problemas impares unidad 2 de simulacion
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PROBLEMAS1.- Determine el ciclo o periodo de vida de los siguientes generadores congruencialesA) B)Xo= 21 Xo= 7a= 21 a= 13c= 15 c= 9m= 31 m= 128
Xi+1=(aXi+c)mod(m) ri=Xi/(m-1) Xi+1=(aXi+c)mod(m) ri=Xi/(m-1)22 0.73333333 100 0.7874015712 0.4 29 0.2283464619 0.63333333 2 0.0157480311 0.36666667 35 0.2755905529 0.96666667 80 0.62992126
4 0.13333333 25 0.196850396 0.2 78 0.61417323
17 0.56666667 127 10 0 124 0.97637795
15 0.5 85 0.6692913420 0.66666667 90 0.70866142
1 0.03333333 27 0.212598435 0.16666667 104 0.81889764
27 0.9 81 0.6377952824 0.8 38 0.299212623 0.76666667 119 0.93700787
2 0.06666667 20 0.1574803126 0.86666667 13 0.1023622
3 0.1 50 0.3937007916 0.53333333 19 0.149606310 0.33333333 0 0
8 0.26666667 9 0.0708661428 0.93333333 126 0.9921259814 0.46666667 111 0.8740157530 1 44 0.3464566925 0.83333333 69 0.5433070913 0.43333333 10 0.07874016
9 0.3 11 0.0866141718 0.6 24 0.1889763821 0.7 65 0.5118110222 0.73333333 86 0.67716535
103 0.8110236268 0.53543307
125 0.9842519798 0.77165354
3 0.0236220548 0.37795276
121 0.9527559146 0.36220472
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95 0.748031592 0.7244094553 0.4173228358 0.45669291
123 0.9685039472 0.5669291349 0.38582677
6 0.0472440987 0.68503937
116 0.91338583109 0.85826772
18 0.14173228115 0.90551181
96 0.75590551105 0.82677165
94 0.7401574879 0.6220472412 0.0944881937 0.29133858
106 0.83464567107 0.84251969120 0.94488189
33 0.2598425254 0.4251968571 0.5590551236 0.2834645793 0.7322834666 0.5196850499 0.7795275616 0.1259842589 0.700787414 0.1102362263 0.4960629960 0.4724409421 0.1653543326 0.2047244191 0.7165354340 0.3149606317 0.13385827
102 0.8031496155 0.4330708784 0.6614173277 0.60629921
114 0.897637883 0.6535433164 0.5039370173 0.5748031562 0.48818898
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47 0.37007874108 0.8503937
5 0.0393700874 0.5826771775 0.5905511888 0.69291339
1 0.0078740222 0.1732283539 0.30708661
4 0.0314960661 0.4803149634 0.2677165467 0.52755906
112 0.8818897657 0.4488189
110 0.8661417331 0.2440944928 0.22047244
117 0.92125984122 0.96062992
59 0.464566938 0.06299213
113 0.8897637870 0.551181123 0.1811023652 0.4094488245 0.3543307182 0.6456692951 0.401574832 0.251968541 0.3228346530 0.2362204715 0.1181102476 0.5984252
101 0.7952755942 0.3307086643 0.3385826856 0.4409448897 0.76377953
118 0.929133867 0.05511811
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C) D)Xo= 23 Xo= 17a= 17 a= 121m= 31 m= 256
X r X r19 0.63333333 138 0.5411764713 0.43333333 3 0.01176471
4 0.13333333 124 0.486274516 0.2 245 0.960784319 0.3 110 0.43137255
29 0.96666667 231 0.9058823528 0.93333333 96 0.3764705911 0.36666667 217 0.85098039
1 0.03333333 82 0.3215686317 0.56666667 203 0.7960784310 0.33333333 68 0.2666666715 0.5 189 0.74117647
7 0.23333333 54 0.2117647126 0.86666667 175 0.68627451
8 0.26666667 40 0.1568627512 0.4 161 0.6313725518 0.6 26 0.1019607827 0.9 147 0.5764705925 0.83333333 12 0.0470588222 0.73333333 133 0.52156863
2 0.06666667 254 0.996078433 0.1 119 0.46666667
20 0.66666667 240 0.9411764730 1 105 0.4117647114 0.46666667 226 0.8862745121 0.7 91 0.3568627516 0.53333333 212 0.8313725524 0.8 77 0.30196078
5 0.16666667 198 0.7764705923 0.76666667 63 0.24705882
184 0.7215686349 0.19215686
170 0.6666666735 0.1372549
156 0.6117647121 0.08235294
142 0.556862757 0.02745098
128 0.50196078
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249 0.97647059114 0.44705882235 0.92156863100 0.39215686221 0.86666667
