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Hypothesis testing question!

  1. Sep 28, 2006 #1
    First and foremost, I am terrible in Stats so bear w/ me on this one. This is my question, if anyone has an idea on how to figure out this problem that would be great!! Here it is: Suppose you flip a coin 100 times and you want to test the hypothesis that the coin is fair, making sure there is less than a 5 percent chance of erroneously rejecting the fair coin hypothesis. How wide should the zone of acceptance be? How wide should the zone be if you flip the coin 5 times?
     
  2. jcsd
  3. Sep 28, 2006 #2

    CRGreathouse

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    What you want is a range balanced around the mean which has cumulative probability 95%. The chance of 2 or 3 heads out of 5 flips is
    ((5 choose 2) + (5 choose 3)) / 2^5 = 20/32
    The chance of 1 to 4 heads is
    ((5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4)) / 2^5 = 30/32

    With 100 flips, you are probably intended to use the normal curve as an approximation rather than the explicit binomial formula, although either would work.
     
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