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Math Help - Probability and statistic problem

  1. #1
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    Probability and statistic problem

    Suppose that the manufacturer a of a new medication wants to test the null hypothesis \theta = 0.90 against the alternative hypothesis \theta=0.60 . His test statistic i X, the observed number of suces(recoveries) in 20 trials, and he will accept the null hypothesis if x>14 ; otherwise , he will rejext it.Find \alphaand \beta

    Solution:

    \alpha =  P(X \leqq 14; \theta=0.90)=0.0114

    -------------------------------------------------------------

    Please can anybody tell me hw did he get 0.0114 .If posible hw did u read the binomial table .Because i am not getting the answer.
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  2. #2
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    Quote Originally Posted by zorro View Post
    Suppose that the manufacturer a of a new medication wants to test the null hypothesis \theta = 0.90 against the alternative hypothesis \theta=0.60 . His test statistic i X, the observed number of suces(recoveries) in 20 trials, and he will accept the null hypothesis if x>14 ; otherwise , he will rejext it.Find \alphaand \beta

    Solution:

    \alpha =  P(X \leqq 14; \theta=0.90)=0.0114

    -------------------------------------------------------------

    Please can anybody tell me hw did he get 0.0114 .If posible hw did u read the binomial table .Because i am not getting the answer.
    P(X \le 14|\theta=0.9)=1-P(X>14|\theta=0.9)  =1-[P(X=15|\theta=0.9)+P(X=16|\theta=0.9)+ ... + P(X=20|\theta=0.9)]

    and according to my table this gives:

    P(X \le 14|\theta=0.9)=1-[0.0319+0.0898+0.1901+0.2852+0.2702+0.1216]=0.0112

    .
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