86 0.3372549207 0.81176471
72 0.28235294193 0.75686275
58 0.22745098179 0.70196078
44 0.17254902165 0.64705882
30 0.11764706151 0.59215686
16 0.0627451137 0.5372549
2 0.00784314123 0.48235294244 0.95686275109 0.42745098230 0.90196078
95 0.37254902216 0.84705882
81 0.31764706202 0.79215686
67 0.2627451188 0.7372549
53 0.20784314174 0.68235294
39 0.15294118160 0.62745098
25 0.09803922146 0.57254902
11 0.04313725132 0.51764706253 0.99215686118 0.4627451239 0.9372549104 0.40784314225 0.88235294
90 0.35294118211 0.82745098
76 0.29803922197 0.77254902
62 0.24313725183 0.71764706
48 0.18823529
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169 0.662745134 0.13333333
155 0.6078431420 0.07843137
141 0.552941186 0.02352941
127 0.49803922248 0.97254902113 0.44313725234 0.91764706
99 0.38823529220 0.8627451
85 0.33333333206 0.80784314
71 0.27843137192 0.75294118
57 0.22352941178 0.69803922
43 0.16862745164 0.64313725
29 0.11372549150 0.58823529
15 0.05882353136 0.53333333
1 0.00392157122 0.47843137243 0.95294118108 0.42352941229 0.89803922
94 0.36862745215 0.84313725
80 0.31372549201 0.78823529
66 0.25882353187 0.73333333
52 0.20392157173 0.67843137
38 0.14901961159 0.62352941
24 0.09411765145 0.56862745
10 0.03921569131 0.51372549252 0.98823529117 0.45882353238 0.93333333103 0.40392157224 0.87843137
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89 0.34901961210 0.82352941
75 0.29411765196 0.76862745
61 0.23921569182 0.71372549
47 0.18431373168 0.65882353
33 0.12941176154 0.60392157
19 0.0745098140 0.54901961
5 0.01960784126 0.49411765247 0.96862745112 0.43921569233 0.91372549
98 0.38431373219 0.85882353
84 0.32941176205 0.80392157
70 0.2745098191 0.74901961
56 0.21960784177 0.69411765
42 0.16470588163 0.63921569
28 0.10980392149 0.58431373
14 0.05490196135 0.52941176
0 0121 0.4745098242 0.94901961107 0.41960784228 0.89411765
93 0.36470588214 0.83921569
79 0.30980392200 0.78431373
65 0.25490196186 0.72941176
51 0.2172 0.6745098
37 0.14509804158 0.61960784
23 0.09019608144 0.56470588
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9 0.03529412130 0.50980392251 0.98431373116 0.45490196237 0.92941176102 0.4223 0.8745098
88 0.34509804209 0.81960784
74 0.29019608195 0.76470588
60 0.23529412181 0.70980392
46 0.18039216167 0.65490196
32 0.1254902153 0.6
18 0.07058824139 0.54509804
4 0.01568627125 0.49019608246 0.96470588111 0.43529412232 0.90980392
97 0.38039216218 0.85490196
83 0.3254902204 0.8
69 0.27058824190 0.74509804
55 0.21568627176 0.69019608
41 0.16078431162 0.63529412
27 0.10588235148 0.58039216
13 0.05098039134 0.5254902255 1120 0.47058824241 0.94509804106 0.41568627227 0.89019608
92 0.36078431213 0.83529412
78 0.30588235199 0.78039216
64 0.25098039
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185 0.725490250 0.19607843
171 0.6705882436 0.14117647
157 0.6156862722 0.08627451
143 0.560784318 0.03137255
129 0.50588235250 0.98039216115 0.45098039236 0.9254902101 0.39607843222 0.87058824
87 0.34117647208 0.81568627
73 0.28627451194 0.76078431
59 0.23137255180 0.70588235
45 0.17647059166 0.65098039
31 0.12156863152 0.59607843
17 0.06666667
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E)Xo= 21X1= 43a0= 21a1= 15m= 64
X6262
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3.-y X r intervalo Oi Ei=n/m
32890225 8902 0.8902 [0,00-0,10) 7 5 0.879245604 2456 0.2456 [0,10-0,20) 7 5 0.8
6031936 319 0.0319 [0,20-0,30) 9 5 3.2101761 176 0.0176 [0,30-0,40) 5 5 0
30976 3096 0.3096 [0,40-0,50) 3 5 0.89585216 5852 0.5852 [0,50-0,60) 7 5 0.8
