Ex7 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306 INTRODUCTORY STATISTICS Sem 1 2008 / 2009 EXAMPLE CLASS 7 1. An experiment is carried out to test whether a psychic can really read minds. The psychic is placed in one room and the subject whose mind will be read in another room. The subject chooses one of 10 different geometric shapes and is told to picture this shape mentally. The psychic is then supposed to read the subject’s mind and correctly identify the shape chosen. a) The experimenter believes that the psychic will be unable to read the subject’s mind and thus must guess (pick one of the 10 shapes at random). What is the probability that the psychic guesses correctly in a particular trial? b) The experiment is independently repeated 10 times, and the number X of correct answers given by the psychic is recorded. If the psychic is guessing, state the exact distribution of X. What are the values of the mean and variance of X? c) The experimenter decides that if the psychic gets 8 or more correct answers in the 10 trials of the experiment, this will be evidence that the psychic can read minds. If in fact, the psychic is only guessing, what is the probability that the experimenter will come to a false conclusion that the psychic can read minds? 2.
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This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

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Ex7 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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