## R Code from Pigs Example - 1/16/20

## Test if probability pig lands on its back is 0.20 or not.
## H0: pi = 0.2 vs Ha: pi != 0.2

## Class data: 4 pigs landed on their back out of 10 tosses

## Likelihood function: n = 10 ,y = 4
curve(x^4 * (1-x)^6, 0, 1, xlab = "pi", ylab= "Likelihood")
# Maximized at pi = 4/10

## p-value?
## Find probability of 4 or something less likely
barplot(dbinom(0:10, 10, 0.2), names.arg = 0:10)
abline(h = dbinom(4, 10, .2))
1-pbinom(3, 10, .2)

# or use built-in function
binom.test(4, 10, .2)

## What if we observed the same sample proportion in 100 tosses?
barplot(dbinom(0:100, 100, 0.2), names.arg = 0:100)
# Now 40 is extremely unlikely
binom.test(40, 100, .2)