34245904 2459 0.2459 [0,60-0,70) 3 5 0.86046681 466 0.0466 [0,70-0,80) 2 5 1.8
217156 1715 0.1715 [0,80-0,90) 3 5 0.82941225 9412 0.9412 [0,90-1,00) 5 5 0
88585744 5857 0.5857 9.834304449 3044 0.3044 62.031
9265936 2659 0.26597070281 702 0.0702 la chi cuadrada de calculada es menor que la de tablas por lo tanto se acepta
492804 9280 0.92886118400 1184 0.1184
1401856 4018 0.401816144324 1443 0.1443
2082249 822 0.0822675684 7568 0.7568
57274624 2746 0.27467540516 5405 0.5405
29214025 2140 0.2144579600 5796 0.5796
33593616 5936 0.593635236096 2360 0.236
5569600 5696 0.569632444416 4444 0.444419749136 7491 0.749156115081 1150 0.115
1322500 3225 0.322510400625 4006 0.400616048036 480 0.048
230400 3040 0.3049241600 2416 0.24165837056 8370 0.837
70056900 569 0.0569323761 2376 0.2376
5645376 6453 0.645341641209 6412 0.641241113744 1137 0.1137
1292769 2927 0.29278567329 5673 0.5673
32182929 1829 0.18293345241 3452 0.3452
11916304 9163 0.9163
(Ei-Oi)²/Ei
x²=
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83960569 9602 0.960292198404 1984 0.1984
3936256 9362 0.936287647044 6470 0.64741860900 8609 0.8609
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la chi cuadrada de calculada es menor que la de tablas por lo tanto se acepta
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5.-a= 71Xo= 167m= 357A) PRUEBA DE CORRIDAS ARRIBA Y ABAJO
X r76 0.21348315 s= {0,1,1,0,0,1,0,1,0,0,1,1,0,1,1}41 0.1151685455 0.15449438 Co= 10
335 0.94101124 α= 5%223 0.62640449125 0.3511236 10.3333307 0.86235955
20 0.05617978 2.5222349 0.98033708146 0.41011236 -0.13214654
13 0.03651685209 0.58707865 Z5%/2= 1.96202 0.56741573
62 0.1741573118 0.33146067 no se rechaza que lo nùmeros del conjunto ri son independientes167 0.46910112
B) PRUEBAS DE CORRIDAS ARRIBA Y DEBAJO DE LA MEDIA
S= { 0,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0}
Co= 9n0= 10n1= 6
2.9
3.25
1.87692308
como 1,87692308 cae dentro del intervalo ± 1,96 no se puede rechazar que los numeros del conjunto ri son independientes
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± 1,96 no se puede rechazar que los numeros del conjunto ri son independientes
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7.-
TD TD 1P 1P 1P 2P TD 1P1P TD TD TD 1P T TD TDTD TD 2P TD TD 1P 1P 2PT TD TD 1P 1P TD 1P TDTD 2P T TD T T TD 1P1P TD TD TD TD 1P TD 1PTD TD TD TD 1P TD 1P TD1P T 1P 1P TD TD 1P TDTD 1P TD T 1P TD 1P 1PTD TD TD 1P 1P 1P T TD1P 1P TD 1P TD 1P 1P 2P
CATEGORIA Oi EiTD 52 55.44 0.2134487731P 44 47.52 0.2607407412P 6 2.97 3.091212121T 8 3.96 4.121616162P 0 0.11 0.11
7.79701779711.833612.3904 11.07
9.180916.3216
0.0121
(Ei-Oi)²/Ei
X²=
el estadistico 7,797017797 es menor que x² = 11,07 por lo tanto se acepta que los numeros del conjunto ri son independientes
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1P 1P1P 1P1P 1P1P TDTD TDTD 1PTD TD2P 1PTD TDTD 1PTD TD
² = 11,07 por lo tanto se acepta que los numeros del conjunto ri son independientes
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9.-12808 60889 26283 46160 1836769033 41046 60884 14974 1016540909 63569 12156 49935 5569134089 13191 17046 86429 77515 media 42650.7446302 48360 42288 45982 1227630398 85061 50230 16918 4890693165 36933 71184 30569 2938911500 30430 51163 81305 7414052476 17440 11274 16008 5362327722 55864 47513 48928 54051
prueba de corridas arriba y abajo
S={ 1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0,1,1,0,1,0,1,1}
Co= 31α= 5%
33
8.5666
-0.2334
Z5%/2= 1.96
