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    I'm not entirely sure how to do these.

    I can find the critical region fine, but how do I prove whether a test is significant?

    for example

    in the Heinemann book; 4C question 5.
    Carry out the following test.

    H0: p = 0.5
    H1: p does not = 0.5

    n=20, x=7
    using a 10% level of significance

    ---

    Ok, here's what I'm doing, can anyone point out my mistake?

    X~B(20,0.5)

    P(X<=7)= 0.1316
    P(X>=7)= 1 - 0.9423

    not significant.
    The answer in the back is also not significant, but it says 0.2632!

    what am I doing wrong?
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    You're doing a one-sided test. The test with critical region

    X <= 7 or X >= 13

    has significance level 2*0.1316.
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    (Original post by Jonny W)
    You're doing a one-sided test. The test with critical region

    X <= 7 or X >= 13

    has significance level 2*0.1316.
    where did X >= 13 come from?

    I don't quite understand you.. what am I doing wrong?
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    (Original post by Jonny W)
    You're doing a one-sided test. The test with critical region

    X <= 7 or X >= 13

    has significance level 2*0.1316.
    why do you double it?
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    (Original post by kimoni)
    where did X >= 13 come from?

    I don't quite understand you.. what am I doing wrong?
    One-sided test
    H0: p = 0.5
    H1: p < 0.5
    You reject H0 when X <= 10 - k. The significance level is the value of P(X <= 10 - k) when p = 0.5.

    Two-sided test
    H0: p = 0.5
    H1: p not equal 0.5
    You reject H0 when X <= 10 - k or X >= 10 + k (ie, when |X - 10| >= k). The significance level is the value of P(X <= 10 - k or X >= 10 + k) when p = 0.5. The symmetry of the normal distribution about its mean implies that P(X <= 10 - k or X >= 10 + k) = 2P(X <= 10 - k). That's why your answer is wrong by a factor of 2.
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    (Original post by Jonny W)
    One-sided test
    H0: p = 0.5
    H1: p < 0.5
    You reject H0 when X <= 10 - k. The significance level is the value of P(X <= 10 - k) when p = 0.5.

    Two-sided test
    H0: p = 0.5
    H1: p not equal 0.5
    You reject H0 when X <= 10 - k or X >= 10 + k (ie, when |X - 10| >= k). The significance level is the value of P(X <= 10 - k or X >= 10 + k) when p = 0.5. The symmetry of the normal distribution about its mean implies that P(X <= 10 - k or X >= 10 + k) = 2P(X <= 10 - k). That's why your answer is wrong by a factor of 2.
    OK... *deep breath*

    so in simple terms, when I want to find the significance level of a two tailed test, I must always double my answer?
    and is it always P(X<=x) and not P(X>=x)?
    thanks for your help
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    in simple terms with a two-tailed test (when the alternative hypothesis states that it doesn't equal mean/p) you half the significance level putting half at each end of the distribution and if the z-score (for normal) is more than the z-score of 1/2 the significance level then you reject the null hypothesis
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    (Original post by kimoni)
    OK... *deep breath*

    so in simple terms, when I want to find the significance level of a two tailed test, I must always double my answer?
    and is it always P(X<=x) and not P(X>=x)?
    thanks for your help
    Doubling always works, even if the distribution isn't symmetric (despite what I suggested in my previous post).
 
 
 
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