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“Pruebas de hipótesis: para
dos muestras
Dependientes”
Dr. Jorge Alejandro Obando Bastidas
Muestras apareadas, grupos dependientes
El contraste que se realiza es: 𝐻0 = 𝜇𝑑 = 0
𝐻1 = 𝜇𝑑 ≠ 0
Y se emplea: 𝑡0 =
ҧ
𝑑
ൗ
𝑠𝑑
𝑛
Donde
ҧ
𝑑 =
1
𝑛
෍
𝑗=1
𝑛
𝑑𝑗
𝑠𝑑
2
=
1
𝑛 − 1
෍
𝑗=1
𝑛
𝑑𝑗 − 𝑑 2
En la tabla se dan los datos de 8 proveedores en términos del número promedio de piezas rotas por
envío. ¿Indican los datos, para 0.05, que las nuevas medidas han disminuido el número promedio
de piezas rotas?
Proveedor 1 2 3 4 5 6 7 8
Antes 16 12 18 7 14 19 6 17
Después 14 13 12 6 9 15 8 15
EJEMPLO El encargado de recepción de un distribuidor de productos químicos, se enfrenta con
el problema continuo de recibir tubos de ensayo, platos Petri y matraces rotos
Jeff determinó algunas precauciones adicionales de empaque que se pueden tomar para prevenir la
rotura de las piezas y ha pedido al director de adquisiciones que informe a los proveedores de las
nuevas medidas.
Promedio(D) 19,7
Destandart(D
) 4,17252921
n 10
Raiz(n) 3,16227766
t 14,9302418
Como el valor de t cae en la zona de rechazo,
acepto la hipótesis alterna, se han reducido los
pesos con el tratamiento. El tratamiento sirvió,
por que en general las personas perdieron peso.
Antes Después D
16 14 2
12 13 -1
18 12 6
7 6 1
14 9 5
19 15 4
6 8 -2
17 15 2
17
Media de la diferencia D= 2,12
Desviación estándar de la diferencia = 2,61
𝑇 =
2,12
2,61
8
= 2,29
V= n-1=8-1=7
𝑇𝛼 = 1,89
Grados de
libertad.
Se cumple la hipótesis
alterna y las medidas que
se tomaron para disminuir
el numero de piezas rotas,
si dio resultado, fueron
efectivas.
EJEMPLO
Un club deportivo anuncia un riguroso programa de acondicionamiento físico.
El club asegura que después de un mes de seguir el programa, un participante promedio será capaz de
hacer 8 “lagartijas” más en 2 minutos que las que podía hacer al principio.
¿La muestra aleatoria de 10 participantes en el programa, cuyos datos se dan en la tabla siguiente,
apoya la afirmación del club? Utilice un nivel de significancia de 0.025.
Participante 1 2 3 4 5 6 7 8 9 10
Antes 38 11 34 25 17 38 12 27 32 29
Después 45 24 41 39 30 44 30 39 40 41
Dr. Jorge Alejandro Obando Bastidas
Jorge.obandob@campusucc.edu.co

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Hipotesis2 grupos dependientes

  • 1. “Pruebas de hipótesis: para dos muestras Dependientes” Dr. Jorge Alejandro Obando Bastidas
  • 2. Muestras apareadas, grupos dependientes El contraste que se realiza es: 𝐻0 = 𝜇𝑑 = 0 𝐻1 = 𝜇𝑑 ≠ 0 Y se emplea: 𝑡0 = ҧ 𝑑 ൗ 𝑠𝑑 𝑛 Donde ҧ 𝑑 = 1 𝑛 ෍ 𝑗=1 𝑛 𝑑𝑗 𝑠𝑑 2 = 1 𝑛 − 1 ෍ 𝑗=1 𝑛 𝑑𝑗 − 𝑑 2
  • 3. En la tabla se dan los datos de 8 proveedores en términos del número promedio de piezas rotas por envío. ¿Indican los datos, para 0.05, que las nuevas medidas han disminuido el número promedio de piezas rotas? Proveedor 1 2 3 4 5 6 7 8 Antes 16 12 18 7 14 19 6 17 Después 14 13 12 6 9 15 8 15 EJEMPLO El encargado de recepción de un distribuidor de productos químicos, se enfrenta con el problema continuo de recibir tubos de ensayo, platos Petri y matraces rotos Jeff determinó algunas precauciones adicionales de empaque que se pueden tomar para prevenir la rotura de las piezas y ha pedido al director de adquisiciones que informe a los proveedores de las nuevas medidas.
  • 4. Promedio(D) 19,7 Destandart(D ) 4,17252921 n 10 Raiz(n) 3,16227766 t 14,9302418 Como el valor de t cae en la zona de rechazo, acepto la hipótesis alterna, se han reducido los pesos con el tratamiento. El tratamiento sirvió, por que en general las personas perdieron peso.
  • 5. Antes Después D 16 14 2 12 13 -1 18 12 6 7 6 1 14 9 5 19 15 4 6 8 -2 17 15 2 17 Media de la diferencia D= 2,12 Desviación estándar de la diferencia = 2,61 𝑇 = 2,12 2,61 8 = 2,29 V= n-1=8-1=7 𝑇𝛼 = 1,89 Grados de libertad. Se cumple la hipótesis alterna y las medidas que se tomaron para disminuir el numero de piezas rotas, si dio resultado, fueron efectivas.
  • 6. EJEMPLO Un club deportivo anuncia un riguroso programa de acondicionamiento físico. El club asegura que después de un mes de seguir el programa, un participante promedio será capaz de hacer 8 “lagartijas” más en 2 minutos que las que podía hacer al principio. ¿La muestra aleatoria de 10 participantes en el programa, cuyos datos se dan en la tabla siguiente, apoya la afirmación del club? Utilice un nivel de significancia de 0.025. Participante 1 2 3 4 5 6 7 8 9 10 Antes 38 11 34 25 17 38 12 27 32 29 Después 45 24 41 39 30 44 30 39 40 41
  • 7. Dr. Jorge Alejandro Obando Bastidas Jorge.obandob@campusucc.edu.co