Ejercicios Estadistica Inferencial II

8/12/2019 Ejercicios Estadistica Inferencial II

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INSTITUTO TECNOLGICO SUPERIOR DE PEROTE

ESTADSTICAINFERENCIAL II

EJERCICIOS

FRANCISCO JAVIER ALFONSO ARROYO 1002E011

19/12/2013

ESPECIALIDAD: ING. INDUSTRIAL

NOMBRE DEL DOCENTE: SUBDIRECTOR MEDINA

SEMESTRE Y GRUPO:7 501 A

PEROTE, VER. DICIEMBRE / 2013


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FCO. JAVIER ALFONSO ARROYO

2

Ejercicio 1.1

Pureza (%) Hidrocarburos (%)

86,91 1,0289,85 1,11

90,28 1,43

86,34 1,11

92,58 1,01

87,33 0,95

86,29 1,11

91,86 0,87

95,61 1,43

89,86 1,02

96,73 1,4699,42 1,55

98,66 1,55

96,07 1,55

93,65 1,40

87,31 1,15

95,00 1,01

96,85 0,99

85,20 0,95

90,56 0,98


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(%) is statistically significant (p < 0,05).The relationship between Pureza (%) and Hidrocarburos

> 0,50,10,050

NoYes

P = 0,003

for by the regression model.35,52% of the variation in Pureza (%) can be accounted

100%0%

R-sq (adj) = 35,52%

increase.Hidrocarburos (%) increases, Pureza (%) also tends toThe positive correlation (r = 0,62) indicates that when

10-1

0,62

1,61,41,21,0

100

95

90

85

Hidrocarburos (%)

Pureza(%)

causes Y.A statistically significant relationship does not imply that Xa desired value or range of values for Pureza (%).find the settings for Hidrocarburos (%) that correspond toto predict Pureza (%) for a value of Hidrocarburos (%), orIf the model fits the data well, this equation can be used Y = 77,86 + 11,80 X

relationship between Y and X is:The fitted equation for the linear model that describes the

Y: Pureza (%)X: Hidrocarburos (%)

Is there a relationship between Y and X?Fitted Line Plot for Linear Model

Y = 77,86 + 11,80 X

Comments

Regression for Pureza (%) vs Hidrocarburos (%)Summary Report

%of variation accounted for by model

Correlation between Y and XNegative No correlation Positive

Ejercicio 1.2

Radio Viscocidad

1,0 0,45

0,9 0,20

0,8 0,34

0,7 0,58

0,6 0,70

0,5 0,57

0,4 0,55

0,3 0,44


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statistically significant (p > 0,05).The relationship between Radio and Viscocidad is not

> 0,50,10,050

NoYes

P = 0,248

the regression model.8,38% of the variation in Radio can be accounted for by

100%0%

R-sq (adj) = 8,38%

statistically significant (p > 0,05).The correlation between Radio and Viscocidad is not

10-1

-0,46

0,60,40,2

1,0

0,8

0,6

0,4

Viscocidad

Radio

causes Y.A statistically significant relationship does not imply that Xor range of values for Radio.settings for Viscocidad that correspond to a desired valueto predict Radio for a value of Viscocidad, or find theIf the model fits the data well, this equation can be used Y = 0,9968 - 0,7243 X


Y: RadioX: Viscocidad


Y = 0,9968 - 0,7243 X

Comments

Regression for Radio vs ViscocidadSummary Report



Ejercicio 1.3

Estudiante Evaluacin a mediosemestre

Calificacin final

1 82 76

2 73 83

3 95 89

4 66 76

5 84 796 89 73

7 51 62

8 82 89

9 75 77

10 90 85

11 60 48


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12 81 69

13 34 51

14 49 25

15 87 74

and Calificacin final is statistically significant (p < 0,05).The relationship between Evaluacin a medio semestre

> 0,50,10,050

NoYes

P = 0,001

can be accounted for by the regression model.56,80% of the variation in Evaluacin a medio semestre

100%0%

R-sq (adj) = 56,80%

also tends to increase.Calificacin final increases, Evaluacin a medio semestreThe positive correlation (r = 0,77) indicates that when

