## Question

###### Problem Five (Hypothesis Testing) Suppose want to test if Yifu claims to have Extrasensory Perception (ESP) , and that if draw card drawn randomly and with replacement from an ordinary deck of cards, he can guess the suit without seeing the cardam sceptical and propose to test his claim_ formulate the hypothesis that when he tells me the suit; he is just guessing and the probability of his getting it right is 25%Therefore perform 100 trials where shuffle the deck, draw card, ask him to guess the

Problem Five (Hypothesis Testing) Suppose want to test if Yifu claims to have Extrasensory Perception (ESP) , and that if draw card drawn randomly and with replacement from an ordinary deck of cards, he can guess the suit without seeing the card am sceptical and propose to test his claim_ formulate the hypothesis that when he tells me the suit; he is just guessing and the probability of his getting it right is 25% Therefore perform 100 trials where shuffle the deck, draw card, ask him to guess the suit, and then replace the card: decide that since ESP is about guessing the card"s suit correctly; will make this one-sided (right) test with LOS 0.05. We perform the test and Yifu identifies 32 of the cards correctly: Now at this point; realize that if use the normal distribution, it will be an estimate and am not sure how well it will work; because B(100,0.25) is not symmetric. So decide for maximum precision | Il use the binomial directly; but how to calculate an LOS that goes along with discrete distribution (think about how to calculate the top % of B(3,1/2)4)? So decide to reason backwards: I'Il calculate P(X > 32) and see if it is ess than my LOS (which would mean it has to be in the critical region). (A) Perform the test as specified. Reject if P(X > 32) < LOS and fail to reject otherwise (B) What is the smallest number of cards Yifu would have to identify to make me reject my hypothesis at the % LOS? Hint: use binom cdf