 28.778 28.823 29.503
es
#. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo
daos utlice la prueba *+i-*uadrada.
9.526 9.695 9.766 10.118 10.412 10.441 10.452 10.475 10.522 10.634 10.653 10.671 10.771
1 2 3 ! " # $ % 1&
i 0-2
Oi 0
Ei 10
((Ei-Oi)^2)/Ei 10
2. -4
0
10
10
4.-6
0
10
10
6. -8
0
10
10
8. -10
3
10
4.9
10. - 12
51
10
168.1
12. -14
42
10
102.4
14 -16
4
10
3.6
16 -18
0
10
10
18- 20
0
10
10
1&&
1&&
33%
10.883 10.893 10.902 10.999
Viendo en tablas
11.002 11.019
Conclusion como: 339<16.9 no se aceptan los i como uni!omes
11.052 11.148 11.252 11.264 11.309 11.346 11.363 11.369 11.381 11.399 11.61 11.617 11.65 11.654 11.664 11.665 11.689 11.728 11.743 11.765 11.769 11.792
'isribucion ognoral
11.793 11.836 11.843 11.845 11.854 11.855 11.866 11.873 11.931 11.931 11.936 11.985 11.991 12.038 12.074 12.131 12.146 12.157 12.161 12.204 12.212 12.247 12.273 12.286 12.299 12.316 12.347 12.357 12.363 12.437 12.48 12.503 12.533 12.548 12.556 12.566 12.571 12.656 12.659 12.66 12.683 12.763 12.809 12.863 12.957
13.013 13.049 13.172 13.271 13.317 13.577 13.598 13.61 13.83 13.94 14.086 14.116 14.121 14.374
. &mplee la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 9'%, q ditribuci!n i"uen lo dato. Compruebe con la herramienta (tat))*it de +roodel.
0.003 0.046 0.081 0.121 0.123 0.151 0.156 0.161 0.223 0.234 0.235 0.256 0.28 0.347 0.355 0.382 0.412
1 2 3 ! " # $ % 1&
i 0-1 1 - 2. 2. - 3 3. - 4
Oi 41 26 20 6
Ei 10 10 10 10
4. - 5
2
10
5. - 6
1
10
6. - 7
1
10
7. - 8
2
10
8. - 9
1
10
9. - 10
0
10
1&&
1&&
0.464 0.468 0.486 0.494
Viendo en tab
0.504 0.504
Conclusion como: 339<16.9 no se aceptan lo
0.518 0.531 0.561 0.585 0.598 0.635 0.654 0.667 0.684 0.699 0.754 0.754 0.761 0.776 0.831 0.904 0.922 0.951
'isribucion ognoral
1.019 1.182 1.182 1.187 1.202 1.228 1.229 1.243 1.337 1.38 1.383 1.419 1.424 1.427 1.45 1.458 1.506 1.525 1.597 1.613 1.639 1.662 1.679 1.78 1.876 1.962 2.06 2.087 2.198 2.258 2.294 2.312 2.327 2.393 2.451 2.516 2.606 2.628 2.66 2.7 2.756 2.771 2.775 2.815 2.898
2.933 3.141 3.192 3.258 3.399 3.582 3.591 4.518 4.923 5.715 6.985 7.145 7.66 8.055
é tipo de
((Ei-Oi)^2)/Ei 96.1 25.6 10 1.6 6.4 8.1 8.1 6.4 8.1 10
1$&.
las i como uni!omes
'. $etermine, con un nivel de confianza de 9 '%, qué tipo de ditribuci!n i"uen lo d"ito emplee la prueba de /olmo"orov-(mirnov.
0.189 0.891
1 2 3
1.313 1.368 1.544
!
1.669 1.784
" # $ % 1&
1.992 2.005 2.5 2.549 2.695 2.831
i 0-3 3 - 6. 6. - 9
Oi
Ei 10 10 10
((Ei-Oi)^2)/Ei 10 10 10
9. - 12
10
10
12. - 15
10
10
15. - 18
10
10
18 - 21
10
10
21 - 24
10
10
24 - 27
10
10
27 - 30
10
10
1&&
1&&
&
13
3.14 3.178 3.186 3.372
Viendo en tablas
3.643 3.706
Conclusion como: 339<16.9 no se aceptan los i como uni!omes
3.724
'isribucion ognoral
3.775 3.779 4.057 4.367 4.449 4.594 4.688 4.688 5.078
13
5.271
19
5.542
18
5.599
19
18
6.265
9
6.62
13
6.645
6
6.934
1
7.058
3
7.103 7.16 7.419
7.422 7.508 7.603 7.805 7.844 8.185 8.231 8.322 8.423 8.936
18
9.049 9.051 9.579 10.165 10.212 10.257 10.317 10.335 10.663 10.745 10.784 10.962 11.118 11.143 11.157 11.475 11.555 11.963
18
12.082 12.299 12.561 12.831 13.234 13.26 13.528 14.405 14.624 15.154 15.33 15.334 15.497 15.584 15.696 16.143 16.256
9
16.432 16.675 16.877 17.583 17.901
13
18.993 19.171 19.204 20.599 21.127 21.5
6
24.93
1
25.998 27.334 31.066
3
", 'eerine, con un niel de conana de %&0, qué tpo de disribuci eplee la prueba de ologoro-irno. *opruebe con la +erra
i
%i
17.574
16.257
13.345
22.863
18.338
23.217
15.495
17.403
2.69
20.232
21.411
21.107
"edia# 18.9699
21.427
14.581
23.523
19.87
Vaian$a # 0.2863
15.305
21.17
16.155
22.88
21.151
14.817
14.702
27.014
14.24
24.154
19.501
16.238
18.739
14.206
17.471
18.59
22.658
22.24
19.916
16.537
24.477
17.673
22.422
13.373
i&n
i-1&n
'i&n(-i
i-'i-1&n(
)*
9.7840 -9.7507
1
9.784
0.0333
0.0000
-9.7507
2
10.279
0.0667
0.0333
-10.2123
10.2457
3
12.858
0.1000
0.0667
-12.7580
12.7913
4
15.907
0.1333
0.1000
-15.7737
15.8070
5
16.032
0.1667
0.1333
-15.8653
15.8987
6
16.452
0.2000
0.1667
-16.2520
16.2853
7
16.463
0.2333
0.2000
-16.2297
16.2630
8
16.677
0.2667
0.2333
-16.4103
16.4437
9
16.713
0.3000
0.2667
-16.4130
16.4463
10
16.939
0.3333
0.3000
-16.6057
16.6390
11
17.487
0.3667
0.3333
-17.1203
17.1537
12
17.532
0.4000
0.3667
-17.1320
17.1653
13
17.926
0.4333
0.4000
-17.4927
17.5260
14
18.436
0.4667
0.4333
-17.9693
18.0027
15
18.515
0.5000
0.4667
-18.0150
18.0483
16
18.825
0.5333
0.5000
-18.2917
18.3250
17
19.209
0.5667
0.5333
-18.6423
18.6757
18
19.301
0.6000
0.5667
-18.7010
18.7343
19
19.364
0.6333
0.6000
-18.7307
18.7640
20
20.169
0.6667
0.6333
-19.5023
19.5357
21
20.346
0.7000
0.6667
-19.6460
19.6793
22
21.073
0.7333
0.7000
-20.3397
20.3730
23
21.878
0.7667
0.7333
-21.1113
21.1447
24
22.029
0.8000
0.7667
-21.2290
21.2623
25
22.208
0.8333
0.8000
-21.3747
21.4080
26
23.479
0.8667
0.8333
-22.6123
22.6457
27
23.787
0.9000
0.8667
-22.8870
22.9203
28
24.076
0.9333
0.9000
-23.1427
23.1760
)-
29
26.853
0.9667
0.9333
-25.8863
25.9197
30
28.501
1.0000
0.9667
-27.5010
27.5343
27.5343
+n tablas 0.220 Como 0.22<27.5343 se aceptan los nume
,os datos siu
ón siguen los daos iena a445i de 6ro7odel. 12.846
15.557
1 6 .5 2 6
22.671
17.469
1 8 .4 8 9
14.238
20.098
1 9 .8 8 1
16.021
18.107
1 3 .3 1 5
20.774
14.255
1 2 .4 7 8
12.165
16.597
2 1 .4 0 4
20.795
25.924
1 8 .8 7 4
18.587
19.929
2 5 .3 5 4
23.96
14.417
1 8 .3 3 8
21.971
20.549
2 4 .5 0 9
)
27.5343
os
en una distibucion lonomal uni!ome
. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n
siguen los daos usando la prueba de ologoro-irno, *opruebe con a445i.
