TABLAS ESTADISTICAS

Tabla 1. Areas bajo la curva normal estndar

zArea entre

z y +zArea en

dos colas

< -z y > +zArea en una cola

< -z o > +zzArea entre

z y +zArea en dos colas

< -z y > +zArea en una cola

< -z o > +z

0.00

0.05

0.10

0.15

0.20

0.250.000

0.040

0.080

0.119

0.159

0.1971.000

0.960

0.920

0.881

0.841

0.8030.500

0.480

0.460

0.440

0.421

0.4011.55

1.60

1.64521.65

1.70

1.750.879

0.890

0.900

0.901

0.911

0.9200.121

0.110

0.100

0.099

0.089

0.0800.061

0.055

0.050

0.049

0.045

0.040

0.30

0.35

0.40

0.45

0.500.236

0.274

0.311

0.347

0.3830.764

0.726

0.689

0.653

0.6170.382

0.363

0.345

0.326

0.3091.80

1.85

1.90

1.95

1.9622.000.928

0.936

0.943

0.949

0.950

0.9540.072

0.064

0.057

0.051

0.050

0.0460.036

0.032

0.029

0.026

0.025

0.023

0.55

0.60

0.65

0.70

0.750.418

0.451

0.484

0.516

0.5470.582

0.549

0.516

0.484

0.4530.291

0.274

0.258

0.242

0.2272.05

2.10

2.15

2.20

2.250.960

0.964

0.968

0.972

0.9760.040

0.036

0.032

0.028

0.0240.020

0.018

0.016

0.014

0.012

0.80

0.85

0.90

0.95

1.00

0.576

0.605

0.632

0.658

0.683

0.424

0.395

0.368

0.342

0.3170.212

0.198

0.184

0.171

0.1592.30

2.32622.35

2.40

2.45

2.500.979

0.980

0.981

0.984

0.986

0.9880.021

0.020

0.019

0.016

0.014

0.0120.011

0.010

0.009

0.008

0.007

0.006

1.05

1.10

1.15

1.20

1.25

1.2820.706

0.729

0.750

0.770

0.789

0.8000.294

0.271

0.250

0.230

0.211

0.2000.147

0.136

0.125

0.115

0.106

0.1002.55

2.57522.60

2.65

2.70

2.750.989

0.990

0.991

0.992

0.993

0.9940.011

0.010

0.009

0.008

0.007

0.0060.005

0.005

0.005

0.004

0.003

0.003

1.30

1.35

1.40

1.45

1.500.806

0.823

0.838

0.853

0.8660.194

0.177

0.162

0.147

0.340.097

0.089

0.081

0.074

0.0672.80

2.85

2.90

2.95

3.000.995

0.996

0.996

0.997

0.9970.005

0.004

0.004

0.003

0.0030.003

0.002

0.002

0.002

0.001

Tabla2. Distribucin t de Student Acumulativa

g.l.P

0.750.800.850.900.950.9750.9900.9950.9995

11.00051.3761.9633.0786.31412.70631.82163.657636.619

2 0.8161.0611.3861.8362.9204.3036.9659.92531.598

30.7650.9781.2501.6382.3533.1824.5415.84112.941

40.7410.9411.1901.5332.1322.7763.7474.6048.610

50.7270.9201.1561.4762.0152.5713.3654.0326.859

60.7180.9061.1341.4401.9432.4473.1433.7075.959

70.7110.8961.1191.4151.8952.3-652.9983.4995.405

80.7060.8891.1081.3971.8602.3062.8963.3555.041

90.7030.8831.1001.3831.8332.2622.8213.2504.781

100.7000.8791.0931.3721.8122.2282.7643.1694.58Z

110.6970.8761.0881.3631.7962.2012.7183.1064.437

120.6950.8731.0831.3561.7822.1792.6813.0554.318

130.6940.8701.0791.3501.7712.1602.6503.0124.221

140.6920.8681.0761.3451.7612.1452.6242.9774.140

150.6.910.8661.0741.3411.7532.1312.6022.9474.073

160.6900.8661 .0711.3371.7462.1202.5842.9214.015

170.6890.8631.0691.3331.7402.1102.5672.8983.965

180.6880.8621.0671.3301.7342.1012.5522.8783.922

190.6880.8611.0661.3281.7292.0932.5402.8613.883

200.6870.8601.0641.3251.7252.0862.5282.8453.850

210.6860.8591.0631.3231.7212.0802.5182.8313.819

