A student majoring in psychology designs an experiment to test for extrasensory perception (ESP). In this experiment, a card is randomly selected from a shuffled deck, and the blindfolded subject must guess the suit (clubs, diamonds, hearts, spades) of the card selected. The experiment is repeated 25 times, with the card replaced and the deck reshuffled each time.
a. For subjects who make random guesses with no ESP, find the expected mean number of correct responses.
b. For subjects who make random guesses with no ESP, find the expected standard deviation for the numbers of correct responses.
c. For subjects who make random guesses with no ESP, find the probability of getting more than 12 correct responses.
d. If a subject gets more than 12 correct responses, test the claim that he or she made random guesses. Use a 0.05 level of significance.
e. You want to conduct a survey to estimate the percentage of adult Canadians who believe that some people have ESP. How many people must you survey if you want 90% confidence that your sample percentage is in error by no more than four percentage points?