(2) 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. 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. (2) 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. 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