Suppose you are going to test a coin to see if it is fair.
a) You decide to flip it 200 times and to conduct a binomial test with the data you collect. Suppose the coin is actually biased so that it comes up heads 55% of the time. What is the probability that your test will have a p-value less than 0.05?
b) How does your answer change if you flip the coin 400 times instead?
c) How many flips must you perform if you want a 90% chance of detecting a coin that comes up heads 55% of the time. (Assume here again that we will reject the null hypothesis if the p-value is less than 0.05.)