i
%i
i&n
1.979
6.097
3.823
5.52
4.203
5.53
6.891
5.997
6.64
6.376
3.863
1.738
2.913
5.171
6.856
7.228
6.03
6.184
7.6
5.716
4.72
5.771
4.521
3.715
5.368
6.176
5.059
5.325
6.478
4.229
6.459
3.083
6.199
2.59
7.407
4.364
8.986
4.195
2.952
3.59
6.101
2.625
4.463
7.9
3.715
6.739
7.049
5.743
5.448
3.958
i-1&n
'i&n(-i
i-'i-1&n(
1
4.548
0.0333
0 .0 0 0 0
-4.5147
4 .5 4 8 0
2
3.242
0.0667
0 .0 3 3 3
-3.1753
3 .2 0 8 7
3
6.303
0.1000
0 .0 6 6 7
-6.2030
6 .2 3 6 3
4
5.225
0.1333
0 .1 0 0 0
-5.0917
5 .1 2 5 0
5
5.307
0.1667
0 .1 3 3 3
-5.1403
5 .1 7 3 7
6
6.536
0.2000
0 .1 6 6 7
-6.3360
6 .3 6 9 3
7
4.769
0.2333
0 .2 0 0 0
-4.5357
4 .5 6 9 0
8
3.154
0.2667
0 .2 3 3 3
-2.8873
2 .9 2 0 7
9
5.427
0.3000
0 .2 6 6 7
-5.1270
5 .1 6 0 3
10
3.404
0.3333
0 .3 0 0 0
-3.0707
3 .1 0 4 0
11
5.366
0.3667
0 .3 3 3 3
-4.9993
5 .0 3 2 7
12
5.919
0.4000
0 .3 6 6 7
-5.5190
5 .5 5 2 3
13 14
8.503 4.743
0.4333 0.4667
0 .4 0 0 0 0 .4 3 3 3
-8.0697 -4.2763
8 .1 0 3 0 4 .3 0 9 7
15
6.093
0.5000
0 .4 6 6 7
-5.5930
5 .6 2 6 3
16
3.822
0.5333
0 .5 0 0 0
-3.2887
3 .3 2 2 0
17
2.938
0.5667
0 .5 3 3 3
-2.3713
2 .4 0 4 7
18
6.316
0.6000
0 .5 6 6 7
-5.7160
5 .7 4 9 3
19
6.532
0.6333
0 .6 0 0 0
-5.8987
5 .9 3 2 0
20
2.917
0.6667
0 .6 3 3 3
-2.2503
2.2837
21
3.136
0.7000
0 .6 6 6 7
-2.4360
2 .4 6 9 3
22
4.705
0.7333
0 .7 0 0 0
-3.9717
4 .0 0 5 0
23
6.476
0.7667
0 .7 3 3 3
-5.7093
5 .7 4 2 7
24
5.966
0.8000
0 .7 6 6 7
-5.1660
5 .1 9 9 3
25
8.546
0.8333
0 .8 0 0 0
-7.7127
7.7460
26
8.441
0.8667
0 .8 3 3 3
-7.5743
7 .6 0 7 7
27
4.484
0.9000
0 .8 6 6 7
-3.5840
3 .6 1 7 3
)*
)-
- 2 .2 5 0 3
7.746
28
3.546
0.9333
0.9000
-2.6127
2.6460
29
3.431
0.9667
0.9333
-2.4643
2.4977
30
5.769
1.0000
0.9667
-4.7690
4.8023
+n tablas 0.220 Como 0.22<7.746 se aceptan los numeos
,os datos siuen una distib
)
4.972
8.429
6.86
5.991
5.665
3.396
5.781
4.465
1.871
1.629
5.619
4.062
7.001
8.501
7.356
6.269
4.881
7.41
6.632
7.036
cion lonomal e/ponencial
1. Utilice la prueba de Anderon-$arlin" para determinar, con u qué tpo de disribución siguen los daos. *opruebe con
i
i
50*1-i
2i-1
PEA(Yi)
-1.413
0.066
-0.618
-1.425
1.542
0.27
-1.152
0.512
-0.93
0.121
-0.418
1.317
1.567
-1.717
0.913
-0.697
0.01
-0.429
1.077
0.2
1-PEA(Y50+1-i)
Ln (PEA(Yi))
1
0.889
-1.525
1
0.143
0.0123 -1.94491065
2
-1.553
-1.691
3
0.0332
0.0241 -3.4052054
3
-0.204
-2.477
5
0.0433
0.0586 -3.13960264
4
0.436
-3.541
7
0.888
0.0786 -0.11878354
5
1.672
-5.343
9
0.089
0.0962 -2.41911891
6
-1.638
-4.12
11
0.0978
0.1098 -2.3248307
7
0.431
-5.983
13
0.1174
0.111 -2.14216837
8
0.564
-7.965
15
0.1252
0.1227 -2.07784282
9
1.24
-7.373
17
0.1256
0.1484 -2.07465302
10
1.219
-7.528
19
0.1931
0.1707 -1.64454709
11
-0.056
-11.631
21
0.2207
0.1787 -1.51095097
12
1.51
-11.104
23
0.232
0.184 -1.46101791
13
-2.067
-12.281
25
0.2389
0.2887 -1.43171022
14
-0.869
-13.952
27
0.2529
0.2943 -1.37476113
15
-1.293
-14.296
29
0.2741
0.3012 -1.29426228
16
-1.018
-14.717
31
0.2865
0.3021 -1.25001674
17
-1.322
-15.635
33
0.314
0.3033 -1.15836229
18
2.295
-15.267
35
0.3205
0.3543
19
-1.108
-18.86
37
0.3214
0.3593 -1.13506883
20
0.095
-18.11
39
0.3756
0.3624 -0.97923053
21
1.583
-20.354
41
0.4029
0.3721 -0.90906689
22
0.824
-20.317
43
0.4203
0.4194 -0.86678654
23
1.905
-19.79
45
0.4392
0.4425 -0.82280039
24
-0.112
-21.03
47
0.4514
0.4494 -0.79540141
25
-0.559
-24.289
49
0.4871
0.4521 -0.71928584
26
-0.289
-25.559
51
0.5479
0.5129 -0.60166249
27
1.97
-26.112
53
0.5506
0.5486 -0.59674669
28
2.21
-25.095
55
0.5575
0.5608 -0.58429278
-1.137873
29
0.683
-27.176
57
0.5806
0.5797 -0.54369323
30
-0.354
-27.417
59
0.6279
0.5971 -0.46537436
31
0.89
-29.905
61
0.6376
0.6244 -0.45004415
32
-0.86
-32.108
63
0.6407
0.6786 -0.44519395
33
1.733
-29.705
65
0.6457
0.6795 -0.43742028
34
0.365
-34.322
67
0.6967
0.686 -0.36140038
35
0.283
-35.018
69
0.6979
0.7135 -0.35967945
36
-0.296
-36.293
71
0.6988
0.7259 -0.3583907
37
-0.952
-36.869
73
0.7057
0.7471 -0.34856506
38
-0.281
-39.067
75
0.7113
0.7611
39
-0.104
-36.49
77
0.816
0.768 -0.20334092
40
-1.631
-39.056
79
0.8213
0.7793 -0.19686683
41
1.472
-38.781
81
0.8293
0.8069 -0.18717331
42
0.627
-39.76
83
0.8516
0.8744 -0.16063835
43
-0.965
-41.436
85
0.8773
0.8748 -0.13090627
44
0.017
-42.569
87
0.889
0.8826 -0.11765804
45
0.88
-45.638
89
0.8902
0.9022 -0.11630912
46
-1.343
-43.328
91
0.9038
0.911 -0.10114718
47
-0.541
-45.564
93
0.9232
0.9112 -0.07990938
48
-0.477
-47.204
95
0.9414
0.9567 -0.06038715
49
-0.691
-49.553
97
0.9759
0.9668 -0.02439516
50
-1.525
-48.111
99
0.9877
0.9857 -0.01237627
-0.340661
,os datos siu
nivel de confianza de 90%,
ai445i.
-0.423
-0.174
-1.139
0.061
0.7
-0.078
2.293
-0.889
0.099
2.324
0.654
-1.281
0.595
0.597
-0.185
0.249
0.937
-0.67
0.125
-0.608
1.027
-0.145
-1.088
0.137
-1.42
-0.07
1.517
-0.959
-0.144
-1.169
Ln(1-PEA(Y50+1-i))
(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i)))
-4.3981560166
-6.3430666653
-3.7255434385
-21.3922465246
-2.8370205824
-29.8831161319
-2.5433835795
-18.6351698088
-2.3413259213
-42.844003475
-2.2090947499
-49.8731799703
-2.1982250777
-56.4251148404
-2.0980129273
-62.6378362137
-1.9078439482
-67.7024485443
-1.7678476492
-64.8355000359
-1.7220468568
-67.8929542733
-1.6928195214
-72.5382608598
-1.2423671923
-66.8519354241
-1.2231556237
-70.1437522243
-1.1999807831
-72.3330487032
-1.1969971906
-75.8574319359
-1.1930328643
-77.5960401929
-1.0376112671
-76.1419494406
-1.0235975849
-79.87065719
-1.0150067048
-77.775252222
-0.9885926436
-77.804040747
-0.8689301605
-74.6358179919
-0.8153148145
-73.7151841494
-0.7998419192
-74.97643669
-0.7938518847
-74.1437484197
-0.6676743846
-64.7361806263
-0.6003857005
-63.4480164979
-0.5783909433
-63.94760454
-0.5452445506
-62.0694533476
-0.5156706754
-57.8816571412
-0.4709640903
-56.1815027527
-0.3877234266
-52.4737947491
-0.3863980454
-53.5481911081
-0.3768776513
-49.4646278896
-0.3375728421
-48.1104083567
-0.3203430147
-48.1900937944
-0.291556234
-46.7288545332
-0.2729905237
-46.0238640714
-0.2639655458
-35.9825981786
-0.2493591981
-35.2518560831
-0.2145555341
-32.5400361739
-0.1342173421
-24.4730221109
-0.1337599902
-22.4966321023
-0.1248831821
-21.1010866285
-0.102919054
-19.5113077003
-0.0932123817
-17.6867202992
-0.0929928668
-16.0799092572
-0.0442654163
-9.9419937997
-0.0337636302
-5.6414023378
-0.0144032303
-2.6511706365
en uns distibucion lonomal una distibucion uni!ome
9. $etermine, con un nivel de confianza de 90% r qué tipo de ditribuci!n i"uen lo da to utilice la prueba de /olmo"orov-(mirnov.
i
%i
i&n
21.92
7.902
10.824
22.258
13.343
11.536
10.187
11.442
13.396
13.07
24.956
5.442
12.996
5.073
13.62
5.481
2.959
7.503
4.159
23.466
6.08
9.053
5.178
18.7
9.056
2.491
10.123
3.244
9.433
11.774
25.237
7.588
1.152
8.059
26.399
9.888
13.798
15.255
20.507
11.147
2.898
20.041
10.228
9.553
19.87
6.848
7.197
12.156
1.674
8.582
i-1&n
'i&n(-i
i-'i-1&n(
1
7.982
0.0333
0.0000
-7.9487
7.9820
2
18.951
0.0667
0.0333
-18.8843
18.9177
3
6.361
0.1000
0.0667
-6.2610
6.2943
4
3.382
0.1333
0.1000
-3.2487
3.2820
5
37.134
0.1667
0.1333
-36.9673
37.0007
6
17.684
0.2000
0.1667
-17.4840
17.5173
7
6.839
0.2333
0.2000
-6.6057
6.6390
8
3.274
0.2667
0.2333
-3.0073
3.0407
9
22.836
0.3000
0.2667
-22.5360
22.5693
10
12.427
0.3333
0.3000
-12.0937
12.1270
11
40.122
0.3667
0.3333
-39.7553
39.7887
12
12.348
0.4000
0.3667
-11.9480
11.9813
13
6.405
0.4333
0.4000
-5.9717
6.0050
14 15
14.387 21.099
0.4667 0.5000
0.4333 0.4667
-13.9203 -20.5990
13.9537 20.6323
16
8.814
0.5333
0.5000
-8.2807
8.3140
17
7.073
0.5667
0.5333
-6.5063
6.5397
18
7.325
0.6000
0.5667
-6.7250
6.7583
19
14.432
0.6333
0.6000
-13.7987
13.8320
20
11.811
0.6667
0.6333
-11.1443
11.1777
21
5.862
0.7000
0.6667
-5.1620
5.1953
22
8.725
0.7333
0.7000
-7.9917
8.0250
23
34.45
0.7667
0.7333
-33.6833
33.7167
24
10.037
0.8000
0.7667
-9.2370
9.2703
25
9.021
0.8333
0.8000
-8.1877
8.2210
26
22.939
0.8667
0.8333
-22.0723
22.1057
27
10.708
0.9000
0.8667
-9.8080
9.8413
28
10.046
0.9333
0.9000
-9.1127
9.1460
)*
)-
-3.0073
39.7887
29
14.65
0.9667
0 .9 3 3 3
-13.6833
13.7167
30
24.699
1.0000
0 .9 6 6 7
-23.6990
23.7323
+n tablas 0.220 Como 0.22<39.7887 se aceptan los numeos
11.045
2 3 .6 0 3
13.668
7 .9 5 4
11.02
1 1 .7 2 9
5.219
1 1 .7 1 3
6.647
5 .7 6 7
3.271
1 0 .3 9
29.285
2 2 .3 5
19.691
7 .7 1 1
8.52
2 6 .1 8 2
16.293
1 6 .1 2 6
)
39.7887
0. A partir de la prueba de /olmo"orov-(mirnov, determine con un nivel de co de 90% qué tipo de ditribuci!n i"uen lo dato.
