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Math Help - Chi square Test

  1. #1
    Member roshanhero's Avatar
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    Red face Chi square Test

    The Distribution of digits in numbers chosen at random from the telephone directory are:
    Digit 0 1 2 3 4 5 6 7 8 9
    Frequency 1026 1107 997 966 1075 933 1107 972 964 853
    Test whether the digits may be taken to occur equally frequently in the directory
    My problem is which test to chose and why? Though I think that I should use Chi-square test, I still can't confidently say why? If it is chi-square test, then I don't know how to calculate expected frequency, Is there any specific formula to calculate it?
    Last edited by roshanhero; January 17th 2011 at 08:18 PM. Reason: Mistake
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  2. #2
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    I would use a \displaystyle \chi^2 test.

    With

    \displaystyle<br />
H_0: \text{The observed frequencies are consistent the expected frequencies}

    \displaystyle<br />
H_A: \text{The observed frequencies are not consistent the expected frequencies}

    Reject \displaystyle H_0: if \displaystyle \sum \frac{(0-E)^2}{E}>\chi^2_{\alpha , df}
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  3. #3
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    Quote Originally Posted by roshanhero View Post
    If it is chi-square test, then I don't know how to calculate expected frequency, Is there any specific formula to calculate it?
    For expected frequencies to occur evenly.

    Sum these guys

    Quote Originally Posted by roshanhero View Post
    Frequency 1026 1107 997 966 1075 933 1107 972 964 853
    And divide the result by 10. Allocate this new figure for each digit.

    Sorry about the multi post!
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  4. #4
    Member roshanhero's Avatar
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    Thanks,but how to find the expected frequency when expected frequencies do not occur evenly.
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  5. #5
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    Good question, this can be done but you need more (particular) information on how the expected frequencies are distributed unevenly.

    The way around this is to test the data like in post #1. If you choose to reject the null hypothesis then you say there is evidence to suggest they are not distributed evenly.
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