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Homework Help: Power function

  1. Oct 15, 2008 #1
    A coin is suspected of bias towards heads, so a test is made of the hypothesis H0: p=1/2 against H1:p>1/2, where p is the probability of heads. The test is to count the number of heads, X, in 10 tosses of the coin, and reject H0 if X=8, 9, or 10.
    Show that the power function for this test is given by: p^8(45-80p+36p^2)

    I have no idea how to start. I know that the power function means: P(reject H0 given H0 is false) but i dont know how to continue.

    Any help would be very much appreciated.
    Thank you
  2. jcsd
  3. Oct 15, 2008 #2


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    I think you can ignore the part "given H0 is false" because the test is expressed for an arbitrary p (which may or may not be the value of p under H1).

    So, all you need is to express the probability of obtaining X > 7 in 10 throws using the binomial formula.
  4. Oct 15, 2008 #3
    Oh right
    Thank you v much!!!
    (I should have known that)
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