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CARGA DE DATOS

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Instalamos los siguientes paquetes:

install.packages("readxl")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
## (as 'lib' is unspecified)
install.packages("ggplot2")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
## (as 'lib' is unspecified)
library(readxl)
library(ggplot2)

Cargamos los datos

datos <- read_excel("Bases_Datos_Oceanografia_Hidrogeologia.xlsx", sheet = "Oceanografia_Fondo_Marino")

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PRUEBA DE HIPÓTESIS - MEDIA (Profundidad)

H0: mu = 2000 vs H1: mu != 2000

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t.test(datos$Profundidad_m, mu = 2000, alternative = "two.sided", conf.level = 0.95)
## 
##  One Sample t-test
## 
## data:  datos$Profundidad_m
## t = 5.9715, df = 99, p-value = 3.691e-08
## alternative hypothesis: true mean is not equal to 2000
## 95 percent confidence interval:
##  2687.260 3371.275
## sample estimates:
## mean of x 
##  3029.267

Gráfica: Histograma

ggplot(datos, aes(x = Profundidad_m)) +
  geom_histogram(color = "black", fill = "skyblue", bins = 30) +
  geom_vline(xintercept = mean(datos$Profundidad_m), color = "red", linetype = "dashed") +
  geom_vline(xintercept = 2000, color = "blue", linetype = "dotted") +
  labs(title = "Distribución de Profundidad (m)",
       x = "Profundidad (m)", y = "Frecuencia") +
  theme_minimal()

—————————

PRUEBA DE HIPÓTESIS - PROPORCIÓN (Presencia de Hidrocarburos)

H0: p = 0.5 vs H1: p != 0.5

—————————

x <- sum(datos$Presencia_Hidrocarburos == 1)
n <- length(datos$Presencia_Hidrocarburos)
prop.test(x, n, p = 0.5, alternative = "two.sided", conf.level = 0.95)
## 
##  1-sample proportions test with continuity correction
## 
## data:  x out of n, null probability 0.5
## X-squared = 3.61, df = 1, p-value = 0.05743
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4970036 0.6952199
## sample estimates:
##   p 
## 0.6

Gráfica: Barra

datos$Presencia_Hidrocarburos <- factor(datos$Presencia_Hidrocarburos,
                                        levels = c(0, 1),
                                        labels = c("Ausente", "Presente"))

ggplot(datos, aes(x = Presencia_Hidrocarburos)) +
  geom_bar(fill = "orange", color = "black") +
  labs(title = "Presencia de Hidrocarburos",
       x = "Hidrocarburos", y = "Frecuencia") +
  theme_minimal()

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PRUEBA DE HIPÓTESIS - VARIANZA (Densidad del Sedimento)

H0: sigma^2 = 0.01 vs H1: sigma^2 != 0.01

—————————

var_obs <- var(datos$Densidad_Sedimento_gcm3)
n_var <- length(datos$Densidad_Sedimento_gcm3)
var_hip <- 0.01  # 0.1^2

chi_sq <- (n_var - 1) * var_obs / var_hip
p_value <- 2 * min(pchisq(chi_sq, df = n_var - 1), 1 - pchisq(chi_sq, df = n_var - 1))

cat("Estadístico Chi-cuadrado:", chi_sq, "\n")
## Estadístico Chi-cuadrado: 1396.91
cat("Valor p:", p_value, "\n")
## Valor p: 0

Gráfica: Boxplot

ggplot(datos, aes(y = Densidad_Sedimento_gcm3)) +
  geom_boxplot(fill = "lightgreen", color = "black") +
  labs(title = "Boxplot de Densidad del Sedimento",
       y = "Densidad (g/cm³)") +
  theme_minimal()

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