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Math Help - Hypothesis Testing

  1. #1
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    Hypothesis Testing

    Let X have a binomial distribution with the number of trails n = 10 and with p either 0.25 or 0.5. The simple null hypothesis p = 0.5 is rejected and the alternate hypothesis p = 0.25 is accepted if the observed value of X1, a random sample of size 1, is less than or equal to 3. Find the significance level and the power of the test.

    I believe that the power function is P(X<3) = P(Bin(10,0.25) < 3)and the significane leve would be  = \alpha = P_{H_0}(_{10}C_i 0.5^{10}0.5^{10-i}<3) = 0.171875

    Is this correct?
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  2. #2
    MHF Contributor matheagle's Avatar
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    You said .... is less than or equal to 3, but you only summed less than
    And you don't even say what your i is.


    \alpha=\sum_{i=0}^3 {10\choose i} (.5)^{10}
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  3. #3
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    \alpha=\sum_{i=0}^3 {10\choose i} (.5)^{10} = 0.171875

    I just forgot the equal part (and Sigma), but I have included the '3' in my calculation to calculate alpha.

    Is my power function P(X<=3) = P(Bin(10,0.25) < =3) correct?
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