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## R code to accompany the textbook
## Statistics: The Art & Science of Learning from Data
## by A. Agresti, C. Franklin and B. Klingenberg
## 5th Edition, Pearson 2021
## Web: ArtofStat.com
## Copyright: Bernhard Klingenberg
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###  Chapter 10  ###
###  Example 4   ###
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## Confidence Interval for the Difference of Two Proportions ##
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# Reading in data for the first proportion
x1 <- 347
n1 <- 11535
phat1 <- x1 / n1

# Reading in data for the second proportion
x2 <- 327
n2 <- 14035
phat2 <- x2 / n2

# To compute the mean of the difference
mean <- phat1 - phat2

# To compute the standard error of the difference
se <- sqrt((phat1 * (1 - phat1) / n1) + (phat2 * (1 - phat2) / n2))

# To find the zscore for a 95% confidence interval
zscore <- qnorm(0.975)

# To compute a 95% confidence interval for the difference of two proportions
mean + c(-1, 1) * zscore * se

# Alternatively, you can also use the `prop.test()` function
prop.test(c(347, 327), c(11535, 14035), correct = FALSE)