2.57. 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 da vou collect. Suppose the coin is actually biased so that...

Extracted text: 2.57. 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 da vou 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.) [Hint: How many heads would it take for you to get a p-value less than 0.05?