i
%i
i&n
3.366
12.233
5.725
9.186
8.232
2.91
8.391
2.288
4.582
6.114
11.892
14.542
9.851
11.088
6.301
3.171
7.782
5.682
9.587
12.519
10.263
5.367
3.059
6.341
3.613
5.582
4.836
8.663
6.975
8.441
9.799
7.825
9.464
7.799
6.929
4.141
2.972
14.575
2.248
6.565
9.264
14.575
6.742
5.551
5.313
4.028
6.515
9.474
6.817
1 0 .1 9
i-1&n
'i&n(-i
i-'i-1&n(
1
5.091
0.0333
0 .0 0 0 0
-5.0577
5 .0 9 1 0
2
6.752
0.0667
0 .0 3 3 3
-6.6853
6 .7 1 8 7
3
11.584
0.1000
0 .0 6 6 7
-11.4840
11.5173
4
9.595
0.1333
0 .1 0 0 0
-9.4617
9 .4 9 5 0
5
7.558
0.1667
0 .1 3 3 3
-7.3913
7 .4 2 4 7
6
4.179
0.2000
0 .1 6 6 7
-3.9790
4 .0 1 2 3
7
13.47
0.2333
0 .2 0 0 0
-13.2367
13.2700
8
9.71
0.2667
0 .2 3 3 3
-9.4433
9 .4 7 6 7
9
14.135
0.3000
0 .2 6 6 7
-1 -13.8350
13.8683
10
12.436
0.3333
0 .3 0 0 0
-12.1027
12.1360
11
11.319
0.3667
0 .3 3 3 3
-10.9523
10.9857
12
10.64
0.4000
0 .3 6 6 7
-10.2400
10.2733
13
13.333
0.4333
0 .4 0 0 0
-12.8997
12.9330
14
13.784
0.4667
0 .4 3 3 3
-13.3173
13.3507
15 16
8.12 10.035
0.5000 0.5333
0 .4 6 6 7 0 .5 0 0 0
-7.6200 -9.5017
7 .6 5 3 3 9 .5 3 5 0
17
1.512
0.5667
0 .5 3 3 3
-0.9453
0.9787
18
5.259
0.6000
0 .5 6 6 7
-4.6590
4 .6 9 2 3
19
5.937
0.6333
0 .6 0 0 0
-5.3037
5 .3 3 7 0
20
8.153
0.6667
0 .6 3 3 3
-7.4863
7 .5 1 9 7
21
3.274
0.7000
0 .6 6 6 7
-2.5740
2 .6 0 7 3
22
7.242
0.7333
0 .7 0 0 0
-6.5087
6 .5 4 2 0
23
10.081
0.7667
0 .7 3 3 3
-9.3143
9 .3 4 7 7
24
4.867
0.8000
0 .7 6 6 7
-4.0670
4 .1 0 0 3
25
6.451
0.8333
0 .8 0 0 0
-5.6177
5 .6 5 1 0
26
5.599
0.8667
0 .8 3 3 3
-4.7323
4 .7 6 5 7
27
11.317
0.9000
0 .8 6 6 7
-10.4170
10.4503
28
8.086
0.9333
0 .9 0 0 0
-7.1527
7 .1 8 6 0
29
2.954
0.9667
0 .9 3 3 3
-1.9873
2 .0 2 0 7
)*
)-
1 3 .8 6 8 3
- 0 .9 4 5 3
30
5.418
1.0000
0.9667
-4.4180
4.4513
+n tablas 0.220 Como 0.22<13.8683 se aceptan los numeos
'isribucion ognoral
fianza
6.545
6.481
9.965
10.643
5.35
3.465
9.964
1.298
3.068
7.291
2.064
5.147
8.915
8.007
13.418
5.238
6.348
5.723
4.961
13.263
)
13.8683
. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo dato utilice la prueba de /olmo"orov-(mirnov.
i
%i
0.102
0.285
0.725
5.567
6.773
3.661
3.072
5.193
0.329
2.721
0.664
6.032
0.093
3.856
1.779
2.342
2.954
0.883
1.79
3.847
2.35
3.983
1.517
0.695
3.564
3.986
2.416
0.577
0.617
1.494
0.852
4.342
0.064
0.299
0.214
4.276
0.371
4.52
0.408
0.113
2.859
0.799
4.718
8.664
0.339
2.852
0.04
1.86
0.716
3.551
i&n
i-1&n
'i&n(-i
i-'i-1&n(
)*
0.9667 0.3380
1
1.338
0.0333
0.0000
0.3380
2
1.198
0.0667
0.0333
-0.8020
1.9333
3
1.852
0.1000
0.0667
-1.1480
2.9000
4
3.05
0.1333
0.1000
-0.9500
3.8667
5
1.003
0.1667
0.1333
-3.9970
4.8333
6
0.286
0.2000
0.1667
-5.7140
5.8000
7
2.283
0.2333
0.2000
-4.7170
6.7667
8
0.388
0.2667
0.2333
-7.6120
7.7333
9
0.095
0.3000
0.2667
-8.9050
8.7000
10
0.265
0.3333
0.3000
-9.7350
9.6667
11
0.58
0.3667
0.3333
-10.4200
10.6333
12
0.294
0.4000
0.3667
-11.7060
11.6000
13
1.586
0.4333
0.4000
-11.4140
12.5667
14
4.117
0.4667
0.4333
-9.8830
13.5333
15
1.645
0.5000
0.4667
-13.3550
14.5000
16
0.395
0.5333
0.5000
-15.6050
15.4667
17
0.483
0.5667
0.5333
-16.5170
16.4333
18
2.156
0.6000
0.5667
-15.8440
17.4000
19
1.355
0.6333
0.6000
-17.6450
18.3667
20
7.487
0.6667
0.6333
-12.5130
19.3333
21
0.53
0.7000
0.6667
-20.4700
20.3000
22
0.049
0.7333
0.7000
-21.9510
21.2667
23
1.426
0.7667
0.7333
-21.5740
22.2333
24
4.688
0.8000
0.7667
-19.3120
23.2000
25
0.46
0.8333
0.8000
-24.5400
24.1667
26
1.581
0.8667
0.8333
-24.4190
25.1333
27
0.774
0.9000
0.8667
-26.2260
26.1000
28
0.429
0.9333
0.9000
-27.5710
27.0667
29
2.267
0.9667
0.9333
-26.7330
28.0333
30
2.032
1.0000
0.9667
-27.9680
29.0000
+n tablas 0.220 Como 0.22<29 se aceptan los numeos
'isribucion ognoral
0.101
5.549
0.988
0.716
1.729
1.456
2.659
3.622
0.573
0.204
0.468
1.037
3.294
0.345
0.24
2.923
1.892
1.262
0.493
0.269
)-
)
29
2. $etermine, con un nivel de confianza de 9'%, qué 3ipo de ditribuci!n i"uen lo dato
eplee la prueba de ologoro-irno. *opruebe con a 45i.
i
%i
i&n
18.39
19.825
23.279
23.206
19.351
24.364
19.2
21.265
16.905
27.313
22.105
25.105
22.137
27.514
15.766
15.625
16.168
29.769
18.158
18.293
19.743
24.525
18.112
26.259
19.466
25.275
24.56
22.09
19.608
15.447
22.189
20.807
27.339
22.556
24.059
29.122
27.19
26.915
26.844
19.573
24.007
28.127
25.213
19.964
27.141
24.985
17.717
19.063
29.986
24.074
i-1&n
'i&n(-i
i-'i-1&n(
1
26.739
0.0333
0.0000
-26.7057
26.7390
2
23.396
0.0667
0.0333
-23.3293
23.3627
3
21.326
0.1000
0.0667
-21.2260
21.2593
4
17.539
0.1333
0.1000
-17.4057
17.4390
5
26.421
0.1667
0.1333
-26.2543
26.2877
6
20.931
0.2000
0.1667
-20.7310
20.7643
7
28.013
0.2333
0.2000
-27.7797
27.8130
8
25.57
0.2667
0.2333
-25.3033
25.3367
9
22.518
0.3000
0.2667
-22.2180
22.2513
10
29.791
0.3333
0.3000
-29.4577
29.4910
11
22.607
0.3667
0.3333
-22.2403
22.2737
12
28.553
0.4000
0.3667
-28.1530
28.1863
13
15.138
0.4333
0.4000
-14.7047
14.7380
14
19.921
0.4667
0.4333
-19.4543
19.4877
15 16
18.044 18.562
0.5000 0.5333
0.4667 0.5000
-17.5440 -18.0287
17.5773 18.0620
17
26693
0.5667
0.5333 -26692.4333
26692.4667
18
18.746
0.6000
0.5667
-18.1460
18.1793
19
18.883
0.6333
0.6000
-18.2497
18.2830
20
17.89
0.6667
0.6333
-17.2233
17.2567
21
19.584
0.7000
0.6667
-18.8840
18.9173
22
24.449
0.7333
0.7000
-23.7157
23.7490
23
21.15
0.7667
0.7333
-20.3833
20.4167
24
22.216
0.8000
0.7667
-21.4160
21.4493
25
25.744
0.8333
0.8000
-24.9107
24.9440
26
26.714
0.8667
0.8333
-25.8473
25.8807
27
29.751
0.9000
0.8667
-28.8510
28.8843
28
16.818
0.9333
0.9000
-15.8847
15.9180
29
26.128
0.9667
0.9333
-25.1613
25.1947
)*
)-
29.491
30
15.515
1.0000
0.9667
-14.5150
14.5483
+n tablas 0.240 Como 0.24-14.515 o se aceptan los numeos
-14.515
15.24
15.792
18.097
20.233
22.029
25.164
15.858
25.111
26.276
25.948
29.631
28.821
15.724
21.614
26.853
17.053
25.458
26.06
23.517
20.733
)
29.491
,os datos no siuen ninuna distibucion
#. $etermine, don un nivel de confianza de 90%, qué tipo de ditribuci!n li"uen lo dato uando la prueba de Anderon-$arlin". Compruebe con (tat )*it
7.717
7.971
5.261
5.994
7.215
6.1
6.876