el estadistico Zo es menor que el de la tabla por lo tanto no se rechaza que los numeros del conjunto son independientes
B) PRUEBAS DE CORRIDAS ARRIBA Y DEBAJO DE LA MEDIA
S={0,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,1,0,1,1,1,1}
Co= 28 n0= 24 n1= 26
25.46
12.2049
0.208113
como 0,208113 cae dentro del intervalo ± 1,96 no se puede rechazar que los numeros del conjunto ri son independientes
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PRUEBA DE POKER
12808 60889 26283 46160 1836769033 41046 60884 14974 1016540909 63569 12156 49935 5569134089 13191 17046 86429 7751546302 48360 42288 45982 1227630398 85061 50230 16918 4890693165 36933 71184 30569 2938911500 30430 51163 81305 7414052476 17440 11274 16008 5362327722 55864 47513 48928 54051
1P 1P 1P 1P TD1P 1P 1P TD 1P2P 1P 1P 1P 1PTD T TD TD 2PTD TD 2P TD 1P1P TD 1P 1P TDTD T 1P TD 1P2P 2P 1P TD 1PTD 1P 1P 1P 1PTP 1P TD 1P 1P
CATEGORIA Oi EiTD 15 15.12 0.000952381P 27 25.2 0.128571432P 5 5.4 0.02962963TP 1 0.45 0.67222222T 2 3.6 0.71111111P 0 0.225 0.225Q 0 0.005 0.005
1.77248677
0.0144 12.5923.240.16
0.30252.56
0.0506250.000025
(Ei-Oi)²/Ei
X²=
el estadistico 1,77248677 es menor que x² = 12,592 por lo tanto se acepta que los numeros del conjunto ri son independientes
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el estadistico Zo es menor que el de la tabla por lo tanto no se rechaza que los numeros del conjunto son independientes
± 1,96 no se puede rechazar que los numeros del conjunto ri son independientes
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² = 12,592 por lo tanto se acepta que los numeros del conjunto ri son independientes
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11.-S={ 1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,1,0,1,0,1,0}
Co=28 no=24 n1=26
25.46
12.2049
0.208113
como 0,208113 cae dentro del intervalo ± 1,645 no se puede rechazar que los numeros del conjunto ri son independientes
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± 1,645 no se puede rechazar que los numeros del conjunto ri son independientes
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13.-0.172909930.16042939 0.172909930.62402592 0.160429390.81520631 0.624025920.85160568 0.815206310.72274065 0.851605680.86531546 0.722740650.63997937 0.865315460.85714119 0.639979370.04051174 0.857141190.01288959 0.040511740.51213024 0.012889590.48605289 0.512130240.85387667 0.486052890.14489023 0.853876670.15912427 0.144890230.19406343 0.159124270.82284107 0.194063430.86329047 0.822841070.47650883 0.86329047
0.4970492 0.476508830.35475831 0.49704920.66041721 0.35475831
0.3776478 0.660417210.56066975 0.37764780.77996415 0.560669750.48401775 0.779964150.02665725 0.484017750.57196768 0.026657250.01517334 0.57196768
0.9811446 0.015173340.75319026 0.98114460.38729524 0.753190260.42464514 0.387295240.81173599 0.424645140.59549437 0.811735990.19877142 0.595494370.80773994 0.198771420.38069584 0.807739940.49933019 0.380695840.29300755 0.499330190.02009571 0.293007550.27266475 0.020095710.33490749 0.272664750.27384234 0.334907490.92352182 0.273842340.89566325 0.92352182
0 0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
1.2
Column B
eje x
eje
y
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0.25056987 0.895663250.8805374 0.25056987
0.66977257 0.88053740.58468762 0.669772570.58119371 0.584687620.83909218 0.581193710.14400236 0.839092180.81671119 0.144002360.05185475 0.816711190.42871422 0.051854750.81989216 0.428714220.63218915 0.819892160.44464372 0.632189150.53273274 0.44464372
