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Math Help - need help with a sign test problem

  1. #1
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    need help with a sign test problem

    Use a sign test to test this claim.
    A researcher wishes to study whether music has any effect on the ability to memorize information. 83 randomly selected adults are given a memory test in a quiet room. They are then given a second memory while listening to classical music. 66 people received a higher score on the second test, 16 a lower score, and 1 received the same score. At the 0.05 significance level , test the claim that the music has no effect on memorization skills.
    Last edited by mr fantastic; June 20th 2009 at 10:44 PM. Reason: Restored question deleted by OP
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  2. #2
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    Quote Originally Posted by tennisair View Post
    Use a sign test to test this claim.
    A researcher wishes to study whether music has any effect on the ability to memorize information. 83 randomly selected adults are given a memory test in a quiet room. They are then given a second memory while listening to classical music. 66 people received a higher score on the second test, 16 a lower score, and 1 received the same score. At the 0.05 significance level , test the claim that the music has no effect on memorization skills.
    Outline:

    + if X_i > Y_i,
    0 if X_i = Y_i,
    - if X_i < Y_i.

    H0: Pr(X > Y) = Pr(X < Y), that is, H0: Pr(+) = Pr(-).

    H1: \Pr(X > Y) \neq \Pr(X < Y), that is, H1: \Pr(+) \neq \Pr(-) (why?)

    The test is based on the test statistic Z = freq(+). Under H0, Z ~ Binomial(n = n*, 0.5) where n* is the number of observations of + or - signs.

    Calculate P = 2 \Pr(Z \geq 66) where Z ~ Binomial(n = 82, p = 0.5).
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