A student majoring in psychology designs an experiment to te

A student majoring in psychology designs an experiment to test for extrasensory perception

(ESP). In this experiment, a single card is randomly selected from a shuffled deck of cards, and

the blindfolded subject must guess the suit (spades, hearts, diamonds or clubs) of the card. The

experiment is repeated 50 times (replacing the card and reshuffling the deck each time).

A person with no ESP abilities, that randomly guesses the suit, should be correct 25% of the

time. However, if a person has this ability, they should be able to correctly identify the suit more

than 25% of the time. In other words, the probability of correctly identifying the suit would be

greater than 0.25.

a) Suppose Xorax the Magician does possess the ability to correctly identify the unknown card

50% of the time. If the psychology student administered his test to Xorax, what is the

probability that he would conclude that Xorax has ESP (that is, would reject H0 – this is the

power of the test at = 0.50)? [Hint: restate the rejection region in terms of ˆ , then calculate

the probability of rejecting H0 assuming = 0.50]

b)Suppose the student wanted 90% power to detect someone with Xorax’s abilities. What

sample size (number of card reading attempts) should he employ?