Exact Binomial

This gives the exact p-value from the known distribution.

# EXACT BINOM TEST
x_obs<-50
n<-75
p0<-.5

binom.test(x_obs, n, p0, alternative = "greater")
## 
##  Exact binomial test
## 
## data:  x_obs and n
## number of successes = 50, number of trials = 75, p-value =
## 0.002614
## alternative hypothesis: true probability of success is greater than 0.5
## 95 percent confidence interval:
##  0.5665713 1.0000000
## sample estimates:
## probability of success 
##              0.6666667

Simulated Binomial

# BINOM SIM
nsim<-10000

nullDist<-rbinom(nsim, 75, .5)

hist(nullDist)
abline(v=50, col="red", lwd=2, lty=2)

head(nullDist)
## [1] 42 37 45 43 40 37
head(nullDist>=50)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE
mean(nullDist>=50)
## [1] 0.0032