Question THREE [15] Part B
Do ONE of Part A or Part B.
A psychic claims to be able to tell under which of four inverted
cups you hid a peanut. The following test is made:
The test consists of six trials. One trial consists of hiding
the peanut under a randomly chosen cup of the four cups and
asking the psychic to determine which cup. If the psychic succeeds
in AT LEAST five of the six trials, she/he/it passes the test.
a) Read the rest of this question, then state the null hypothesis.
Trials are independent with 1/4 probability of success
b) Under the null hypothesis, what is the probability of passing
the test, i.e. succeeding in at least 5 of 6 trials?
(1/4)^{6} + 6 (1/4)^{5} (1/4) = 0.00464..
c) Which of these (more than one) are true?
The probability (b) is --
____ The probability the test makes the RIGHT assessment.
____ The probability the test makes the WRONG assessment.
____ The probability the psychic is an utter fraud.
____ The probability the psychic has some ability
(though not necessarily perfect).
_T_ The probability an utter fraud PASSES the test
thus deceiving us.
____ The probability an utter fraud FAILS the test
____ The probability a genuine psychic PASSES the test
____ The probability a genuine psychic FAILS the test and
so is believed a fake.
_T_ The "X" in: If the test is passed, either there
is some amount of genuine ability or something unlikely
to the extent X happened.
____ The "X" in: If the test is failed, either the
psychic is a fraud or something unlikely to the extent
X happened.