# R code to analyze a 1 by c contingency table
# and make inference about the multinomial probabilities

# We look at the blood types data set:

# The observed counts are 465, 394, 96, 45.

# We test whether the corresponding cell probabilities are
# (0.45, 0.4, 0.1, 0.05) using  the chisq.test() function in R:

chisq.test(c(465, 394, 96, 45), p=c(0.45, 0.4, 0.1, 0.05), correct=FALSE)


# Verifying large-sample assumption:

obs.counts <- c(465, 394, 96, 45)
names(obs.counts) <- c("O", "A", "B", "AB")

nullprobs <- c(0.45, 0.4, 0.1, 0.05)
names(nullprobs) <- names(obs.counts) 

exp.counts <- sum(obs.counts) * nullprobs
print(exp.counts)

# The expected cell counts are all at least 5.