# Solution to BPS Exercise 15.16
score.change = c(0,0,0,0,24,24,24,24)

#15.16a
groups = sample(c(1,1,1,1,2,2,2,2))
agroup = score.change[groups == 1]
bgroup = score.change[groups == 2]
print("a group mean:")
print(mean(agroup))
print("b group mean:")
print(mean(bgroup))
print("difference of means")
print(mean(agroup) - mean(bgroup))

#15.16b
n = 10000
trials = replicate(n,{
  groups = sample(c(1,1,1,1,2,2,2,2));
  agroup = score.change[groups == 1];
  bgroup = score.change[groups == 2];
  mean(agroup) - mean(bgroup);
})
barplot(table(trials))