10-1

0,77

80604020

100

80

60

40

Calificacin final

Evaluacinamediosemestre

causes Y.A statistically significant relationship does not imply that XEvaluacin a medio semestre.that correspond to a desired value or range of values forCalificacin final, or find the settings for Calificacin finalto predict Evaluacin a medio semestre for a value ofIf the model fits the data well, this equation can be used Y = 18,09 + 0,7828 Xrelationship between Y and X is:The fitted equation for the linear model that describes the

Y: Evaluacin a medio semestreX: Calificacin final


Y = 18,09 + 0,7828 X

Comments

Regression for Evaluacin a medio semestre vs Calificacin finalSummary Report



Ejercicio 1.4


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statistically significant (p > 0.05).The relationship between ndice and Das is not

> 0.50.10.050

NoYes

P = 0.127

the regression model.9.84% of the variation in ndice can be accounted for by

100%0%

R-sq (adj) = 9.84%

statistically significant (p > 0.05).The correlation between ndice and Das is not

10-1

0.40

100806040

18

17

16

Das

ndice

causes Y.A statistically significant relationship does not imply that Xfor ndice.Das that correspond to a desired value or range of valuesto predict ndice for a value of Das, or find the settings forIf the model fits the data well, this equation can be used Y = 16.59 + 0.01036 X


Y: ndiceX: Das


Y = 16.59 + 0.01036 X

Comments

Regression for ndice vs DasSummary Report




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Ejercicio 1.5

significant (p < 0,05).The relationship between WT and TL is statistically

> 0,50,10,050

NoYes

P = 0,000

the regression model.89,19% of the variation in WT can be accounted for by

100%0%

R-sq (adj) = 89,19%

TL increases, WT also tends to increase.The positive correlation (r = 0,95) indicates that when

10-1

0,95

400300200100

1200

800

400

0

TL

WT

causes Y.A statistically significant relationship does not imply that XWT.that correspond to a desired value or range of values forto predict WT for a value of TL, or find the settings for TLIf the model fits the data well, this equation can be used Y = - 595,6 + 3,567 Xrelationship between Y and X is:The fitted equation for the linear model that describes the

Y: WTX: TL


Y = - 595,6 + 3,567 X

Comments

Regression for WT vs TLSummary Report



Ejercicio 1.6


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Promesas hechas is statistically significant (p < 0,05).The relationship between promesas no cumplidas and

> 0,50,10,050

NoYes

P = 0,001

be accounted for by the regression model.74,82% of the variation in promesas no cumplidas can

100%0%

R-sq (adj) = 74,82%

tends to decrease.Promesas hechas increases, promesas no cumplidasThe negative correlation (r = -0,88) indicates that when

10-1

-0,88

6050403020

6

4

2

Promesas hechas

promesasnocumplidas

causes Y.A statistically significant relationship does not imply that Xpromesas no cumplidas.correspond to a desired value or range of values forhechas, or find the settings for Promesas hechas thatto predict promesas no cumplidas for a value of PromesasIf the model fits the data well, this equation can be used Y = 9,268 - 0,1180 X


Y: promesas no cumplidasX: Promesas hechas


Y = 9,268 - 0,1180 X

Comments

Regression for promesas no cumplidas vs Promesas hechasSummary Report



Ejercicio1.11Regression Analysis: Peso final Y versus Peso Inicial; Alimento Con

The regression equation isPeso final Y = - 23,0 + 1,40 Peso Inicial X1 + 0,218 Alimento Consumido X2

Predictor Coef SE Coef T PConstant -22,99 17,76 -1,29 0,237Peso Inicial X1 1,3957 0,5825 2,40 0,048Alimento Consumido X2 0,21761 0,05777 3,77 0,007


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S = 6,05079 R-Sq = 87,3% R-Sq(adj) = 83,7%

Analysis of Variance

Source DF SS MS F PRegression 2 1764,22 882,11 24,09 0,001Residual Error 7 256,28 36,61Total 9 2020,50

Source DF Seq SSPeso Inicial X1 1 1244,66Alimento Consumido X2 1 519,56

Ejercicio1.12Regression Analysis: Y versus X1; X2; X3; X4

The regression equation isY = - 162 + 0,600 X1 + 9,56 X2 + 1,71 X3 + 0,222 X4

Predictor Coef SE Coef T PConstant -161,9 179,3 -0,90 0,397X1 0,6002 0,3138 1,91 0,097X2 9,558 4,534 2,11 0,073


