The test is h0: p = 0.20 vs. : p ≠ 0.20 . if the null hypothesis is rejected, the conclusion is the subject has esp (extrasensory perception). otherwise the person is deemed a random guesser.

a) what is a type i error in this situation?

b) what is a type ii error in this situation?

c) if the significance level is 0.04, what proportion of random guessers will be incorrectly identified as having esp?

d) suppose that people with psychic ability were to exist. assume for simplicity their powers are such that they have an actual probability of p = 0.21 of guessing correctly. if a significance level 0.04 test is used, what proportion of these people will be identified as random guessers? (n = 200 cards)

e) what is the p-value of a test subject getting 55 correct out of 200, does this p-value depend on the 0.04 significance level?