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Math Help - Hypothesis Testing: Power Function

  1. #1
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    Hypothesis Testing: Power Function



    My attempt:
    a) Test statistic: Z = (X bar - 13) / (4/sqrt n)
    Let μ = μ_a > 13 be a particular value in H_a
    Power(μ_a)
    = 1- beta(μ_a)
    = P(reject Ho | H_a is true)
    = P(reject Ho | μ = μ_a)
    = P(Z>1.645 | μ = μ_a)
    = P(X bar > 13 + [(1.645 x 4)/(sqrt n)] | μ = μ_a)
    I also know that X bar ~ N(μ, 16/n)
    I am stuck here...How can I proceed from here and express the power in terms of μ and n?


    Thank you very much!


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  2. #2
    Senior Member
    Joined
    Jan 2009
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    Now I have a little more progress:

    Power(μ_a)
    = P(X bar > 13 + [(1.645 x 4)/(sqrt n)] when μ = μ_a)
    And X bar has the distribution N(μ, 16/n)

    Here, we know the distribution of X bar, so I believe that we can express P(X bar > 13 + [(1.645 x 4)/(sqrt n)] when μ = μ_a) as an integral of the normal density and replace μ by μ_a, but how can I integrate it and get a compact answer?

    Thank you!
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