1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability question -- A test to see if a coin is fair...

  1. May 29, 2015 #1
    1. The problem statement, all variables and given/known data

    You want to see if a coin is fair. You flip it 5 times and count the number of heads. If H is the number of heads obtained in five flips of the coin, what is the P-value of the test when H equals 4?



    2. Relevant equations
    None

    3. The attempt at a solution

    To solve this problem, I thought that it would be correct to use the binomial PDF, to answer the question "If the probability of getting heads is .5, then what are the chances of getting 4 heads in 5 flips?" This gives .15625, which is not the right P-value. The correct answer is 3/16, but how do I get this value? What probability distribution to I use to obtain this P-value?
     
  2. jcsd
  3. May 29, 2015 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The p-value is not the probability of landing on the exact outcome. It is the probability of obtaining that or a more extreme outcome. I would also disagree on how the "correct" answer has chosen to define an outcome as extreme (getting 1 head is as extreme as getting 4, getting 0 is as extreme as getting 5 - you would typically not design a test which broke the symmetry).
     
  4. May 29, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    For binomial(5, 1/2), they take p-value = P(4) + P(5) = (5/32) + (1/32) = 3/16, so they take p-value = P(4 or more heads).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Probability question -- A test to see if a coin is fair...
Loading...