0.5890644 0.532732740.49145085 0.58906440.82481571 0.491450850.80171751 0.824815710.19835038 0.801717510.22397893 0.198350380.16060039 0.223978930.31779787 0.160600390.35939353 0.317797870.52039555 0.359393530.05120661 0.520395550.99755196 0.051206610.87248859 0.99755196
0.8256951 0.872488590.1642297 0.8256951
0.72321352 0.16422970.48371379 0.723213520.06930395 0.483713790.62409257 0.069303950.89903055 0.624092570.56880991 0.899030550.83736915 0.568809910.11538506 0.837369150.71648107 0.115385060.61268174 0.716481070.12854874 0.612681740.45547333 0.128548740.36457223 0.455473330.14903604 0.36457223
0.4011328 0.149036040.82935065 0.40113280.11090658 0.829350650.04384257 0.110906580.72302802 0.04384257
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0.27326311 0.723028020.79826754 0.273263110.80981969 0.79826754
0.5805857 0.809819690.88185438 0.58058570.54066489 0.881854380.93928197 0.540664890.48009287 0.939281970.75534748 0.48009287
0.6122683 0.755347480.4343608 0.61226830.0006021 0.4343608
0.66236315 0.00060210.45592499 0.662363150.47029833 0.455924990.02683463 0.470298330.13193598 0.026834630.62868512 0.131935980.94617882 0.628685120.52296973 0.946178820.53301243 0.522969730.97317395 0.533012430.01227297 0.973173950.10073448 0.012272970.40023077 0.100734480.32989144 0.400230770.25149393 0.329891440.10777585 0.251493930.80231173 0.107775850.57162939 0.802311730.85102049 0.571629390.42937059 0.851020490.49650755 0.429370590.02107457 0.496507550.53443473 0.021074570.11286821 0.534434730.76148707 0.112868210.94697934 0.761487070.18620959 0.946979340.00946702 0.186209590.86508867 0.009467020.65407243 0.865088670.38458171 0.654072430.04212054 0.384581710.66224104 0.042120540.04403977 0.662241040.88530532 0.044039770.85449299 0.88530532
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0.70439849 0.854492990.73521796 0.704398490.17522527 0.735217960.32728047 0.175225270.58930723 0.327280470.62868995 0.589307230.04860771 0.628689950.20058971 0.048607710.94852377 0.200589710.61533856 0.948523770.10463395 0.61533856
0.2844702 0.104633950.96936768 0.28447020.90795235 0.969367680.05796875 0.907952350.14363351 0.057968750.80870986 0.143633510.71090954 0.808709860.79031776 0.710909540.00149336 0.79031776
0.5631049 0.001493360.32924621 0.56310490.42411743 0.329246210.93795346 0.424117430.63859925 0.937953460.59967688 0.638599250.43191973 0.59967688
0.3293606 0.431919730.98032517 0.32936060.62210106 0.980325170.69854227 0.622101060.04384799 0.698542270.32312742 0.04384799
0.1581547 0.323127420.5214406 0.1581547
0.13459862 0.52144060.78815065 0.134598620.31129221 0.788150650.60769153 0.311292210.81086173 0.607691530.22446049 0.810861730.71360623 0.224460490.21659796 0.713606230.54747816 0.216597960.02080433 0.547478160.50812196 0.020804330.15006832 0.508121960.39807127 0.15006832
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0.32199798 0.398071270.0227408 0.32199798
0.95929012 0.02274080.09135625 0.959290120.52748749 0.091356250.92085098 0.52748749
0.7932655 0.920850980.31325179 0.79326550.01545468 0.31325179
0.01545468
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0 0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
1.2
Column B
eje x
eje
y
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15.-
CATEGORIA Oi EiTD 13851 14040 2.544230771P 5464 5265 7.52155745T 215 195 2.05128205
12.11707033572139601 7.815
400
(Ei-Oi)²/Ei
X²=
el estadistico 12,1170703 es mayor que x² = 7,815 por lo tanto no se acepta que los numeros del conjunto ri son independientes
