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    Ok this is the question:

    It is suggested that one-third of all mathematicians are left-handed. In a survey, 51 out of 174 mathematicians were found to be left-handed. Assuming that the sample was random, carry out a test, at the 5% significance level, of whether or not the sample confirms the suggestion.

    I know it is a binomial distribution, so:

    X\sim B(174,\frac{1}{3}) \approx V\sim N(58,\frac{116}{3})





H_0: p=\frac{1}{3}



H_1: p\not=\frac{1}{3}

    Now here comes my question, how do I know it is P(X\leq 51), rather than P(X\geq 51).

    I know how to do the rest, just this bit. Help is very much appreciated. Thanks in advance!

    - Italy v Holland now
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    i don't think it's any massive reason, just that common sense says those figures make less than a third
    surely if you did it the other way round and took it away from 1 you'd get the same answer anyway?
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    (Original post by T89)
    Ok this is the question:

    It is suggested that one-third of all mathematicians are left-handed. In a survey, 51 out of 174 mathematicians were found to be left-handed. Assuming that the sample was random, carry out a test, at the 5% significance level, of whether or not the sample confirms the suggestion.

    I know it is a binomial distribution, so:

    X\sim B(174,\frac{1}{3}) \approx V\sim N(58,\frac{116}{3})





H_0: p=\frac{1}{3}



H_1: p\not=\frac{1}{3}

    Now here comes my question, how do I know it is P(X\leq 51), rather than P(X\geq 51).

    I know how to do the rest, just this bit. Help is very much appreciated. Thanks in advance!

    - Italy v Holland now
    Your hypothesis is correct and so we have a 2 tail test. The expected value is 58 and the observed value is 51. Hence you want to see is this observed value is in the lower tail - it can't be in the upper tail! Hence you work out the probability that x is <= 51.
    {If your observed value had been 63, for example, then you would work out the probability that x >= 63.}
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    Oh yeah ok makes sense now! Thanks a lot!
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    If you wanted you could have just found the critical regions first, although it is slightly more work, most questions of that type will ask you to do that as a first stage and then later say, x number were left handed what does this mean.
 
 
 
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