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S2 - Finding a critical region

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    im just about there, but i always seem to be one off of what the answer should be. for example:

    The probability of Brand A lotion curing a particular skin complaint it 0.35. Brand B is said to improve the cure rate. Brand B was tested on 20 people, and 10 people were cured of the problem. Show Brand B isnt significant at 0.05, and how many people out of 20 would be needed to be cured so the results are significant to 0.05?
    This means

    H0: p=0.35
    H1: p>0.35

    X~B(20,0.35)


    P(X≥10) = 1-P(X≤9) = 1-0.8782 = 0.1218. >0.05 therefore not significant.


    P(X≥c) ≤ 0.05

    1-P(X≤c-1) ≤ 0.05

    P(X≤c-1) ≥ 0.95

    now from the table,
    P(X=10) = 0.9468
    P(X=11) = 0.9804

    therefore c-1=11 and c=12


    but...the answer says its 11, not 12. what have i done wrong?
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    I can't find anything wrong with your working.
    Where was the question from?
    The only thing I can think of is that they might have rounded 0.9468 to 0.95, but it's very unlikely.
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    I can't see anything wrong with your working either. Where did you get this question from, is from the book or an exam paper?
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    nope, nothing wrong with your answer, think the book is wrong on this one, i hate it when this happens cuz then you keep thinking youve made the mistake and keep goin over an ovr tryin to find something that isnt there.
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    it was from my Heinemann S2 textbook. i seem to get them wrong in past papers by about 1 like i said, so i went back to my textbook and started doing lots of the same type of question.

    im gonna keep practicing them anyway, but its good news that i did it right and it is the answer that is wrong.

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