Exact Binomial

This gives the exact p-value

x_odds=50
n=75
p0=.5

binom.test(x_odds, n, p0, alternative = "greater")
## 
##  Exact binomial test
## 
## data:  x_odds 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