Dr Venkman claims he has extrasensory powers and can tell which of two symbols is on a card turned face down. To test his ability he is asked to do this for a sequence of trials. Let the null hypothesis be that he is just guessing, so that the probability is 1/2 of his getting it right each time, and let the alternative hypothesis be that he can name the symbol correctly more than half the time. Required:
Devise a test with the property that the probability of a type I error (concluding Venkman is psychic when he is in fact a fraud) is less than 0.05 and the probability of a type II error (concluding Venkman is a fraud when he is in fact psychic) is less than 0.05 if Venkman can name the symbol correctly 70 percent of the time.