220.6860.8581.9611.3211.7172.0742.5082.8193.792

230.6850.8581.0601.3191.7142.0692.5002.8073.767

240.6850.8571.0591.3181.7112.0642.4922.7973.745

250.6840.8561.0581.3161.7082.0602.4852.7873.725

260.6840.8561.0581.3151.7062.0562.4772.7793.707

270.6840.8551.0571.3141.7032.0522.4732.7713.690

280.6830.8551.0561.3131.7012.0482.4672.7633.674

290.6830.8541.0551.3111.6992.0452.4622.7563.659

300.6830.8541.0551.3101.6972.0422.4572.7503.646

350.6820.8521.0521.3061.6902.0302.438 2.7243.591

400.6810.8511.0501.3031.6842.0212.4232.7043.551

450.6800.8501.0481.3011.6802.0142.4122.6903.520

500.6800.8491.047 1.2991.6762.0082.4032.6783.496

550.6790.8491.047 1.2971.6732.0042.3962.6693.476

600.6790.8481.046 1.2961.6712.0002.3902.6003.460

700.6780.8471.045 1.2941.6671 .9942.3812.6483.435

800.6780.8471.044 1.2931.6651.9902.3742.6383.416

900.6780.8461.043 1.2911 .6621 .9872.3682.6323.402

1090.6770.8461.042 1.2901.6611.9842.3642.6263.390

2000.6760.844 1.0391.2861 .6531.9722.4452..6013.340

Distribucin t . Student Acumulativag.l.P

0.750.800.850.900.950.9750.9900.9950.9995

3000.6760.843 1.0381 .2851.6501.968 2.4372.5923.323

4000.6760.843 1.0381.2841.6491.9662.4342.5883.315

5000.6760.843 1.0371.2841 .6481.9652.4322.586 3.310

10000.6750.842 1.0371.2831.6471.9622.4272.5813.301

(0.674490.841621.036431.281551.644851.959962.326302.575823.29053

Tabla 3a. Distribucin Ji- Cuadrada Acumulativa

g.l.P

0.00050.0010.0050.010.0250.050. 100.200.30 0.40

10.063930.051570.043930.031570.029820.013930.01580.06420.1480.275

20.021000.012000.01000.02010.05060.1030.2110.4460.711.02

30.01530.02430.07170.1150.2160.3520.5841 .001.421.87

40.06390.09080.2070.2970.4840.7111.061.652.192.75

S0.1580.2100.4120.5540.8311.151.612.343.003.66

60.299 0.381 0.676 0.872 1.24 1.64 2.20 3.073.834.57

70.4850.5980.9891.241.69 2.172.833.824.675.49

80,7100.8571.341 .652.182.733.494.595.536.42

90.9721.151.732.092.703.334.175.386.397.36

101.261.482.162.563.253.944.876.187.278.30

111.591.832.603.053.824.575.586.998.159.24

121.932.213.073.574.405.236.307,819.0310.2

132.312.623.574.115.015.89 7.048.639.9311 .1

142.703.044.074.665.636.577.799.4710.812.1

153.113.484.605.236.267.268.5510.311.713.0

163.543.945.145.816.917.969.3111 .212.614.0

173.984.425.706.417.568.6710.112.013.514.9

184.444.906.267.018.239.3910.-912.914.415.9

194.915.416.847.638.9110.111.713.715.416.9

205.405.927.438.269.5010.9 12.414.616.317.8

215.906.458.038.9010.311.613.215.417.218.8

22 6.406.988.649.5411.012.314.016.318.119.7

236.927.539.2610.211.713.114.817.219.020.7

247.458.089.8910.912.413.815.718.119.921.7

257.998.6510.511.513.114.616.518.920.922.6

268.549.2211.212.213.815.4 17.319.,821.823.6

279.099.8011.812.914.616.218.120.722.724.5

289.6610.412.513.615.316.918.021.623.625.5

2910.211.013.114.316.017.719.822.524.626.5

3010.811.613.815.016.818.520.623.425.527.4

3111.412.214.515.717.519.321.424.326.428.4

3212.012.815.116.418.320.122.325.127.429.4

3312.613.415.817.119.020.923.126.028.330.3

3413.214.116.517.819.821.724.026.929.231.3

