Normal approximation to the binomial distribution
Example A scientist wants to determine if a loonie is a fair coin. He carries out an experiment where he flips the coin 1,000,000 times, and counts the number of heads. Heads come up 543,123 times. Using these data, test the fairness of the loonie.
Inference about means Because is normally distributed:
But... We don’t know A good approximation to the standard normal is then: Because we estimated s, t is not exactly a standard normal!