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X3 1,714 1,445 1,19 0,274X4 0,2224 0,6987 0,32 0,760

S = 14,5781 R-Sq = 77,7% R-Sq(adj) = 64,9%


Source DF SS MS F PRegression 4 5168,6 1292,2 6,08 0,020Residual Error 7 1487,6 212,5Total 11 6656,3

Source DF Seq SSX1 1 3758,9X2 1 1109,4X3 1 278,8X4 1 21,5

Unusual Observations

Obs X1 Y Fit SE Fit Residual St Resid9 75,0 267,00 287,83 10,96 -20,83 -2,17R

R denotes an observation with a large standardized residual.

Ejercicio1.13

Regression Analysis: Y versus X1, X2, X3, X4, X5

The regression equation is


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Y = - 6.51 + 2.00 X1 - 3.68 X2 + 2.52 X3 + 5.16 X4 + 14.4 X5

Predictor Coef SE Coef T PConstant -6.5122 0.9336 -6.98 0.000X1 1.999 2.573 0.78 0.449

X2 -3.675 2.774 -1.32 0.204X3 2.524 6.347 0.40 0.696X4 5.158 3.660 1.41 0.178X5 14.401 4.856 2.97 0.009

S = 0.703452 R-Sq = 96.3% R-Sq(adj) = 95.2%


Source DF SS MS F PRegression 5 208.007 41.601 84.07 0.000Residual Error 16 7.918 0.495Total 21 215.925

Source DF Seq SSX1 1 199.145X2 1 0.127X3 1 4.120X4 1 0.263X5 1 4.352


Obs X1 Y Fit SE Fit Residual St Resid2 1.55 2.900 3.860 0.529 -0.960 -2.07R18 1.72 6.360 7.621 0.390 -1.261 -2.15R


Ejercicio1.14


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Regression Analysis: Q3 versus P1, P2, P3, Q1, Q2

The regression equation isQ3 = 89.0 - 0.079 P1 + 0.090 P2 - 1.29 P3 + 0.403 Q1 + 1.04 Q2

Predictor Coef SE Coef T PConstant 88.97 32.53 2.74 0.011P1 -0.0786 0.3544 -0.22 0.826P2 0.0896 0.4197 0.21 0.833P3 -1.2852 0.2977 -4.32 0.000Q1 0.4035 0.3751 1.08 0.292Q2 1.0369 0.5140 2.02 0.055

S = 13.6522 R-Sq = 59.1% R-Sq(adj) = 50.9%



Source DF Seq SSP1 1 99.2P2 1 533.2P3 1 5024.7Q1 1 322.1Q2 1 758.5


Obs P1 Q3 Fit SE Fit Residual St Resid9 41.0 68.49 40.66 5.36 27.83 2.22R14 49.0 10.70 34.99 9.01 -24.29 -2.37R15 59.0 77.24 50.60 6.67 26.64 2.24R



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Ejercicio1.15

Regression Analysis: All versus Energy, trans, Med

The regression equation isAll = - 3.82 - 0.346 Energy + 1.35 trans + 0.0449 Med

Predictor Coef SE Coef T PConstant -3.818 1.535 -2.49 0.018Energy -0.34637 0.08043 -4.31 0.000trans 1.3462 0.1316 10.23 0.000Med 0.04491 0.03892 1.15 0.257

S = 1.11641 R-Sq = 99.9% R-Sq(adj) = 99.9%


Source DF SS MS F PRegression 3 56279 18760 15051.66 0.000Residual Error 31 39 1Total 34 56318

Source DF Seq SSEnergy 1 51848trans 1 4430

Med 1 2


Obs Energy All Fit SE Fit Residual St Resid15 38 49.300 46.544 0.250 2.756 2.53R16 42 53.800 51.177 0.223 2.623 2.40R35 105 148.200 150.219 0.595 -2.019 -2.14R



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Ejercicio1.16

Welcome to Minitab, press F1 for help.