3513.814.7.17.218.520.622.524.827.830.232.3

3614.415.317.919.221.323.3'25.628.731.133.3

3715.016.018.620.022.124.126.529.632.134.2

3815.616.619.320.722.924.927.330.533.055.2

3916.317.320.021.423.725.728.231.433.036.2

4016.917.920.722.224.426.529.132.334.937.1

4117.518.621.422.925.227.329.933.335.838.1

4218.219.222.123.726.028.130.834.236.839.1

4318.819.922.924.426.829.031.635.137.740.0

4419.520.623.625.127.6 29.832. 536.038.641.0

4520.121.324.325.928.430.633.436.939.642.0

4620.821.925.0.26.729.231.434.237.840.543.0

4721.5 22.625.827.430.032.335.138.741.543.9

4822.123.326.528.230.833.135.939.642.444.9

4922.824.027.228.931.633.936.840.543.445.9

5023.524.728.029.732.434.837.741.444.346.9

Tabla3b. Distribucin Ji- Cuadrada Acumulativa

g.l.P

0.500.6.00.700.800.900.950.9750.990.9950.9990. 9995

10.4550. 7081 .071 .6A2. 713.845.026.637.8810.812.1

21.391.832.413.224.615.997.389.2110.613.815.2

32.372.953.674.646.257.819.3511 .312.816.317.7

43.364.044.885.997.789.4911.113.314.918.520.0

54.365.136.067.299.2411.112.815.116.720.522.1

65.356.217.238.5610.612.614.416.818.522.524.1

76.357.288.389.8012.014. 116.018.520.324.326.0

87.348.359.5211.913.415.517.520.122.026.127.9

98.349.4110.712.214.716.919.021 .723.627.929.7

109.3410.511 .813.416.'018.320.523.225.229.631 .4

1110.31.1.512.914.617.319.721.924.726.831.333.1

1211.3T2.614.015.818.521.023.326.228.332.934.8

1312.313.615.117.019.822.424.727.729.834.536.5

1413.314.716.218.221.123.726.129.131.336.138.1

1514.315.717.319.322.325.027.530.632.837.739.7

1615.316.818.420.523.526.328.832.034.339.341.3

1716.317.819.521.624.827.630.233.435.740.842.9

1817.318.9.20.622.826.028.931.534.837.242.344.4

1918.319.921.723.927.230.132.936.238.643.846.0

2019.321.022.825.028.431.434.237.240.045.347.5

212.322.023.926.229.632.735.538.941.446.849.0

2221.323.024.927.330.833.936.840.342.848.350.5

2322.324.126.028.432.035.238.141 .644.2 49.752.0

2423.325.127.129.633.236.439.443.0-45.651.253.5

2524.3 26.128.230.734.437.740.644.346.952.654.9

2625.327.229.231.835.638.941 .945.648.354.156.4

2726.328.230.332.936.740.143.247.049.655.557.9

2827.329.231.434.037.941 .344.548.351.056.959.3

2928.330.332.535.139.142.645.749.652.358.360.7

3029.331.333.536.340.343.847.050.953.759.762.2

3130.332.3'34.637.441.445.048.252.255.061.163.6

3231.333.435.738.542.646.249.553.556.362.565.0

3332.334.436.739.643.747.450.754.857.663.966.4

3433.335.437.840.744.948.652.056.159.065.267.8

3534.336.538.941.846.149.853.257.360.366.669.2

3635.337.539.942.947.251.054.458.661.668.070.6

3736.338.541 .044.048.452.255.759.962.969.372.0

3837.339.642.045.149.553.456.961.264.270.773.4

3938.340.643.146.250.754.658.162.465.572.174.7

4039.341 .644.247.351.855.859.363.766.873.476.1

4140.342.745.248.452.956.960.665.0-68.174.777.5

4241.343.746.349.554.158.161 .866.269.376.178.8

4342.344.747.350.555.259.363.067.570.677.480.2

4443.345.748.451.656.460.564.268.771.978.781.5

4544.346.849.552.757.561.765.470.073.280.182.9

4645.347.850.553.858.662.866.671.274.481.484.2

