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    I'm having trouble with hypothesis testing. Could someone please give me hints on how to do this particular question (from Jan 09)?

    A single observation x is to be taken from a Binomial distribution B(20, p).
    This observation is used to test H0 : p = 0.3 against H1 : p ? 0.3

    (a) Using a 5% level of significance, find the critical region for this test.
    The probability of rejecting either tail should be as close as possible to 2.5%.


    (b) State the actual significance level of this test.


    The actual value of x obtained is 3.
    (c) State a conclusion that can be drawn based on this value giving a reason for your
    answer.

    Any help would be greatly appreciated.
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    For the alternative hypothesis is it P not equal to 0.3 ? Or more than ?
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    sorry, I didn't see that. For the alt hypothesis, P is not equal to 0.3
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    X ? B(20, 0.3)
    P (X less than or equal to 2) = 0.0355
    P(X more than or equal to 11) = 1 – 0.9829 = 0.0171
    Critical region is (X less than or equal to 2) with (X more than or equal to 11)

    (b) Significance level = 0.0355 + 0.0171, = 0.0526 or 5.26%

    (c) Insufficient evidence to reject H0
    x = 3 ( or the value) is not in the critical region or 0.1071> 0.025
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    Could you please explain why you chose P (X less than or equal to 2) and P(X more than or equal to 11)? i.e why can't it be P(X is less than or equal to 3) etc.

    Thanks
 
 
 
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