Distribución de probabilidades para resolver problemas de diferencia entre medias y proporciones muestrales

Distribución de probabilidades para resolver problemas de diferencia entre medias y proporciones muestrales
Para resolver problemas de diferencia entre medias y proporciones muestrales, la distribución de probabilidad más comúnmente utilizada es la distribución normal en ciertos escenarios, o la distribución t de Student cuando la varianza poblacional es desconocida y la muestra es pequeña. Aquí te resumo los principales enfoques:[br][br][b]1. Diferencia entre medias muestrales[/b][list][*]Cuando la varianza poblacional es conocida y la muestra es grande (n ≥ 30):[br]La diferencia entre medias se modela como una distribución normal:[/*][/list][br][math]Z=\frac{\left(X_1-X_2\right)-\left(\mu_1-\mu_2\right)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}\Longrightarrow N\left(0,1\right)[/math][br][br][list][*]Cuando la varianza poblacional es desconocida y la muestra es pequeña:[br]Se usa la distribución t de Student:[/*][/list][math]T=\frac{\left(X_1-X_2\right)-\left(\mu_1-\mu_2\right)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\Longrightarrow t_{df}[/math][br][br][br]​En donde [math]s^2_1[/math]​, [math]s_2^2[/math] son las varianzas muestrales y [math]df[/math]df son los grados de libertad, calculados con fórmulas específicas (por ejemplo, de Welch).[br][br][br][b]2. Diferencia entre proporciones muestrales[/b][br][br]La diferencia entre proporciones se modela mediante una distribución normal cuando las muestras son grandes, gracias a la Teorema Central del Límite:[br][br][math]Z=\frac{\left(p'_1-p'_2\right)-\left(p_1-p_2\right)}{\sqrt{p\left(1-p\right)\frac{1}{n_1}+\frac{1}{n_2}}}\Longrightarrow N\left(0,1\right)[/math][br][br][br]En donde [math]p'_1[/math], [math]p'_2[/math] ​ son las proporciones muestrales y [math]p[/math] es una proporción combinada.
Ejemplo práctico 1.
[i]El sueldo mensual de los licenciados en educación en Bogotá es de $920.000 como promedio, con una desviación estándar de $31.500. En la misma ciudad, el salario mensual de los economistas en la administración pública es de $925.000, con una desviación estándar de $52.500. Se toma una muestra aleatoria de 100 de cada población. ¿Cuál es la probabilidad de que la diferencia en las asignaciones B sea superior a las de A en $12.510?[/i][br][br][b]Datos [/b][b]que nos proporciona el enunciado:[/b][br][br][b]Población A:[/b][br][br]Media [math]\text{(μ_A) = 920,000}[/math][br]Desviación estándar [math]\text{(σ_A ) = 31,500}[/math] [img width=93,height=16]file:///C:/Users/Usuario/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png[/img][br]Muestra [math]\text{(n_A ) = 100}[/math][br][br][b]Población B:[/b][br][br]Media [math](μ_B​)=925,000[/math][br]Desviación estándar [math](σ_B​)=52,500[/math][br]Muestra [math](n_B​)=100[/math][br][br] [br][b]Objetivo:[/b][br][br]Calcular [math]P((XˉB​−XˉA​)>12,510)[/math][br] [br][br][b]1. Media de la diferencia de medias:[br][/b][br][math]\text{μ_Δ =μ_B -μ_A =925,000-920,000=5,000}[/math][br][br][b][br]2. Desviación estándar de la diferencia de medias:[/b][br][br][img]data:image/png;base64,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[/img][br][br][b] [/b][br][b]3. Puntuación Z:[/b][br][br]Queremos [i]P[/i]([i]X[/i]ˉ[i]B[/i]​−[i]X[/i]ˉ[i]A[/i]​>12,510). La variable Z es:[br][br][br] [b]4. Buscar la probabilidad en la tabla Z:[/b][br][br][math]P(Z>1.227)=1−P(Z<1.227)[/math][br][br]Desde la tabla Z o una calculadora:[br][br][math]P(Z<1.227)=0.8907[/math][br][br]Por lo tanto,[br][br][math]P(Z>1.227)=1−0.8907=0.1093[/math][br][br]Y en porcentaje:[br][br][math]0.1093×100=10.93\%[/math][br][br][br][b]Respuesta.- [/b]La probabilidad de que la diferencia en las medias sea mayor a $12,510 en favor de B es aproximadamente [b]10.93%[/b].[br][br]

Information: Distribución de probabilidades para resolver problemas de diferencia entre medias y proporciones muestrales