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Tabla de Valores Críticos t-Student

This document discusses the t-distribution of Student, which arises in statistical analysis when the population variance is unknown and must be estimated from a sample. It presents the derivation of the t-distribution, showing that when random variables are normally distributed with unknown variance, the ratio of the mean difference to the standard error has a t-distribution. The t-distribution depends on the degrees of freedom but not the true mean or variance. Finally, it provides the probability density function of the t-distribution.

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Juan Carlos Marulanda Delgado
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800 views2 pages

Tabla de Valores Críticos t-Student

This document discusses the t-distribution of Student, which arises in statistical analysis when the population variance is unknown and must be estimated from a sample. It presents the derivation of the t-distribution, showing that when random variables are normally distributed with unknown variance, the ratio of the mean difference to the standard error has a t-distribution. The t-distribution depends on the degrees of freedom but not the true mean or variance. Finally, it provides the probability density function of the t-distribution.

Uploaded by

Juan Carlos Marulanda Delgado
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Tabla de valores crticos de la distribucin t de

Student
/2

Niveles de Significancia DOS COLA


0.500
1.00
0.82
0.76
0.74
0.73
0.72
0.71
0.71
0.70
0.70
0.70
0.70
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.250

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

0.250
2.41
1.60
1.42
1.34
1.30
1.27
1.25
1.24
1.23
1.22
1.21
1.21
1.20
1.20
1.20
1.19
1.19
1.19
1.19
1.18
1.18
1.18
1.18
1.18
1.18
1.18
1.18
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
1.17
0.125

0.200
3.08
1.89
1.64
1.53
1.48
1.44
1.41
1.40
1.38
1.37
1.36
1.36
1.35
1.35
1.34
1.34
1.33
1.33
1.33
1.33
1.32
1.32
1.32
1.32
1.32
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.30
1.30
1.30
1.30
0.100

0.100
6.31
2.92
2.35
2.13
2.02
1.94
1.89
1.86
1.83
1.81
1.80
1.78
1.77
1.76
1.75
1.75
1.74
1.73
1.73
1.72
1.72
1.72
1.71
1.71
1.71
1.71
1.70
1.70
1.70
1.70
1.70
1.69
1.69
1.69
1.69
1.69
1.69
1.69
1.68
1.68
0.050

0.050
12.71
4.30
3.18
2.78
2.57
2.45
2.36
2.31
2.26
2.23
2.20
2.18
2.16
2.14
2.13
2.12
2.11
2.10
2.09
2.09
2.08
2.07
2.07
2.06
2.06
2.06
2.05
2.05
2.05
2.04
2.04
2.04
2.03
2.03
2.03
2.03
2.03
2.02
2.02
2.02
0.025

0.025
25.45
6.21
4.18
3.50
3.16
2.97
2.84
2.75
2.69
2.63
2.59
2.56
2.53
2.51
2.49
2.47
2.46
2.45
2.43
2.42
2.41
2.41
2.40
2.39
2.38
2.38
2.37
2.37
2.36
2.36
2.36
2.35
2.35
2.35
2.34
2.34
2.34
2.33
2.33
2.33
0.013

0.020
31.82
6.96
4.54
3.75
3.36
3.14
3.00
2.90
2.82
2.76
2.72
2.68
2.65
2.62
2.60
2.58
2.57
2.55
2.54
2.53
2.52
2.51
2.50
2.49
2.49
2.48
2.47
2.47
2.46
2.46
2.45
2.45
2.44
2.44
2.44
2.43
2.43
2.43
2.43
2.42
0.010

Niveles de Significancia UNA COLA

0.010
63.66
9.92
5.84
4.60
4.03
3.71
3.50
3.36
3.25
3.17
3.11
3.05
3.01
2.98
2.95
2.92
2.90
2.88
2.86
2.85
2.83
2.82
2.81
2.80
2.79
2.78
2.77
2.76
2.76
2.75
2.74
2.74
2.73
2.73
2.72
2.72
2.72
2.71
2.71
2.70
0.005

0.005
127.32
14.09
7.45
5.60
4.77
4.32
4.03
3.83
3.69
3.58
3.50
3.43
3.37
3.33
3.29
3.25
3.22
3.20
3.17
3.15
3.14
3.12
3.10
3.09
3.08
3.07
3.06
3.05
3.04
3.03
3.02
3.01
3.01
3.00
3.00
2.99
2.99
2.98
2.98
2.97
0.003

En probabilidad y estadstica, la distribucin-t o distribucin t de Student es una distribucin de


probabilidad que surge del problema de estimar la media de una poblacin normalmente distribuida
cuando el tamao de la muestra es pequeo. sta es la base del popular test de la t de Student para la
determinacin de las diferencias entre dos medias muestrales y para la construccin del intervalo de
confianza para la diferencia entre las medias de dos poblaciones.
La distribucin t surge, en la mayora de los estudios estadsticos prcticos, cuando la desviacin
estndar o varianza de una poblacin se desconoce y debe ser estimada a partir de los datos de una
muestra.
Aparicin y especificaciones de la distribucin t de Student
Supongamos que X1,..., Xn son variables aleatorias independientes distribuidas normalmente, con
media y varianza 2. Sea

la media muestral y

la varianza muestral. Entonces, est demostrado que

se distribuye segn una normal de media 0 y varianza 1.


Gosset estudi una expresin relacionada,

y mostr que T tiene la siguiente funcin de densidad:

Con igual a n 1.
La distribucin de T se llama ahora la distribucin-t. El parmetro se llama
convencionalmente el nmero de grados de libertad. La distribucin depende de , pero no de
o ; la independencia de y es lo que hace a la distribucin t tan importante en la teora y en
la prctica. es la funcin gamma.

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