6.377
6.155
7.512
7.936
7.96
6.157
5.796
6.15
5.983
6.061
7.492
6.974
5.386
6.347
6.174
5.962
6.153
6.838
5.741
5.478
5.471
7.814
6.238
7.484
6.15
7.561
7.734
5.595
7.354
5.826
5.858
5.316
7.081
6.476
7.394
7.99
5.793
5.057
5.245
6.246
7.538
7.314
7.495
6.004
7.374
7.071
5.549
6.932
6.262
5.021
6.8
7.322
7.84
5.547
5.601
6.524
6.351
6.438
7.76
7.771
7.118
5.5
5.901
i
Yi
Y50+1-i
2*i-1
PEA(Yi)
1-PEA(Y50+1-i)
Ln (PEA(Yi))
1
5.021
7.99
1
0.143
0.0123
-1.9449
2
5.057
6.99
3
0.0332
0.0241
-3.4052
3
5.245
5.99
5
0.0433
0.0586
-3.1396
4
5.261
4.99
7
0.888
0.0786
-0.1188
5
5.316
3.99
9
0.089
0.0962
-2.4191
6
5.547
2.99
11
0.0978
0.1098
-2.3248
7
5.549
1.99
13
0.1174
0.111
-2.1422
8
5.741
0.99
15
0.1252
0.1227
-2.0778
9
5.793
-0.01
17
0.1256
0.1484
-2.0747
10
5.826
-1.01
19
0.1931
0.1707
-1.6445
11
5.858
-2.01
21
0.2207
0.1787
-1.5110
12
5.962
-3.01
23
0.232
0.184
-1.4610
13
5.983
-4.01
25
0.2389
0.2887
-1.4317
14
5.994
-5.01
27
0.2529
0.2943
-1.3748
15
6.004
-6.01
29
0.2741
0.3012
-1.2943
16
6.061
-7.01
31
0.2865
0.3021
-1.2500
17
6.15
-8.01
33
0.314
0.3033
-1.1584
18
6.15
-9.01
35
0.3205
0.3543
-1.1379
19
6.153
-10.01
37
0.3214
0.3593
-1.1351
20
6.155
-11.01
39
0.3756
0.3624
-0.9792
21
6.174
-12.01
41
0.4029
0.3721
-0.9091
22
6.238
-13.01
43
0.4203
0.4194
-0.8668
23
6.246
-14.01
45
0.4392
0.4425
-0.8228
24
6.351
-15.01
47
0.4514
0.4494
-0.7954
25
6.377
-16.01
49
0.4871
0.4521
-0.7193
26
6.438
-17.01
51
0.5479
0.5129
-0.6017
27
6.8
-18.01
53
0.5506
0.5486
-0.5967
28
6.838
-19.01
55
0.5575
0.5608
-0.5843
29
6.974
-20.01
57
0.5806
0.5797
-0.5437
30
7.071
-21.01
59
0.6279
0.5971
-0.4654
31
7.081
-22.01
61
0.6376
0.6244
-0.4500
32
7.118
-23.01
63
0.6407
0.6786
-0.4452
33
7.215
-24.01
65
0.6457
0.6795
-0.4374
34
7.322
-25.01
67
0.6967
0.686
-0.3614
35
7.354
-26.01
69
0.6979
0.7135
-0.3597
36
7.374
-27.01
71
0.6988
0.7259
-0.3584
37
7.484
-28.01
73
0.7057
0.7471
-0.3486
38
7.492
-29.01
75
0.7113
0.7611
-0.3407
39
7.495
-30.01
77
0.816
0.768
-0.2033
40
7.512
-31.01
79
0.8213
0.7793
-0.1969
41
7.561
-32.01
81
0.8293
0.8069
-0.1872
42
7.717
-33.01
83
0.8516
0.8744
-0.1606
43
7.76
-34.01
85
0.8773
0.8748
-0.1309
44
7.771
-35.01
87
0.889
0.8826
-0.1177
45
7.814
-36.01
89
0.8902
0.9022
-0.1163
46
7.84
-37.01
91
0.9038
0.911
-0.1011
47
7.936
-38.01
93
0.9232
0.9112
-0.0799
48
7.96
-39.01
95
0.9414
0.9567
-0.0604
49
7.971
-40.01
97
0.9759
0.9668
-0.0244
50
7.99
-41.01
99
0.9877
0.9857
-0.0124
os daos siguen una disribucion uni8ore
7.514
6.409
6.679
7.579
6.45
6.719
5.053
5.129
5.922
7.745
5.057
5.548
7.587
5.235
7.872
5.304
5.175
6.499
5.909
6.215
6.949
5.531
6.335
5.271
6.169
5.484
6.823
5.104
7.633
6.074
Ln(1-PEA(Y50+1-i))
(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i)))
-4.3982
-1.9326
-3.7255
-10.1433
-2.8370
-15.4050
-2.5434
-0.2813
-2.3413
-20.9063
-2.2091
-24.3653
-2.1982
-26.4052
-2.0980
-29.3271
-1.9078
-32.7463
-1.7678
-28.0031
-1.7220
-27.9773
-1.6928
-29.3714
-1.2424
-28.5753
-1.2232
-29.1725
-1.2000
-28.7988
-1.1970
-29.3854
-1.1930
-28.2171
-1.0376
-27.4251
-1.0236
-28.7034
-1.0150
-24.0564
-0.9886
-22.0156
-0.8689
-19.2376
-0.8153
-17.1135
-0.7998
-16.2621
-0.7939
-13.0921
-0.6677
-4.5269
-0.6004
-2.5518
-0.5784
-1.2921
-0.5452
2.0524
-0.5157
7.7718
-0.4710
10.6357
-0.3877
14.7046
-0.3864
15.7352
-0.3769
21.7482
-0.3376
24.4136
-0.3203
26.0932
-0.2916
29.0931
-0.2730
31.5329
-0.2640
43.4787
-0.2494
46.0122
-0.2146
50.1979
-0.1342
59.2422
-0.1338
63.2310
-0.1249
66.5500
-0.1029
69.9443
-0.0932
73.6966
-0.0930
77.3100
-0.0443
85.1497
-0.0338
91.4133
-0.0144
96.3590
60.197 60.659
. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confian
qué tpo de disribución siguen los daos. *opruebe con ia445i.
60.747 61.771 62.614 62.686
1
62.849
2 3 !
63.185 63.391 63.479 63.499 63.766 64.31 65.272 66.832 68.147
i 60-64 64-68
Oi 3
Ei 10 10
12
68-72
13
10
72-76
11
10
76-80
10
10
" #
80-84
10
10
84-88
5
10
$ % 1&
88-92
14
10
92-96
9
10
96-100
13
10
1&&
1&&
68.18 68.181 68.51 68.775 69.235 69.346 69.716 69.933 70.205 70.569 70.684 71.68 72.537 72.55 73.105 73.495 73.711 73.864 74.473 75.107 75.425 75.734 75.734 76.159 76.248 76.276 76.753 77.024 77.148
,a distibucion ue se siuen en estos dat
77.388 77.588 79.007 79.56 80.042 80.15 81.057 81.149 81.931 82.187 82.416 83.537 83.704 83.945 84.366 86.06 86.162 86.478 86.95 88.371 88.431 88.819 89.36 89.607 90.108 90.591 90.697 90.854 91.051 91.262 91.325 91.54 91.917 92.229 92.978 93.2 93.535 93.645 95.076 95.181 95.804 95.882 96.594 96.829 96.893
96.937 97.305 97.491 97.58 97.844 97.891 97.926 98.002 98.783 99.813
a de 9'%
((Ei-Oi)^2)/Ei 0.4 4.9 0.9 0.1 0 0 2.5 1.6 0.1 0.9
11.
s es uni!ome
'. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo
daos Eplee 9a prueba *+i-*uadrada : copruebe con a445i 0: inomial 1: ta )istibucion 1.316 1.34 i 1.443 0-1 1 1.556 1.677 1.689 1.806 1.81
Oi 9
Ei 16.6
((Ei-Oi)^2)/Ei 3.4795
2 3
1-2.
22
16.6
1.7566
2-3.
28
16.6
7.8289
3-4.
26
16.6
5.3229
! "
4-5.
11
16.6
1.8892
5-6.
4
16.6
9.5639
Err4!22
Err4!22
Err4!22
1.874 2.076 2.171
1.61
Viendo en tablas
2.173 2.225
Conclusion como: 29.84<1.61 no se aceptan los i como uni!omes
2.246 2.33 2.369
;&4
'isribucion
2.37
2.37 2.499 2.639 2.649 2.682 2.727
9neralo 0-4 5 6 7 8.-9
=o. de Obseraciones Oi 10 9 14 7 10
p(>) 0.1521 0.2091 0.273 0.2292 0.1366
Ei?!&@p(>) 7.605 10.455 13.65 11.46 6.83
otal
50
1
50
2.744 2.749 2.782 2.804 2.848 2.912 2.919 2.949 3.009 3.018 3.028 3.046 3.049 3.137 3.2 3.206
3.292 3.309 3.347 3.351 3.361 3.408 3.449 3.501 3.572 3.587 3.722 3.724 3.775 3.786 3.796 3.82 3.899 3.903 3.953 3.964 4.035 4.043 4.057 4.075 4.098 4.102 4.111 4.123 4.142 4.164 4.328 4.339 4.344 4.347 4.374 4.375 4.398 4.463 4.574 4.606 4.87 4.879 4.907 4.951 4.968
4.993 5.006 5.08 5.187 5.246 5.329 5.331 5.337 5.444 5.617 5.813 5.828 6.351 6.385 6.43 6.767
(Ei-Oi)2/Ei 0.7537 0.2023 0.009 1.7345 1.4698 4.1693
4. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo da to
utlice la prueba de Anderson-'arling. *opruebe con a45i.
