It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. What is the actual p-value for this test? Round answer to 4 decimal places.

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?