Inference for Categorical Data

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Here is the R script from class.

library(tidyverse)

p_hat <- 0.657
n <- 680 + 105

# Create a table that mimics the resulting counts
df <- data.frame(
  Group = c(rep('Duke', 69 + 36), rep('American', 454+226)),
  Respone = c(rep('Yes', 69), rep('No', 36), rep('Yes', 454) , rep('No', 226)
  )
)

table(df$Group, df$Respone) # Verify the counts are the same

# Estimate the bootstrap sample
boots <- numeric()
for(i in 1:1000) {
  temp <- df[sample(nrow(df), size = nrow(df), replace = TRUE),]
  temp2 <- table(temp$Group, temp$Respone) %>% prop.table(1)
  boots[i] <- diff(temp2[,2])
}
mean(boots)
sd(boots)

# 95% Confidence Interval
c(mean(boots) - 1.96 * sd(boots), mean(boots) + 1.96 * sd(boots))
# Bootstrap distribution
hist(boots)