198.912
193.496
198.169
186.553
186.699
189.485
197.916
186.72
175.625
193.319
208.652
180.861
189.234
179.564
186.615
191.5
191.643
201.017
187.908
180.002
192.118
191.445
184.243
185.089
194.686
188.845
194.979
203.149
183.463
193.388
193.112
194.638
184.73
188.484
194.847
191.088
178.781
199.534
191.382
173.618
193.244
185.665
176.583
187.396
198.267
181.183
186.406
192.473
193.006
193.267
192.581
195.991
200.364
188.597
188.87
191.077
198.414
174.54
194.575
184.283
194.842
186.476
196.176
203.231
192.099
177.14
172.582
188.939
183.386
180.174
;&4 os daos siguen la disribucion =oral
0: omal 1: ta distibucion
i
Yi
Y50+1-i
2*i-1
PEA(Yi)
1-PEA(Y50+1-i)
Ln (PEA(Yi))
1
172.582
191.077
1
0.143
0.0123
-1.9449
2
172.773
190.077
3
0.0332
0.0241
-3.4052
3
173.618
189.077
5
0.0433
0.0586
-3.1396
4
174.54
188.077
7
0.888
0.0786
-0.1188
5
175.524
187.077
9
0.089
0.0962
-2.4191
6
175.625
186.077
11
0.0978
0.1098
-2.3248
7
176.583
185.077
13
0.1174
0.111
-2.1422
8
176.613
184.077
15
0.1252
0.1227
-2.0778
9
177.14
183.077
17
0.1256
0.1484
-2.0747
10
178.781
182.077
19
0.1931
0.1707
-1.6445
11
179.564
181.077
21
0.2207
0.1787
-1.5110
12
179.576
180.077
23
0.232
0.184
-1.4610
13
180.002
179.077
25
0.2389
0.2887
-1.4317
14
180.174
178.077
27
0.2529
0.2943
-1.3748
15
180.861
177.077
29
0.2741
0.3012
-1.2943
16
181.175
176.077
31
0.2865
0.3021
-1.2500
17
181.183
175.077
33
0.314
0.3033
-1.1584
18
181.189
174.077
35
0.3205
0.3543
-1.1379
19
182.241
173.077
37
0.3214
0.3593
-1.1351
20
183.386
172.077
39
0.3756
0.3624
-0.9792
21
183.463
171.077
41
0.4029
0.3721
-0.9091
22
183.73
170.077
43
0.4203
0.4194
-0.8668
23
184.097
169.077
45
0.4392
0.4425
-0.8228
24
184.243
168.077
47
0.4514
0.4494
-0.7954
25
184.283
167.077
49
0.4871
0.4521
-0.7193
26
184.548
166.077
51
0.5479
0.5129
-0.6017
27
184.73
165.077
53
0.5506
0.5486
-0.5967
28
185.089
164.077
55
0.5575
0.5608
-0.5843
29
185.665
163.077
57
0.5806
0.5797
-0.5437
30
185.913
162.077
59
0.6279
0.5971
-0.4654
31
186.406
161.077
61
0.6376
0.6244
-0.4500
32
186.476
160.077
63
0.6407
0.6786
-0.4452
33
186.553
159.077
65
0.6457
0.6795
-0.4374
34
186.615
158.077
67
0.6967
0.686
-0.3614
35
186.699
157.077
69
0.6979
0.7135
-0.3597
36
186.72
156.077
71
0.6988
0.7259
-0.3584
37
187.396
155.077
73
0.7057
0.7471
-0.3486
38
187.85
154.077
75
0.7113
0.7611
-0.3407
39
187.908
153.077
77
0.816
0.768
-0.2033
40
188.484
152.077
79
0.8213
0.7793
-0.1969
41
188.597
151.077
81
0.8293
0.8069
-0.1872
42
188.845
150.077
83
0.8516
0.8744
-0.1606
43
188.87
149.077
85
0.8773
0.8748
-0.1309
44
188.939
148.077
87
0.889
0.8826
-0.1177
45
189.234
147.077
89
0.8902
0.9022
-0.1163
46
189.485
146.077
91
0.9038
0.911
-0.1011
47
189.795
145.077
93
0.9232
0.9112
-0.0799
48
190.21
144.077
95
0.9414
0.9567
-0.0604
49
190.292
143.077
97
0.9759
0.9668
-0.0244
50
191.077
142.077
99
0.9877
0.9857
-0.0124
184.548
176.613
194.656
200.401
206.452
185.913
200.353
197.755
190.21
202.014
179.576
181.175
199.871
172.773
181.189
192.927
175.524
189.795
192.881
182.241
187.85
206.708
190.292
198.489
183.73
197.7
184.097
195.355
193.626
206.255
Ln(1-PEA(Y50+1-i))
(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i)))
-4.3982
-1.9326
-3.7255
-10.1433
-2.8370
-15.4050
-2.5434
-0.2813
-2.3413
-20.9063
-2.2091
-24.3653
-2.1982
-26.4052
-2.0980
-29.3271
-1.9078
-32.7463
-1.7678
-28.0031
-1.7220
-27.9773
-1.6928
-29.3714
-1.2424
-28.5753
-1.2232
-29.1725
-1.2000
-28.7988
-1.1970
-29.3854
-1.1930
-28.2171
-1.0376
-27.4251
-1.0236
-28.7034
-1.0150
-24.0564
-0.9886
-22.0156
-0.8689
-19.2376
-0.8153
-17.1135
-0.7998
-16.2621
-0.7939
-13.0921
-0.6677
-4.5269
-0.6004
-2.5518
-0.5784
-1.2921
-0.5452
2.0524
-0.5157
7.7718
-0.4710
10.6357
-0.3877
14.7046
-0.3864
15.7352
-0.3769
21.7482
-0.3376
24.4136
-0.3203
26.0932
-0.2916
29.0931
-0.2730
31.5329
-0.2640
43.4787
-0.2494
46.0122
-0.2146
50.1979
-0.1342
59.2422
-0.1338
63.2310
-0.1249
66.5500
-0.1029
69.9443
-0.0932
73.6966
-0.0930
77.3100
-0.0443
85.1497
-0.0338
91.4133
-0.0144
96.3590
'isribucion =oral
, $etermine, con un nivel de confianza de 90 %, qué tipo de ditribuci!n i"uen lo dato.
Eplee la prueba *+i-*uadrada : copruebe con a5i
18.089
14.601
12.091
17.516
12.258
13.025
18.482
19.439
15.032
10.816
16.93
18.475
18.064
16.39
15.989
18.917
18.737
13.028
13.534
14.233
17.552
18.398
10.877
13.538
13.217
14.954
17.131
11.747
16.26
17.652
17.15
17.12
13.871
15.645
17.293
16.648
19.48
16.416
18.18
19.408
17.803
14.342
18.055
14.458
15.287
12.777
15.501
17.047
11.436
16.925
11.779
1
12.082
2
i 10.-11 11.-12
13.163
3
12.-13
1
5
3.2
13.435
4
13-14
3
5
0.8
13.536
5
14-15
6
5
0.2
14.257
6
15-16
9
5
3.2
14.257
7
16-17
7
5
0.8
14.504
8
17-18
14
5
16.2
14.517
9
18-19
7
5
0.8
14.658
10
19-20
1
5
3.2
11.144
14.772 15.188 15.21 15.235 15.281 15.663 15.845 15.881 15.959 15.967 16.082 16.162 16.651 16.733 16.751 16.766 16.805 17.02
Oi 0 2
Ei 5 5
((Ei-Oi)^2)/Ei 5 1.8
17.175 17.206 17.211 17.223 17.239 17.264 17.264 17.497 17.51 17.52 17.551 17.579 17.77 18.129 18.145 18.168 18.345 18.476 18.58 18.93 19.787
,a distibucion ue siuen estos datos es lonomal
1. Utilice la prueba de /olmo"orov-(mirnov para determinar, con u n nivel de confianza de 90%,
qué tpo de disribución siguen los daos. *opruebe con a445i.
2.865
4.419
3.681
6.502
1.141
2.773
2.299
4.589
2.336
2.201
1.186
3.61
0.753
2.653
3.574
3.588
3.42
1.123
3.264
2.219
1.962
2.915
4.282
4.835
1.242
3.725
4.317
1.694
3.286
3.698
3.208
1.628
3.117
1.283
3.821
0.943
1.713
4.715
1.74
2.769
1.904
3.144
3.541
1.494
5.983
1.649
4.02
1.475
1.304
2.151
2.953
1.06
7.8
7.621
2.872
1.474
5.632
2.941
2.274
1.841
1.651
4.009
2.54
2.669
2.285
4.579
3.631
6.574
1.941
3.255
1.372
2.284
2.819
3.47
3.158
2.194
1.524
2.105
2.806
4.819
i
%i
i&n
i-1&n
'i&n(-i
i-'i-1&n(
)*
1
1.123
0.0333
0.0000
-1.0897
1.1230 -1.0897
2
1.186
0.0667
0.0333
-1.1193
1.1527
3
1.242
0.1000
0.0667
-1.1420
1.1753
4
1.283
0.1333
0.1000
-1.1497
1.1830
5
1.304
0.1667
0.1333
-1.1373
1.1707
6
1.904
0.2000
0.1667
-1.7040
1.7373
7
2.151
0.2333
0.2000
-1.9177
1.9510
8
2.201
0.2667
0.2333
-1.9343
1.9677
9
2.274
0.3000
0.2667
-1.9740
2.0073
10
2.285
0.3333
0.3000
-1.9517
1.9850
11
2.336
0.3667
0.3333
-1.9693
2.0027
12
2.819
0.4000
0.3667
-2.4190
2.4523
13
2.865
0.4333
0.4000
-2.4317
2.4650
14
2.941
0.4667
0.4333
-2.4743
2.5077
15
2.953
0.5000
0.4667
-2.4530
2.4863
16
3.117
0.5333
0.5000
-2.5837
2.6170
17
3.144
0.5667
0.5333
-2.5773
2.6107
18
3.158
0.6000
0.5667
-2.5580
2.5913
19
3.264
0.6333
0.6000
-2.6307
2.6640
20
3.42
0.6667
0.6333
-2.7533
2.7867
21
3.47
0.7000
0.6667
-2.7700
2.8033
22
3.541
0.7333
0.7000
-2.8077
2.8410
23
3.631
0.7667
0.7333
-2.8643
2.8977
24
3.681
0.8000
0.7667
-2.8810
2.9143
)-
25
3.725
0.8333
0.8000
-2.8917
2.9250
26
3.821
0.8667
0.8333
-2.9543
2.9877
27
4.317
0.9000
0.8667
-3.4170
3.4503
28
4.419
0.9333
0.9000
-3.4857
3.5190
29
4.579
0.9667
0.9333
-3.6123
3.6457
30
5.632
1.0000
0.9667
-4.6320
4.6653
4.6653
+n tablas 0.220 Como 0.22<4.6653 se aceptan los numeo
os daos siguen una disribucion binoral
)
7.142
1.783
3.128
3.1
3.057
1
3.704
1.02
2.877
3.956
1.802
1.569
2.18
2.395
1.539
1.917
4.499
4.037
1.946
3.197
4.6653
s
9, $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo da to uando
la pruebo do ologoro-irno. *opruebe con a445i.
174.847
402.174
282.143
859.252
36.146
164.428
116.195
432.915
119.609
107.279
38.269
271.768
21.4
151.421
266.496
268.621
244.874
35.337
223.936
108.878
87.316
180.701
378.203
479.587
40.973
288.761
384.365
67.65
226.819
284.664
216.767
63.229
205.085
43.048
303.22
27.863
68.959
456.507
70.826
164.015
82.842
208.481
261.858
54.809
989.3
64.625
334.56
53.719
44.148
102.905
185.161
32.573
1231.86
1176.46
175.667
53.632
647.174
183.747
113.87
78.092
64.731
332.889
139.595
153.12
114.911
431.138
274.864
877.946
85.668
222.815
47.822
114.754
169.609
251.844
210.369
106.671
56.651
98.984
168.127
476.397
%i
i&n
)*
)-
i
i-1&n
'i&n(-i
i-'i-1&n(
1
35.337
0.0333
0.0000
-35.3037
35.3370 -35.3037
2
38.269
0.0667
0.0333
-38.2023
38.2357
3
40.973
0.1000
0.0667
-40.8730
40.9063
4
43.048
0.1333
0.1000
-42.9147
42.9480
5
44.148
0.1667
0.1333
-43.9813
44.0147
6
82.842
0.2000
0.1667
-82.6420
82.6753
7
102.905
0.2333
0.2000
-102.6717
102.7050
8
107.279
0.2667
0.2333
-107.0123
107.0457
9
113.87
0.3000
0.2667
-113.5700
113.6033
10
114.911
0.3333
0.3000
-114.5777
114.6110
11
119.609
0.3667
0.3333
-119.2423
119.2757
12
169.609
0.4000
0.3667
-169.2090
169.2423
13
174.847
0.4333
0.4000
-174.4137
174.4470
14
183.747
0.4667
0.4333
-183.2803
183.3137
15
185.161
0.5000
0.4667
-184.6610
184.6943
16
205.085
0.5333
0.5000
-204.5517
204.5850
17
208.481
0.5667
0.5333
-207.9143
207.9477
18
210.369
0.6000
0.5667
-209.7690
209.8023
19
223.936
0.6333
0.6000
-223.3027
223.3360
20
244.874
0.6667
0.6333
-244.2073
244.2407
21
251.844
0.7000
0.6667
-251.1440
251.1773
22
261.858
0.7333
0.7000
-261.1247
261.1580
23
274.864
0.7667
0.7333
-274.0973
274.1307
24
282.143
0.8000
0.7667
-281.3430
281.3763
25
288.761
0.8333
0.8000
-287.9277
287.9610
26
303.22
0.8667
0.8333
-302.3533
302.3867
27
384.365
0.9000
0.8667
-383.4650
383.4983
28
402.174
0.9333
0.9000
-401.2407
401.2740
29
431.138
0.9667
0.9333
-430.1713
430.2047
30
647.174
1.0000
0.9667
-646.1740
646.2073
646.2073
+n tablas 0.220 Como 0.22<646.2073 se aceptan los nume
1034.5
73.83
206.518
203.016
197.647
30.094
285.525
30.911
176.297
324.298
75.188
59.444
105.45
125.164
57.566
83.781
416.533
337.344
86.082
215.32
)
646.2073
os
os 8aos siguen una disribucion lognoral : e>ponencial.
