Question

Subjects tested for ESP (extrasensory perception) are presented one of five types of cards, “circle”, “plus”,”wavy lines”, “square” and “star”. The type of card is hidden from the subject, and the subject attempts to use “psychic powers” to determine the card. (https://psychicscience.org/esp3) The test we are conducting is ?0 : ? = 0.20 vs. ??: ? ≠ 0.20 . Note that a person without ESP (that is, a “random guesser”) would be characterized at having ? = 0.20. Someone with ESP would be characterized as having ? ≠ 0.20

a) Suppose someone is presented 200 cards, and gets 51 correct. Compute the p-value.

b) Suppose someone is presented 200 cards, and gets 29 correct. Compute the p-value.

c) Suppose someone is presented 200 cards, and gets 59 correct. Compute the p-value.

d) Suppose that the significance level of the test is set at ? = 0.008, and a sample of size 200 is to be chosen. Find the rejection region, that is, find the set of values of ?̂ that would lead to the rejection of ?0 .

e) What percent of random guessers, when administered this test, will be (incorrectly) diagnosed as having ESP? If 10,000 random guessers are given the test, what is the expected number to be incorrectly categorized as having ESP? For these people, what type of error is committed?

f) Suppose the significance level of the test is set at ? = 0.008, and a sample of size 200 is to be chosen. What is the probability that the test will fail to detect a person with ESP, if in reality ? = 0.21 for this person? If this event were to happen, would it be a type I error, type II error or a correct decision?

Answer 1

a)

b)

c)

d)

Rejection region :

or,

or,