###### R command for chapter 4

#### 4.5-2
### Example 2
## Prob of type I error: P(Y <= 1 | p=0.03)
pbinom(1, size=100, prob=0.03)
# 0.1946221
## Prob of type II error: P(Y >= 2 | p=0.01)
1 - pbinom(1, size=100, prob=0.01)
# 0.264238

## try other rejection region
c(pbinom(0, size=100, prob=0.03),1 - pbinom(0, size=100, prob=0.01))
#0.04755251 0.63396766
c(pbinom(2, size=100, prob=0.03),1 - pbinom(2, size=100, prob=0.01))
#0.4197751 0.0793732

## try other sample size
c(pbinom(0, size=300, prob=0.03),1 - pbinom(0, size=300, prob=0.01))
#[1] 0.0001075277 0.9509591059
c(pbinom(1, size=300, prob=0.03),1 - pbinom(1, size=300, prob=0.01))
#[1] 0.001105207 0.802350336
c(pbinom(2, size=300, prob=0.03),1 - pbinom(2, size=300, prob=0.01))
#[1] 0.005718189 0.577936082
c(pbinom(4, size=300, prob=0.03),1 - pbinom(4, size=300, prob=0.01))
# 0.05243413 0.18388883
c(pbinom(5, size=300, prob=0.03),1 - pbinom(5, size=300, prob=0.01))
#[1] 0.11202003 0.08290356
c(pbinom(6, size=300, prob=0.03),1 - pbinom(6, size=300, prob=0.01))
#0.20262746 0.03275095

## operating characteristic curve OC(p)
focp <- function(p) {
  1 - pbinom(1, size=100, prob=p);
}
focp3 <- function(p) {  # with different sample size
  1 - pbinom(5, size=300, prob=p);
}
## plot OC(p)
par(mfrow=c(1,1))
plot(focp, xlim=c(0,0.05), xlab="p", ylab="OC(p)", main="Figure 4.5-2")
plot(focp3, xlim=c(0,0.05), lty=2, add=T)
legend(0.03,0.4,legend=c("n=100","n=300"),lty=c(1,2))