4746.348.851.654.959.864.067.872.475.782.785.6

4847.349.852.656.060.965.269.073.777.084.086.9

4948.350.953.757.162.066.370.274.978.285.488.2

5049.351.954.758.263.267.571.476.279.586.780.6

Tabla C2: CUANTILAS DE LA PRUEBA DE KOLMOGOROV SMIRNOV

p (Prueba bilateral) p

n.80.90.95.98.99n .80.90.95.98.99

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20.900

.684

.565

.493

.447

.410

.381

.358

.339

.323

.308

.296

.285

.275

.266

.258

.250

.244

.237

.232.950

.776

.636

.565

.509

.468

.436

.410

.387

.369

.352

.338

.325

.314

.304

.295

.286

.279

.271

.265.975

.842

.708

.624

.563

.519

.483

.454

.430

.409

.391

.375

.361

.349

.338

.327

.318

.309

.301

.294.990

.900

.785

.689

.627

.577

.538

.507

.480

.457

.437

.419

.404

.390

.377

.366

.355

.346

.337

.329.995

.929

.829

.734

.669

.617

.576

.542

.513

.489

.468

.449

.432

.418

.404

.392

.381

.371

.361

.352 21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40.226

.221

.216

.212

.208

.204

.200

.197

.193

.190

.187

.184

.182

.179

.177

.174

.172

.170

.168

.165.259

.253

.247

.242

.238

.233

.229

.225

.221

.218

.214

.211

.208

.205

.202

.199

.196

.194

.191

.189.287

.281

.275

.269

.264

.259

.254

.250

.246

.242

.238

.234

.231

.227

.224

.221

.218

.215

.213

.210.321

.314

.307

.301

.295

.290

.284

.279

.275

.270

.266

.262

.258

.254

.251

.247

.244

.241

.238

.235.344

.337

.330

.323

.317

.311

.305

.300

.295

.290

.285

.281

.277

.273

.269

.265

.262

.258

.255

.252

Aproximacin para n > 40

Tabla C3: Cuantilas del test estadstico para normalidad de Lilliefors

nP

0.800.850.900.950.99

40.3000.3190.3520.3810.417

50.2850.2990.3150.3370.405

60.2650.2770.2940.3190.364

70.2470.2580.2760.3000.348

80.2330.2440.2610.2850.331

90.2230.2330.2490.2710.311

100.2150.2240.2390.2580.294

110.2060.2170.2300.2490.284

120.1990.2120.2230.2420.275

130.1900.2020.2140.2340.268

140.1830.1940.2070.2270.261

150.1770.1870.2010.2200.257

160.1730.1820.1950.2130.250

170.1690.1770.1890.2060.245

180.1660.1730.1840.2000.239

190.1630.1690.1790.1950.235

200.1600.1660.1740.1900.231

250.1420.1470.1580.1730.200

300.1310.1360.1440.1610.187

( 30

ESTIMACION POR INTERVALOParmetro

RequisitosIntervalo de confianza

(1- ()Tamao de muestra

Media

(Varianza (2 conocida

-Todo n de poblacin Normal

- n grande de cualquier

poblacin

Poblac. grande

Poblac. finita

Varianza (2 desconocida

- n grande (n ( 30) de cualquier poblacin

Varianza (2 desconocida

- n ( 30 de poblacin

Normal

Varianza

(2La poblacin es normal

Proporcin

PPoblacin grande

Muestra grande Poblac grande.

Poblac finita

Poblacin finita

Muestra grande

ParmetroRequisitosIntervalo de confianza (1- ()

Diferencia de medias

(1 - (2Varianzas (21, (22 conocidas

-Todo n1, n2 de poblaciones normales.

-n1( 30, n2( 30 en general

Varianzas (21, (22 desconocidas

- n1( 30, n2( 30

Varianzas (21, (22 Desconocidas-n1