20. A partir de la prueba de /olmo"orov-(mirnov, determine con un nivel de confianza de
%&0 qué tpo de disribución siguen los daos. *opruebe con a445i. 0.488
0.116
0.731
0.094
0.684
0.093
0.368
0.09
0.995
0.908
0.183
0.146
0.633
0.567
0.058
0.507
0.088
0.382
0.707
0.413
0.581
0.254
0.44
0.447
0.149
0.427
0.743
0.434
0.26
0.738
0.3
0.302
0.731
0.313
0.908
0.845
0.937
0.607
0.025
0.302
0.591
0.781
0.85
0.048
0.58
0.346
0.723
0.787
0.745
0.005
0.256
0.845
0.445
0.777
0.896
0.245
0.307
0.692
0.905
0.046
0.128
0.766
0.366
0.513
0.084
0.08
0.16
0.028
0.714
0.454
0.913
0.666
0.967
0.28
0.333
0.531
0.285
0.504
0.837
0.681
i
%i
i&n
i-1&n
'i&n(-i
i-'i-1&n(
1
0.005
0.0333
0.0000
0.0283
0.0050
2
0.08
0.0667
0.0333
-0.0133
0.0467
3
0.084
0.1000
0.0667
0.0160
0.0173
4
0.088
0.1333
0.1000
0.0453
-0.0120
5
0.116
0.1667
0.1333
0.0507
-0.0173
6
0.149
0.2000
0.1667
0.0510
-0.0177
7
0.16
0.2333
0.2000
0.0733
-0.0400
8
0.183
0.2667
0.2333
0.0837
-0.0503
9
0.256
0.3000
0.2667
0.0440
-0.0107
10
0.28
0.3333
0.3000
0.0533
-0.0200
11
0.307
0.3667
0.3333
0.0597
-0.0263
12
0.313
0.4000
0.3667
0.0870
-0.0537
13
0.333
0.4333
0.4000
0.1003
-0.0670
14
0.382
0.4667
0.4333
0.0847
-0.0513
15
0.427
0.5000
0.4667
0.0730
-0.0397
16
0.488
0.5333
0.5000
0.0453
-0.0120
17
0.591
0.5667
0.5333
-0.0243
0.0577
18
0.692
0.6000
0.5667
-0.0920
0.1253
19
0.707
0.6333
0.6000
-0.0737
0.1070
20
0.731
0.6667
0.6333
-0.0643
0.0977
21
0.731
0.7000
0.6667
-0.0310
0.0643
22
0.743
0.7333
0.7000
-0.0097
0.0430
23
0.745
0.7667
0.7333
0.0217
0.0117
24
0.781
0.8000
0.7667
0.0190
0.0143
25
0.85
0.8333
0.8000
-0.0167
0.0500
26
0.905
0.8667
0.8333
-0.0383
0.0717
27
0.908
0.9000
0.8667
-0.0080
0.0413
)*
)-
0.1003
0.1253
28
0.908
0.9333
0.9000
0.0253
0.0080
29
0.967
0.9667
0.9333
-0.0003
0.0337
30
0.995
1.0000
0.9667
0.0050
0.0283
+n tablas 0.220 Como 0.22<0.1253 se eca$a los numeo
os daos siguen una disribucion uni8ore : lognoral
0.761
0.42
0.78
0.139
0.251
0.87
0.314
0.423
0.608
0.078
0.535
0.61
0.335
0.194
0.302
0.833
0.213
0.373
0.209
0.626
)
0.1253
2 . . $etermine, con un nivel de confianza de 90%, i la variable aleatoria repreentada por la
i"uiente tabla de frecuencia i"ue una ditribuci!n e5ponencial e5ponencial con media .
nte nte; ;al alo o
ecu ecuen enci cia a
0--1
29
1--2
18
2--3
18
3--4
12
4--5
8
5--6
3
6--7
2
7--8
5
8--9
3
9--10
0
10--=
2
35 30 25 20 15 10 5 0 0--1
1--2
2--3
3--4
4--5
0: +/ponencial 1: ta )istibucion
9neralo 0--1 1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--=
Oi 29 18 18 12 8 3 2 5 3 0 2
6oi 0.29 0.18 0.18 0.12 0.08 0.03 0.02 0.05 0.03 0 0.02
Doal
100
1
+l ;alo estadis>co es C#0.3947
6OAi 0.29 0.47 0.65 0.77 0.85 0.88 0.9 0.95 0.98 0.98 1
6EAi 0.6321 0.8647 0.9502 0.9817 0.9933 0.9975 0.9991 0.9997 0.9999 1 1
B6OAi - 6EAiC 0.3421 0.3947 0.3002 0.2117 0.1433 0.1175 0.0991 0.0497 0.0199 0 .0 2 0
C
0.3947
5--6
6--7
)0.1?100 # 0.1220 @e eca$a la ipotesis de ue los numeos siuen una distibucion +/ponencial.
7--8 7--8
8--9 8--9 9--1 9--10 0 10--= 10--=
22. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo
dato emplee la prueba de Anderon-$arlin" 6 compruebe con (tat))*it.
nte;alo
ecuencia
18
=-12
3
12.0-12.5
4
16
12.5-13.0
3
14
13.0-13.5
6
12
13.5-14.0
8
10
14.0-14.5
15
14.5-15.0
12
15.0-15.5
13
15.5-16.0
7
4
16.0-16.5
16
2
16.5-17.0
7
0
17.0-=
6
8 6
= 2 0 5 5 0 0 0 5 0 5 5 . . . . . . . . . . 1 3 3 4 5 6 7 2 5 6 0 . = 1 1 1 1 4 1 1 1 1 1 1 7 1 5 0 0 5 5 5 0 5 0 0 . . . . . . . . . . 2 3 4 4 5 6 2 3 5 6 1 1 1 1 1 1 1 1 1 1
2#. $etermine, con un nivel de confianza de 9'%, qué tipo de ditribuci!n
siguen los daos. tlice la prueba *+i-*uadrada,
9neralo =--150
5recuencia 0
150--151
13
151--152
8
152--153
11
153--154
15
154--155
7
155--156
8
156--157
9
157--158
11
158--159
10
159--160
8
160--=
0
1 2 3 4 5 6 7 8 9 10
11 12 Doal
i =--150 150--151 151--152 152--153 153--154 154--155 155--156 156--157 157--158 158--159 159--160 160--=
Oi 0 13 8 11 15 7 8 9 11 10 8 0
Ei 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33
((Ei-Oi)^2)/Ei 8.330 2.618 0.013 0.856 5.341 0.212 0.013 0.054 0.856 0.335 0.013 8.330
1&&
%%.%"
2".%#1
+n tablas 4.575 con ados de libetad de 11 con un 95A de conBabilidad. o lo tanto como 4.575 <26.971 no se aceptan los numeos como numeos aleatoios.
2. $etermine con un nivel de confianza de 90% r qué tipo de ditribuci!n
siguen los daos eplee la prueba *+i-*uadrada.
9neralo 0--2
5recuencia 39
2--4
57
4--6
47
6--8
23
8--10
18
10--12
9
12--14
2
14--16
3
16--18
1
18--20
1
20--22
0 200
1
2
3
4
5 6 7 8 9 10
11 Doal
i 0--2 2--4 4--6 6--8 8--10 10--12 12--14 14--16 16--18 18--20 20--22
Oi 39 57 47 23 18 9 2 3 1 1 0
Ei 18.18 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33
((Ei-Oi)^2)/Ei 23.843 284.366 179.516 25.835 11.226 0.054 4.810 3.410 6.450 6.450 8.330
2&&
1&1.$
!!.2%1
os daos siguen una disribucion lognoral.
2'. Utilice la prueba de /olmo"orov-(mirnov para determinar con un nivel de confianza de 9'%
4 4 4 3 2 7 5 6 3 1
5 6 4 4 5 2 5 4 3 2
3 4 3 5 3 4 5 6 2 5
5 3 3 2 4 4 2 6 5 2
5 5 3 3 4 2 4 2 3 3
4 2 2 4 1 4 4 4 5 1
3 2 2 3 4 1 5 4 1 5
2 3 3 3 5 5 4 2 3 3
4 3 2 5 4 4 4 2 2 2
3 4 3 3 5 4 1 2 4 5 00
;o)
7ntervalo
=i
+oi +=Ai
+&Ai
+=Ai - +&Ai
0 2 4
-
1 3 5
6 0.06 0.06 0.09792 43 0.43 0.49 0.37459 46 0.46 0.95 0.61319
-0.0379 0.1154 0.3368
6
-
α
5 0.05 1.00 1.00000 00 .00 c>
0.0000 0.#
Tomando como base: α: 1.38 ß: 5.19
0.136
&$7A U&(38A :A87A;
qué tipo de ditribuci!n i"uen lo dato.
