# Heights in the call above 5 feet. ----
men=c(10,12,13,12,9,8,16,12,22,13,8)
women=c(6,7,6,4,5,0,11,5,9,5,5,3,5,5,3,3,7,8,4,7,3,3)

men.mean = mean(men)
men.var = var(men)
men.n = length(men)

women.mean = mean(women)
women.var = var(women)
women.n = length(women)

# We compute the pooled variance using 
# intermediate values so it looks nicer
a = (men.n-1)*men.var + (women.n-1)*women.var
a = a/(men.n + women.n -2)
b = 1/men.n + 1/women.n
pooledVar = a*b
tstatistic = (men.mean-women.mean)/pooledVar
df = men.n + women.n - 2
p.value = 1-pt(tstatistic, df)

#Display the relevant numbers
men.mean
men.n
men.var
women.mean
women.n
women.var

tstatistic
p.value

# NHST with alpha = 0.05
alpha = 0.05
print(p.value)
# p.value << .05 so we reject H_0 in favor of the 
# hypothesis that men are taller than woment
if (p.value < alpha)
  print("Rejected the null hypothesis")
if (p.value >= alpha)
  print("Failed to reject the null hypothesis")