Regression Analysis: Iron versus Phos

The regression equation isIron = 0.171 - 0.0273 Phos

Predictor Coef SE Coef T PConstant 0.17124 0.02574 6.65 0.000Phos -0.02732 0.03181 -0.86 0.406

S = 0.0659626 R-Sq = 5.4% R-Sq(adj) = 0.0%




Obs Phos Iron Fit SE Fit Residual St Resid1 0.05 0.3300 0.1699 0.0246 0.1601 2.62R15 2.00 0.1700 0.1166 0.0475 0.0534 1.17 X

R denotes an observation with a large standardized residual.X denotes an observation whose X value gives it large leverage.


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Ejercicio1.17Regression Analysis: y versus t

The regression equation isy = 1.98 + 1.39 t

Predictor Coef SE Coef T PConstant 1.9800 0.8590 2.30 0.033t 1.39432 0.07730 18.04 0.000

S = 1.99334 R-Sq = 94.8% R-Sq(adj) = 94.5%


Source DF SS MS F P

Regression 1 1292.8 1292.8 325.37 0.000Residual Error 18 71.5 4.0Total 19 1364.4


Obs t y Fit SE Fit Residual St Resid20 19.0 32.425 28.472 0.859 3.953 2.20R



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Ejercicio1.18

Regression Analysis: Perdida de Peso y versus Mes despues de Producido x

The regression equation isPerdida de Peso y = - 0.422 + 2.88 Mes despues de Producido x

Predictor Coef SE Coef T PConstant -0.4220 0.5184 -0.81 0.439Mes despues de Producido x 2.8778 0.3342 8.61 0.000

S = 0.758866 R-Sq = 90.3% R-Sq(adj) = 89.0%




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Ejercicio1.19

Regression Analysis: Y versus X

The regression equation isY = 12.3 - 0.0308 X

Predictor Coef SE Coef T PConstant 12.2909 0.7491 16.41 0.000X -0.030773 0.003571 -8.62 0.000

S = 0.749146 R-Sq = 89.2% R-Sq(adj) = 88.0%




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Ejercicio1.20

Regression Analysis: Carbonatacin y versus Temperaturas X1, Presin X2

The regression equation isCarbonatacin y = - 140 + 1.38 Temperaturas X1 + 4.67 Presin X2

Predictor Coef SE Coef T PConstant -139.75 23.38 -5.98 0.000Temperaturas X1 1.3812 0.8061 1.71 0.121Presin X2 4.6730 0.2986 15.65 0.000

S = 1.03173 R-Sq = 97.2% R-Sq(adj) = 96.6%



Source DF Seq SSTemperaturas X1 1 71.83Presin X2 1 260.78


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EJERCICIO 3.1

Factor Type Levels ValuesQuimico fixed 5 Q1. Q2. Q3. Q4. Q5

Analysis of Variance for Prenda, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PQuimico 4 14,00 14,00 3,50 0,30 0,876Error 15 177,75 177,75 11,85


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Total 19 191,75

S = 3,44238 R-Sq = 7,30% R-Sq(adj) = 0,00%

Unusual Observations for Prenda

Obs Prenda Fit SE Fit Residual St Resid6 67,0000 73,2500 1,7212 -6,2500 -2,10 R


EJERCICIO 3.2

Factor Type Levels ValuesSOLUCIN fixed 3 S1. S2. S3

Analysis of Variance for DAS, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PSOLUCIN 2 703,5 703,5 351,8 2,73 0,118Error 9 1158,8 1158,8 128,8Total 11 1862,3

S = 11,3468 R-Sq = 37,78% R-Sq(adj) = 23,95%


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EJERCICIO 3.4

Factor Type Levels ValuesDistancia (ft) fixed 4 D10. D4. D6. D8

Analysis of Variance for Sujeto, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PDistancia (ft) 3 67,600 67,600 22,533 2,66 0,083Error 16 135,600 135,600 8,475Total 19 203,200

S = 2,91119 R-Sq = 33,27% R-Sq(adj) = 20,76%

Unusual Observations for Sujeto

Obs Sujeto Fit SE Fit Residual St Resid1 17,0000 8,2000 1,3019 8,8000 3,38 R


EJERCICIO 3.5

Factor Type Levels ValuesLUGAR fixed 3 L1A. L2B. L3C

Analysis of Variance for RENDIMIENTO, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PLUGAR 2 24,50 24,50 12,25 0,52 0,613Error 9 213,50 213,50 23,72Total 11 238,00