3.49 1.7676
50 45 40 35 30 25 20 15 10 5 0 1 0
3 2
5 4
α 6
24. $etermine, con un nivel de confianza de 90 %, qué tipo de ditribuci!n i"uen lo da to uando la
1 0 0 1 1 0 1 1 1 0
0 0 0 0 0 1 2 0 0 0 H0 H1
0 0 1 1 1 1 0 1 0 0
1 1 0 2 2 0 1 2 0 1
0 0 0 1 0 0 1 0 0 0
0 0 0 1 0 1 1 0 0 1
1 0 0 1 1 1 0 1 0 2
0 0 0 0 1 2 1 2 0 1
Es una distibuci!n "oisson Es ota distibuci!n
media> 0.5100 varianza> 0.39384 n> 100 m> 3 ?> 5 #
0 0 1 0 0 1 0 1 1 0
0 0 1 0 1 0 1 0 0 0
7ntervalo 0 1 2
=i 56 37 7
+=i 0.56 0.37 0.07
+=Ai 0.56 0.93 1
60
50
40
30
c
$ 0.0',00 0.0405 $ 0.1360
20
10
%o &odemos ec'a(a )a 'i&otesis 0 0
1
+&Ai 0.6005 0.9067 0.9848 c
prueba de /olmo"orov-(mirnov
@+=Ai - +&Ai@ 0.0405 0.0233 0.0152 0.0405
2
0.4119 0.3210 0.3063
2. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo dato ue la prue
5 3 11 4 5 1 7 4 4 5
3 2 5 7 4 4 6 5 5 7
2 4 9 7 5 5 4 5 4 3
4 6 3 3 3 4 6 2 6 7
6 2 7 3 6 6 4 4 2 0
4 8 4 4 4 2 5 2 5 4
3 6 7 8 4 5 4 3 7 5
2 3 2 4 3 5 2 6 5 7
2 0 3 3 7 3 2 7 1 3 4 8 2 5 3 5 4 6 5 11 ;o) 00
&$7A U&(38A :A87A;
45 40 35 30 25 20 15
7ntervalo 0 2 4 6 8 10
-
1 3 5 7 9 11
12
-
α
=i 4 29 40 21 4 2
+oi +=Ai 0.04 0.29 0.40 0.21 0.04 0.02
0 0.00 00 .00
Tomando como base: α: 1.38 ß: 5.19
+&Ai
+=Ai - +&Ai
0.09792 0.37459 0.61319 0.77934 0.88206 0.94037
-0.0579 -0.0446 0.1168 0.1607 0.0979 0.0596
1.00 1.00000 c>
0.0000 0.##2'
0.04 0.33 0.73 0.94 0.98 1.00
0.12
10 5 0
a de /olmo"orov-(mirnov 6 compruebe con (tat))*it
4.46 4.2913
0-1 2-3 4-5 6-7 8-9 10 - 11 12 - α
(3A3))*73
21. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo da to. Ue la prueba de /o
10 9 8 10 14 15 11 6 8 7 8 9 9 12 15 7 4 12 13 7 12 11 14 9 9 14 11 5 11 8 5 9 9 9 8 4 7 9 13 10
H0 H1
9 8 13 10 12 10 5 10 10 8 10 5 5 9 14 12 7 7 18 5 13 14 10 10 11 2 10 15 11 11 7 10 9 8 13 12 11 6 9 10
16 9 3 11 9 10 4 13 15 15
Es una distibuci!n "oisson Es ota distibuci!n > 9.9000 > 10.45455 n> 100 m> 9 ?> 5 #
13 12 13 10 10 15 15 5 15 7
7ntervalo 1 - 2 3 - 4 5 - 6 7 - 8 9 - 10 11 - 12 13 - 14 15 - 16 17 - 18
=i 1 4 9 16 31 16 13 9 1
+=i 0.01 0.04 0.09 0.16 0.31 0.16 0.13 0.09 0.01
+=Ai 0.01 0.05 0.14 0.3 0.61 0.77 0.9 0.99 1
+&Ai 0.0030 0.0312 0.1366 0.3442 0.5955 0.8009 0.9216 0.9750 0.9935 c
35 30 25 20 15
c
$ 0.0',00 0.0442 $ 0.1360
10 5
%o &odemos ec'a(a )a 'i&otesis 0 2
4
6
8
10
12
14
lmo"orov-(mirnov 6 compruebe con la herramienta (tat))*it.
(3A3))*73 @+=Ai - +&Ai@ 0.0070 0.0188 0.0034 0.0442 0.0145 0.0309 0.0216 0.0150 0.0065 0.0442
16
18
29. A partir de la prueba Chi-Cuadrada, determine con un nivel de confianza de 90% qué tipo de ditribuci!n i"
2
1
2
0
1
1
2
1
0
1
1 1 2 1 2 1 1 0 1
2 1 0 1 0 2 1 1 2
2 0 0 1 3 3 1 0 0
1 2 1 1 2 0 0 1 0
0 2 2 2 0 0 2 0 1
0 0 1 1 0 0 0 1 1
0 0 0 1 1 0 0 1 0
0 2 0 1 2 1 0 2 0
1 1 2 2 1 1 3 3 2
1 0 2 0 1 0 1 2 0
7ntervalo 0 1 2 3
Es una distibuci!n "oisson Es ota distibuci!n
media> 0.9600 varianza> 0.74586 n> 100 intervalo> 4 nivel confianza ?> 10 #
35 30 25 20 15 10 5
c 2.4305
$
D 0.,# 6.2514
%o &odemos ec'a(a )a 'i&otesis
+5B
35 0.3829 38 0.3676 23 0.1764 4 0.0565 100 0.983367
40 H0 H1
=i
0 0
en lo dato
&i5B
&i-=iBDE&i
38.2893 36.7577 17.6437 5.6460 C>
1
0.2826 0.0420 1.6261 0.4799 2.4305
2
3
#0. $etermine, con un nivel de confianza de 90% qué tipo de ditribuci!n i"uen lo dato emplee la prueba Chi-Cu
0 0 0 0 1 0
0 0 1 0 0 0
0 1 1 0 0 0
0 0 0 0 1 0
0 1 0 0 0 0
0 0 1 0 0 1
0 1 1 0 0 0
1 0 1 0 1 0
0 0 1 0
1 0 1 1
1 0 0 0
1 0 0 0
0 0 0 0
0 0 1 0
1 1 0 0
0 0 0
1
0 1 0 0 1 1 0 0 0 0
0 0 1 0 0 1 0 0 0 0
7ntervalo 0 1
80
=i 72 28
+5B 0.7000 0.3000 1.0000
&i 70.0000 30.0000 C>
72
70 60 50
H0 H1
Es una distibuci!n *inomia) Es ota distibuci!n n> 100 m> 2 ?> 10 #
40 28
30 20 10 0 1
c
D 0., 0.1905 $ 2.7055
%o &odemos ec'a(a )a 'i&otesis
2
adrada.
&i-=iBDE&i 0.0571 0.1333 0.1905
#. $etermine, con un nive7 de confianza de 9'% , qué tipo de ditribuci!n i"uen lo dato emplee la prueba Chi
8 8 6 7 6 4 6 5 5 4
H0 H1
8 8 8 5 8 5 5 7 6 4
6 5 6 8 8 6 7 6 6 4
6 4 8 7 5 5 4 6 5 4
4 6 7 6 6 8 7 5 8 7
7 5 5 8 7 4 8 5 4 7
Es una distibuci!n "oisson Es ota distibuci!n
5 4 4 5 4 5 8 6 8 8
4 4 6 5 4 8 4 5 5 8
6 6 5 4 7 4 5 5 6 5
6 4 6 7 6 8 4 5 7 7
7ntervalo 4 5 6 7 8
30
20 15 10 5
c 17.7777
+
D 0.0', 9.4877
,e ec'a(a )a 'i&otesis
+5B
21 0.1401 24 0.1642 22 0.1604 14 0.1342 19 0.0983 100 0.697210
25 media> 5.8600 varianza> 1.98020 n> 100 intervalo> 5 nivel confianza ?> 5 #
=i
0 4
-cuadrada
&i5B
&i-=iBDE&i
14.0092 16.4188 16.0357 13.4242 9.8332 C>
3.4885 3.5005 2.2184 0.0247 8.5456 17.7777
6
7
8
#2. Utilce la prueba Chi-cuadrada para determinar, con un nivel de confianza de 9'%, qué tipo de ditribuci!n
1 2 1 0 0 0 0 0 0 1
2 1 1 1 1 0 0 2 2 1
0 1 2 0 1 2 0 2 2 0
1 1 1 0 1 0 1 1 0 1
2 1 1 1 0 0 1 0 1 0
1 2 0 0 0 0 0 1 3 0
0 0 0 2 0 2 0 2 1 1
0 2 0 0 0 0 1 1 2 1
1 2 1 1 1 1 0 2 0 2
2 1 1 2 0 2 2 1 1 2
7ntervalo 0 1 2 3
=i 38 38 23 1 100
+5B 0.4190 0.3645 0.1586 0.0460 0.9880
&i &i-=iBDE&i 41.8952 0.3621 36.4488 0.0660 15.8552 3.2196 4.5980 2.8155 C> 6.4633
40
H0 H1
Es una distibuci!n "oisson Es ota distibuci!n
35
> 0.8700 > 0.63949 n> 100 m> 4 ?> 5 #
25
30
20 15 10 5 0
c
D 0.0',# 6.4633 $ 7.8147
%o &odemos ec'a(a )a 'i&otesis
0
1
2
i"uen 7o dato. Compruebe con (tat)fit
3
(3A3))*73
##. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo dato. Utilice la prueba de
4 5 3 3 5 4 5 3 3 5
5 5 3 5 5 4 5 4 4 5
4 4 4 5 4 5 5 4 3 3
4 4 5 5 5 3 3 5 4 4
4 3 3 5 4 3 5 3 3 5
4 5 5 3 5 3 3 3 5 4
5 5 4 5 5 5 5 4 3 5
4 4 4 5 4 4 4 2 5 5
5 4 4 3 4 5 4 5 5 5
3 5 5 3 4 4 4 5 3 4
7ntervalo 2 3 4 5
=i
+5B
1 0.1343 23 0.1867 34 0.1947 42 0.1624 100 0.678140
45
H0 H1
Es una distibuci!n "oisson Es ota distibuci!n
40 35 30
media> 4.1700 varianza> 0.66778 n> 100 intervalo> 4 nivel confianza ?> 10 #
25 20 15 10 5 0 2
c 64.2393
+
D 0.,# 6.2514
,e ec'a(a )a 'i&otesis
3
olmo"orov-(mirnov 6 compruebe con (tat))*it
&i5B
&i-=iBDE&i
13.4349 18.6745 19.4682 16.2364 C>
4
11.5093 1.0019 10.8472 40.8809 64.2393
5
(3A3))*73
#. $etermine, con un nivel de confianza de 9'%, qué tipo de ditribuci!n i"uen lo dato emplee la prueba Chi-cu
H0 H1
Es una distibuci!n "oisson Es ota distibuci!n > 1.9900 > n> 100 m> 6 ?> 5 #
c
D 0.0',' 3.7647 $ 11.0705
%o &odemos ec'a(a )a 'i&otesis
,uma 0 29 62 42 36 30 199
7ntervalo 0 2 # '
=i 29 # 9 4
+5B 0.1367 0.272 0.2707 0.1795 0.0893 0.0355 0.9838
&i 13.66954 27.20239 27.06638 17.95403 8.93213 3.554988
&i-=iBDE&i 0.521338 0.118791 0.571683 0.870799 0.000516 1.681605 3.764732
35 30 25 20 15 10 5 0 0
1
2
3
4
5
adrada 6 compruebe con (tat) )*it
(3A3))*73
#'. $etermine, con un nivel de confianza de 90%, qué tipo de ditribuci!n i"uen lo dato ue la prueba Chi-c
0 6 1 2 0 4 1 0 7 0
H0 H1
1 0 2 2 1 2 1 5 0 0
0 0 1 2 0 0 0 0 0 5
2 0 0 0 0 1 3 0 2 9
2 3 1 1 2 8 2 1 0 1
1 1 4 0 1 0 0 1 2 2
0 4 0 0 0 2 0 1 0 4
2 0 0 0 0 0 0 0 2 0
5 0 0 4 9 6 3 1 0 0
0 2 1 3 3 1 1 0 2 0
7ntervalo 0 1 2 3 4 5 6 7 8 9
+5B
44 0.2254 20 0.3358 17 0.2502 5 0.1243 5 0.0463 3 0.0138 2 0.0034 1 0.0007 1 0.0001 2 0.0000 100 0.999996
Es una distibuci!n "oisson Es ota distibuci!n
media> 1.4900 varianza> 4.17162 n> 100 intervalo> 10 nivel confianza ?> 10 #
=i
50 45 40 35 30 25 20 15 10 5
c 1901.6251
+
D 0.,9 14.6837
,e ec'a(a )a 'i&otesis
0 0
1
2
3
4
adrada. Compruebe con (tat))*it
&i5B
&i-=iBDE&i
22.5373 20.4394 33.5805 5.4922 25.0175 2.5694 12.4254 4.4374 4.6284 0.0298 1.3793 1.9044 0.3425 8.0207 0.0729 11.7888 0.0136 71.6562 0.0022 1775.2867 C> 1901.6251
5
6
7
8
9
(3A3))*73
#4. &mplee la prueba Ch i cuadrada para determinar, con un nivel de confianza de 90%, qué tipo de ditrib
25 20 15 10 5 0 0
H0 H1
1
2
3
Es una distibuci!n eometica Es ota distibuci!n > > p> n> ?>
3.7700 0.5 100 5 #
c D 0.0',99 12841.1769 + 123.2252 ,e ec'a(a )a 'i&otesis
H0 H1
Es una distibuci!n eometica Es ota distibuci!n
media> varianza> p> n> ?>
1.3200 0.5 100 5 #
c D 0.0',99 82.7000 $ 123.2252 %o &odemos ec'a(a )a 'i&otesis
4
5
6
7
8
9
10
11
12
13
14
7ntervalo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
=i 21 17 14 9 8 6 6 1 4 4 1 0 1 2 6
+5B 0.5000 0.2500 0.1250 0.0625 0.0313 0.0156 0.0078 0.0039 0.0020 0.0010 0.0005 0.0002 0.0001 0.0001 0.0000 1.0000
&i 50.0000 25.0000 12.5000 6.2500 3.1250 1.5625 0.7813 0.3906 0.1953 0.0977 0.0488 0.0244 0.0122 0.0061 0.0031
7ntervalo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
=i 21 17 14 9 8 6 6 1 4 4 1 0 1 2 6
+5B 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 0.06666667 1.0000
&i 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667
ci!n i"uen lo dato.