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² = 7,815 por lo tanto no se acepta que los numeros del conjunto ri son independientes
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17.-
si aceptaria la hipotesis de independencia
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19.-n= 357500
2p 17500
CATEGORIA PROBA.2p 0.108 17500 38610 11541.8829318829
Se rechaza la hipotesis de independencia
Oi E1
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21.-
92 85 90 9388 98 93 9096 91 86 88
100 85 84 81
Ho= independienteH1= dependiente
intervalo Oi Ei=n-1/m
1 100 90 1.111111112 85 90 0.277777783 84 90 0.44 81 90 0.95 96 90 0.46 91 90 0.011111117 86 90 0.177777788 88 90 0.044444449 88 90 0.04444444
10 98 90 0.7111111111 93 90 0.112 90 90 013 92 90 0.0444444414 85 90 0.2777777815 90 90 016 93 90 0.1
1440 1440 4.6
24.996x²=
mi X² de tablas es mayor que la calculada por lo tanto Ho se acepta
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23.-0.52220543 0.46689069 0.63429937 0.39893586 0.51210733 0.56304921 0.50121769 0.835473720.35141018 0.71734213 0.47060916 0.70597023 0.10770064 0.29561921 0.03849417 0.575990830.58541118 0.37860494 0.72001898 0.52631862 0.5135264 0.65878476 0.61753945 0.501315480.37872994 0.83575505 0.31540443 0.96674142 0.27784772 0.32454468 0.05910183 0.346359990.46223393 0.43861372 0.22095392 0.84355334 0.53482743 0.58450083 0.54843791 0.342062610.09412615 0.62672139 0.92516847 0.89429724 0.70642959 0.76518771 0.36766605 0.483315440.22364802 0.43647084 0.15761661 0.24632912 0.70663406 0.37601083 0.43527693 0.36022558
0.6011947 0.50491705 0.28650269 0.91182324 0.68419365 0.77578796 0.81282921 0.139576480.25278556 0.88524578 0.37547834 0.0496024 0.15112422 0.91727914 0.85471327 0.004970520.96857426 0.97309479 0.1429841 0.80307218 0.30080196 0.81154537 0.4131457 0.36762767
prueba de medias prueba de varianza prueba de uniformidad
Ho= ri es uniformeH1= ri no es uniforme
media= 0.494689469 varianza= 0.073626169 intervalo OiLI= 0.443419674 LI= 0.10809638 [0,00-0,10) 9LS= 0.556580326 LS= 0.061755051 [0,10-0,20) 7
[0,20-0,30) 10Ho se acepta Ho se acepta [0,30-0,40) 16
[0,40-0,50) 9[0,50-0,60) 14[0,60-0,70) 7[0,70-0,80) 7[0,80-0,90) 13[0,90-1,00) 8
100
Ho: µri=o.5 Ho: σ²ri=1/12H1: µri≠o.5 H1: σ²ri≠1/12
la x² calculada es menor que la de tablas por lo tanto se acepta Ho
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0.27779852 0.053672210.43133477 0.084885530.14648457 0.807766620.25042406 0.093924220.17002028 0.688805640.85698325 0.203733360.97066179 0.373308090.92599652 0.853156650.07056533 0.332930050.54401853 0.85997823
Ei=n/m10 0.110 0.910 010 3.610 0.110 1.610 0.910 0.910 0.910 0.4
100 9.4123.2222
(Ei-Oi)²/Ei
x²=² calculada es menor que la de tablas por lo tanto se acepta Ho
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25.-ho= independientesh1= dependientes
≥5(0.5,0.8)S={ 1,0,0,0,0,0,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1}
0.5858 0.8863 0.8378 0.3203 0.4115 0.271 0.9238 0.19790.6213 0.436 0.6279 0.8415 0.5786 0.0543 0.3567 0.16550.1931 0.0843 0.9152 0.6093 0.7587 0.4515 0.3203 0.51390.1242 0.8826 0.9921 0.8523 0.7723 0.854 0.4722 0.47810.8658 0.4028 0.6136 0.872 0.1126 0.5857 0.9172 0.8943
H= 12 α= 0.5 β= 0.8
Oi Ei= (h)(β-α)(1-(β-α))i
0 3 3.6 0.11 2 2.52 0.107301592 2 1.764 0.03157373 1 1.2348 0.044647754 0 0.86436 0.864365 4 2.01684 1.95004244
12 3.09792547
11.07
se acepta H:o
Tamaño del hueco
X0=
X^2α,m-1=
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0.9268 0.67020.338 0.8080.707 0.9123
0.2101 0.1680.8095 0.6408