Suppose a marriage counselor wants to investigate how regional background of a spouse affects marital success. He randomly assigns a participant into two groups where group A constitute marriage partner from the same region of the country and group B comprises of those whose marriage partners are from different regions. Ratings of the success of the marriage, the higher the rating, the better the marriage. The following data were observed for group A; 10 9 8 8 9 10 9 8 7 8 for group B; 6 7 8 8 7 7 6 5 8 6 Use T-test to answer the above question
Question
Suppose a marriage counselor wants to investigate how regional background of a spouse affects marital success. He randomly assigns a participant into two groups where group A constitute marriage partner from the same region of the country and group B comprises of those whose marriage partners are from different regions. Ratings of the success of the marriage, the higher the rating, the better the marriage. The following data were observed for group A; 10 9 8 8 9 10 9 8 7 8 for group B; 6 7 8 8 7 7 6 5 8 6
Use T-test to answer the above question
Solution
Para resolver esta pregunta utilizando una prueba T, seguiremos los siguientes pasos:
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Plantear las hipótesis:
- Hipótesis nula (H0): No hay diferencia significativa en el éxito matrimonial entre los dos grupos.
- Hipótesis alternativa (H1): Hay una diferencia significativa en el éxito matrimonial entre los dos grupos.
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Calcular las medias y las desviaciones estándar de cada grupo:
- Grupo A: 10, 9, 8, 8, 9, 10, 9, 8, 7, 8
- Grupo B: 6, 7, 8, 8, 7, 7, 6, 5, 8, 6
Media de Grupo A:
Media de Grupo B:
Desviación estándar de Grupo A:
Desviación estándar de Grupo B:
Calculando estos valores:
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Calcular el estadístico t: Donde .
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Determinar el valor crítico y comparar:
- Grados de libertad:
- Usando una tabla de distribución t para y un nivel de significancia común (por ejemplo, 0.05), el valor crítico es aproximadamente 2.101.
Comparar el valor calculado de t con el valor crítico:
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Conclusión: Dado que el valor calculado de t (3.65) es mayor que el valor crítico (2.101), rechazamos la hipótesis nula. Esto indica que hay una diferencia significativa en el éxito matrimonial entre los dos grupos.
Por lo tanto, podemos concluir que el origen regional de los cónyuges afecta significativamente el éxito matrimonial.
Similar Questions
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