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### 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 --

1. ____ The probability the test makes the RIGHT assessment.
2. ____ The probability the test makes the WRONG assessment.
3. ____ The probability the psychic is an utter fraud.
4. ____ The probability the psychic has some ability (though not necessarily perfect).
5. _T_ The probability an utter fraud PASSES the test thus deceiving us.
6. ____ The probability an utter fraud FAILS the test
7. ____ The probability a genuine psychic PASSES the test
8. ____ The probability a genuine psychic FAILS the test and so is believed a fake.
9. _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.
10. ____ The "X" in:   If the test is failed, either the psychic is a fraud or something unlikely to the extent X happened.
11. _T_ A type I error.
12. ____ A type II error.