S = 4,87055 R-Sq = 10,29% R-Sq(adj) = 0,00%


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EJERCICIO 3.6

Factor Type Levels ValuesESTUDIANTE Y MATERIA fixed 5 E1. E2. E3. E4. E5

Analysis of Variance for CALIFICACIN, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PESTUDIANTE Y MATERIA 4 1618,70 1618,70 404,67 5,26 0,008Error 15 1154,25 1154,25 76,95Total 19 2772,95

S = 8,77211 R-Sq = 58,37% R-Sq(adj) = 47,27%

EJERCICIO 3.7

Factor Type Levels ValuesCURSO fixed 4 A. B. C. D

Analysis of Variance for CALIFICACIN, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PCURSO 3 723,50 723,50 241,17 2,85 0,082Error 12 1014,50 1014,50 84,54Total 15 1738,00

S = 9,19465 R-Sq = 41,63% R-Sq(adj) = 27,04%

Unusual Observations for CALIFICACIN

Obs CALIFICACIN Fit SE Fit Residual St Resid16 97,0000 80,5000 4,5973 16,5000 2,07 R


EJERCICIO 3.8

Factor Type Levels Values

Trabajador fixed 5 1, 2, 3, 4, 5

Analysis of Variance for C2, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PTrabajador 4 12.434 12.434 3.109 2.22 0.104Error 20 28.052 28.052 1.403Total 24 40.486


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S = 1.18431 R-Sq = 30.71% R-Sq(adj) = 16.86%

EJERCICIO 3.9

Source DF Seq SS Adj SS Adj MS F PDIA 4 15,440 15,440 3,860 0,40 0,804Error 20 191,200 191,200 9,560Total 24 206,640

S = 3,09192 R-Sq = 7,47% R-Sq(adj) = 0,00%

EJERCICIO 3.10

Analysis of Variance for EFECTO, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PDIA 4 15,440 15,440 3,860 0,40 0,804Error 20 191,200 191,200 9,560Total 24 206,640

UNIDAD 4

4.1 General Linear Model: RENDIMIENTO versus TEMPERATURA, HORNO


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Factor Type Levels ValuesTEMPERATURA fixed 3 t1, t2, t3HORNO fixed 4 H1, H2, H3, H4

Analysis of Variance for RENDIMIENTO, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PTEMPERATURA 2 5194.1 5194.1 2597.0 8.13 0.006HORNO 3 4963.1 4963.1 1654.4 5.18 0.016TEMPERATURA*HORNO 6 3126.3 3126.3 521.0 1.63 0.222Error 12 3833.5 3833.5 319.5Total 23 17117.0

S = 17.8734 R-Sq = 77.60% R-Sq(adj) = 57.07%

4.2 General Linear Model: TIEMPO versus MARCA, SEMANA

Factor Type Levels ValuesMARCA fixed 3 M1, M2, M3SEMANA fixed 3 S0, S3, S7

Analysis of Variance for TIEMPO, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PMARCA 2 32.752 32.752 16.376 1.74 0.195SEMANA 2 227.212 227.212 113.606 12.04 0.000MARCA*SEMANA 4 17.322 17.322 4.330 0.46 0.765Error 27 254.702 254.702 9.433Total 35 531.988

S = 3.07139 R-Sq = 52.12% R-Sq(adj) = 37.94%

Unusual Observations for TIEMPO

Obs TIEMPO Fit SE Fit Residual St Resid5 56.0000 50.5000 1.5357 5.5000 2.07 R15 42.8000 48.6500 1.5357 -5.8500 -2.20 R


4.4 General Linear Model: Rendimiento versus Recover, Humedad

Factor Type Levels ValuesRecover fixed 3 R1, R2, R3Humedad fixed 3 H1, H2, H3

Analysis of Variance for Rendimiento, using Adjusted SS for Tests


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Source DF Seq SS Adj SS Adj MS F PRecover 2 1535021 1535021 767511 6.87 0.002Humedad 2 1020639 1020639 510320 4.57 0.016Recover*Humedad 4 1089990 1089990 272497 2.44 0.061Error 45 5028397 5028397 111742Total 53 8674047

