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Hypothesis test (binomial) problem

  1. Feb 1, 2014 #1
    1. The problem statement, all variables and given/known data

    Hester suspected that a die was biased in favour of a four occuring. She decided to carry out a hypothesis test. When she threw the die 15 times, she obtained a four on 6 occasions. Carry out the test, at the 5% level, stating your conclusion clearly.

    2. Relevant equations
    None.


    3. The attempt at a solution

    Ho: p = 1/6
    H1: p > 1/6

    If Ho is true, then X~B (15, 1/6)
    Reject Ho if P (X >= 6) < 5%

    P (X >= 6) = 1 - P(X <=5)

    = 1- (5/6)^15 - (15C1)(1/6)(5/6)^14 - (15C2)(1/6)^2 (5/6)^13 - (15C3)(1/6)^3 (5/6) ^12 -(15C4)(1/6)^4 (5/6)^11 -(15C5)(1/6)^5 (5/6)^10

    =0.0274
    =3% (1 s.f.)

    Since P (X>=6) < 5%, reject Ho.

    The die is biased in favour of 4.

    (Answer: no evidence that shows die is biased)

    Why am I wrong?
     
  2. jcsd
  3. Feb 1, 2014 #2

    PeroK

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    In my view, you're right. The answer must be wrong.
     
  4. Feb 1, 2014 #3

    Ray Vickson

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    I agree.
     
  5. Feb 1, 2014 #4
    Thanks.
     
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