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Confidence intervals

  1. Dec 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose you receive calls that follow a Poisson process model Y(t).
    There are two hypotheses, Hypothesis1: E[Y(t)] = λ1t = 70t and Hypothesis 2: E[Y(t)] = λ2t = 75t. Let t = 30 the number of calls be 2175.

    Find and compute a significance level α such that both Hypothesis1 and Hypothesis2 are accepted.



    2. Relevant equations

    α = P( (u - E[Y] /stdY > c / stdY)


    3. The attempt at a solution
     
    Last edited: Dec 1, 2013
  2. jcsd
  3. Dec 1, 2013 #2

    Simon Bridge

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    Good question - how are you attempting the problem?
    Presumably you've done problems involving confidence intervals and/or poisson distributon before?
     
  4. Dec 1, 2013 #3
    Opps, I forgot to type my approach. Since n is big, we can approximate the poisson with the normal.
    The variance of a poisson is the same as the expected value.



    Or am I suppose to use a two sided test?
     
    Last edited: Dec 2, 2013
  5. Dec 1, 2013 #4

    Simon Bridge

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    Well to 68% confidence limits, would you accept both hypotheses?
     
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