&i-=iBDE&i 16.82 2.56 0.18 1.21 7.605 12.6025 34.86125 0.950625 74.1153125 155.93765625 18.528828125 0.0244140625 79.9322070313 651.366103516 11784.4830518 12841.1769482
&i-=iBDE&i 30.8166666667 16.0166666667 8.0666666667 0.8166666667 0.2666666667 0.0666666667 0.0666666667 4.8166666667 1.0666666667 1.0666666667 4.8166666667 6.6666666667 4.8166666667 3.2666666667 0.0666666667 82.7
#1. $etermine, con un nivel de confianza de 90%, i lo dato e ditribu6en de acuerdo con una ditribuci!n u
H0 H1
Es una distibuci!n "oisson Es ota distibuci!n
media> 3.7600 varianza> i 1 / 6 n> 100 m> 6 ?> 5 #
,uma 13 28 54 56 105 120 376
7ntervalo 2 # ' 4
=i # 1 2 20
+5B 0.16667 0.16667 0.16667 0.16667 0.16667 0.16667 1
25
c
D 0.0',' 3.5600 $ 11.0705
%o &odemos ec'a(a )a 'i&otesis
20
15
10
5
0 1
2
3
4
iforme dicreta -4B
&i 16.66667 16.66667 16.66667 16.66667 16.66667 16.66667
5
&i-=iBDE&i 0.8066666667 0.4266666667 0.1066666667 0.4266666667 1.1266666667 0.6666666667 3.56
6
. Utilizando cualquier hoFa de cGlculo,"enere 00 variable aleatoria aB e5ponencialmente ditribuida con H > #. b) normalmente ditribuida con media 0 6 varianza . c) uniformemente ditribuida con lmite inferior i"ual a 0 6 limite uperior i"ual a #0. d) trian"u7Grmente ditribuida con lmite inferior > 5, valor ma probable > 0 6 limite uperior > '. e) con ditribuci!n binomial 6 parGmetro N= 5,p = 0.#, q = 0. con ditribuci!n de +oion, con A - #, f) con ditribuci!n de +oion, con H > #. Compruebe con (tat) *it i la variable aleatoria "enerada i"uen la ditribuci!n de probabilidad que e eperara de ella.
Ienerado 0.0190 0.0248 0.0321 0.0323 0.0469 0.0561 0.0641 0.0783 0.0935 0.1154 0.1162 0.1173 0.1357 0.1498 0.1503 0.1701 0.1965 0.2168 0.2271 0.2281 0.2314 0.2377 0.2430 0.2475 0.2516 0.2649 0.2772 0.2814 0.2816 0.2897 0.2905 0.2907 0.3031 0.3225 0.3315 0.3383
a 2.83389 2.78517 2.72442 2.72254 2.60651 2.53503 2.47488 2.37226 2.26593 2.12181 2.11732 2.11024 1.99692 1.91425 1.91099 1.80111 1.66392 1.56543 1.51790 1.51325 1.49862 1.47037 1.44718 1.42783 1.41038 1.35512 1.30592 1.28977 1.28900 1.25805 1.25503 1.25425 1.20851 1.14011 1.10979 1.08736
b 0.05537 0.07161 0.09186 0.09249 0.13116 0.15499 0.17504 0.20925 0.24469 0.29273 0.29423 0.29659 0.33436 0.36192 0.36300 0.39963 0.44536 0.47819 0.49403 0.49558 0.50046 0.50988 0.51761 0.52406 0.52987 0.54829 0.56469 0.57008 0.57033 0.58065 0.58166 0.58192 0.59716 0.61996 0.63007 0.63755
0.00629 0.00632 0.00635 0.00635 0.00642 0.00646 0.00650 0.00656 0.00663 0.00673 0.00674 0.00674 0.00683 0.00690 0.00690 0.00700 0.00713 0.00723 0.00728 0.00728 0.00730 0.00733 0.00736 0.00738 0.00740 0.00747 0.00754 0.00756 0.00756 0.00760 0.00760 0.00761 0.00767 0.00777 0.00782 0.00786
f 0.02004 0.01961 0.01907 0.01906 0.01807 0.01748 0.01699 0.01619 0.01538 0.01434 0.01431 0.01426 0.01348 0.01293 0.01291 0.01220 0.01137 0.01080 0.01053 0.01050 0.01042 0.01027 0.01014 0.01004 0.00994 0.00965 0.00940 0.00932 0.00931 0.00916 0.00914 0.00914 0.00891 0.00858 0.00844 0.00833
0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979
e 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936
0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807
0.3485 0.3669 0.3836 0.3986 0.4038 0.4039 0.4094 0.4109 0.4603 0.4826 0.4938 0.4938 0.4945 0.4973 0.5175 0.5402 0.5511 0.5524 0.5750 0.5780 0.6004 0.6110 0.6163 0.6240 0.6351 0.6576 0.6708 0.6735 0.6789 0.7261 0.7447 0.7514 0.7650 0.7811 0.7935 0.8089 0.8359 0.8363 0.8408 0.8621 0.8744 0.8746 0.8754 0.8846 0.8849 0.8965 0.9009 0.9102 0.9148 0.9311 0.9355
1.05446 0.99799 0.94918 0.90750 0.89343 0.89299 0.87849 0.87458 0.75399 0.70518 0.68193 0.68192 0.68053 0.67491 0.63507 0.59339 0.57417 0.57194 0.53459 0.52978 0.49530 0.47981 0.47227 0.46151 0.44636 0.41721 0.40100 0.39783 0.39142 0.33975 0.32124 0.31483 0.30228 0.28805 0.27749 0.26498 0.24435 0.24408 0.24080 0.22587 0.21773 0.21759 0.21709 0.21112 0.21098 0.20374 0.20105 0.19557 0.19283 0.18367 0.18127
0.64851 0.66734 0.68361 0.69750 0.70219 0.70234 0.70717 0.70847 0.74867 0.76494 0.77269 0.77269 0.77316 0.77503 0.78831 0.80220 0.80861 0.80935 0.82180 0.82341 0.83490 0.84006 0.84258 0.84616 0.85121 0.86093 0.86633 0.86739 0.86953 0.88675 0.89292 0.89506 0.89924 0.90398 0.90750 0.91167 0.91855 0.91864 0.91973 0.92471 0.92742 0.92747 0.92764 0.92963 0.92967 0.93209 0.93298 0.93481 0.93572 0.93878 0.93958
0.00791 0.00801 0.00811 0.00819 0.00822 0.00822 0.00825 0.00826 0.00854 0.00867 0.00874 0.00874 0.00874 0.00876 0.00888 0.00902 0.00908 0.00909 0.00923 0.00925 0.00939 0.00946 0.00949 0.00954 0.00961 0.00976 0.00984 0.00986 0.00990 0.01021 0.01034 0.01039 0.01048 0.01059 0.01068 0.01079 0.01098 0.01098 0.01102 0.01117 0.01126 0.01126 0.01127 0.01134 0.01134 0.01143 0.01146 0.01153 0.01156 0.01169 0.01172
0.00818 0.00793 0.00771 0.00753 0.00747 0.00747 0.00741 0.00739 0.00690 0.00670 0.00661 0.00661 0.00661 0.00659 0.00644 0.00628 0.00621 0.00620 0.00607 0.00605 0.00593 0.00587 0.00585 0.00581 0.00576 0.00566 0.00560 0.00559 0.00557 0.00540 0.00534 0.00532 0.00528 0.00523 0.00520 0.00516 0.00510 0.00509 0.00508 0.00504 0.00501 0.00501 0.00501 0.00499 0.00499 0.00497 0.00496 0.00495 0.00494 0.00491 0.00490
0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979
0.14936 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979
0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807
0.9403 0.9508 0.9524 0.9585 0.9610 0.9629 0.9680 0.9716 0.9724 0.9725 0.9816 0.9907 0.9995
0.17868 0.17311 0.17230 0.16915 0.16789 0.16692 0.16439 0.16264 0.16223 0.16220 0.15785 0.15358 0.14957
0.94044 0.94230 0.94257 0.94362 0.94404 0.94436 0.94520 0.94579 0.94592 0.94593 0.94738 0.94881 0.95014
0.01176 0.01184 0.01185 0.01190 0.01192 0.01193 0.01197 0.01200 0.01201 0.01201 0.01208 0.01215 0.01222
0.00489 0.00488 0.00488 0.00487 0.00486 0.00486 0.00485 0.00485 0.00485 0.00485 0.00483 0.00482 0.00481
0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979
0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979
0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807