S = 334.279 R-Sq = 42.03% R-Sq(adj) = 31.72%

Unusual Observations for Rendimiento

Obs Rendimiento Fit SE Fit Residual St Resid5 1236.00 536.33 136.47 699.67 2.29 R7 130.00 888.50 136.47 -758.50 -2.49 R9 1595.00 888.50 136.47 706.50 2.32 R


4.5 General Linear Model: Rendimiento versus Temperatura, Catalizador

Factor Type Levels ValuesTemperatura fixed 4 t1, t2, t3, t4Catalizador fixed 5 c1, c2, c3, c4, c5


Source DF Seq SS Adj SS Adj MS F PTemperatura 3 430.48 430.48 143.49 10.85 0.000Catalizador 4 2466.65 2466.65 616.66 46.63 0.000Temperatura*Catalizador 12 326.15 326.15 27.18 2.06 0.074

Error 20 264.50 264.50 13.23Total 39 3487.78

S = 3.63662 R-Sq = 92.42% R-Sq(adj) = 85.21%


Obs Rendimiento Fit SE Fit Residual St Resid23 70.0000 62.5000 2.5715 7.5000 2.92 R24 55.0000 62.5000 2.5715 -7.5000 -2.92 R29 73.0000 67.0000 2.5715 6.0000 2.33 R30 61.0000 67.0000 2.5715 -6.0000 -2.33 R


4.6 General Linear Model: Rendimiento versus A, C, B


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Factor Type Levels ValuesA fixed 2 a1, a2C fixed 3 c1, c2, c3B fixed 3 b1, b2, b3


Source DF Seq SS Adj SS Adj MS F PA 1 2.241 2.241 2.241 0.51 0.478C 2 17.651 17.651 8.826 2.02 0.146B 2 56.318 56.318 28.159 6.44 0.004A*B 2 31.471 31.471 15.736 3.60 0.037A*C 2 31.203 31.203 15.601 3.57 0.037C*B 4 21.561 21.561 5.390 1.23 0.312Error 40 174.839 174.839 4.371Total 53 335.284

S = 2.09068 R-Sq = 47.85% R-Sq(adj) = 30.91%


Obs Rendimiento Fit SE Fit Residual St Resid3 22.1000 17.4481 1.0645 4.6519 2.59 R4 11.3000 15.7852 1.0645 -4.4852 -2.49 R49 19.2000 13.4648 1.0645 5.7352 3.19 R52 7.8000 11.6352 1.0645 -3.8352 -2.13 R

4.7 General Linear Model: potencia versus temperatura, estado, dureza

Factor Type Levels Valuestemperatura fixed 3 t1, t2, t3estado fixed 3 e1, e2, e3dureza fixed 3 d1, d2, d3

Analysis of Variance for potencia, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F Ptemperatura 2 0.166169 0.166169 0.083084 12.03 0.000estado 2 0.078252 0.078252 0.039126 5.67 0.005dureza 2 0.019469 0.019469 0.009734 1.41 0.250temperatura*estado 4 0.128454 0.128454 0.032113 4.65 0.002temperatura*dureza 4 0.062804 0.062804 0.015701 2.27 0.067estado*dureza 4 0.126437 0.126437 0.031609 4.58 0.002

Error 89 0.614449 0.614449 0.006904Total 107 1.196032

S = 0.0830898 R-Sq = 48.63% R-Sq(adj) = 38.24%

Unusual Observations for potencia

Obs potencia Fit SE Fit Residual St Resid


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15 0.580000 0.427685 0.034851 0.152315 2.02 R18 0.430000 0.588796 0.034851 -0.158796 -2.11 R49 0.310000 0.474352 0.034851 -0.164352 -2.18 R52 0.660000 0.474352 0.034851 0.185648 2.46 R75 0.780000 0.575185 0.034851 0.204815 2.72 R79 0.740000 0.578796 0.034851 0.161204 2.14 R

103 0.740000 0.556296 0.034851 0.183704 2.44 R


Ejercicios Estadistica Inferencial II

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2 estadistica-inferencial

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