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Math Help - Binomial Distributions and Confidence Intervals

  1. #1
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    Binomial Distributions and Confidence Intervals

    If I have a binomial distribution, can I work out the confidence interval simply by summing up the probabilities of each set of outcomes until I reach 95%?

    e.g. n = 70, p(success) = 0.25. I know that 95% of the distribution falls between 11 and 24.

    Can I take this range as the 95% confidence interval or do I need to approximate to a normal distribution and do a z-test? The interval I have selected is evenly distributed +/-6.5 of the mean.

    The mean of the data is 17.5, SD is 3.62 using this site

    Binomial Distribution Calculator

    (and if you put "Between 11 and 24" you will see that the probability is 0.9480 ~= 95%)

    Here is a sample of my data if you wish to do some rough calculations

    0 0.0000
    1 0.0000
    2 0.0000
    3 0.0000
    4 0.0000
    5 0.0001
    6 0.0003
    7 0.0010
    8 0.0026
    9 0.0059
    10 0.0121
    *11 0.0219
    *12 0.0360
    *13 0.0535
    *14 0.0726
    *15 0.0903
    *16 0.1035
    *17 0.1096
    *18 0.1075
    *19 0.0981
    *20 0.0834
    *21 0.0662
    *22 0.0491
    *23 0.0342
    *24 0.0223
    25 0.0137
    26 0.0079
    27 0.0043
    28 0.0022
    29 0.0011
    30 0.0005
    31 0.0002
    32 0.0001
    33 0.0000

    The thing here is I'm using a discrete variable so I don't think it would be right to approximate this to a normal distribution and then do a z-test.

    Thanks.

    PS: I think I might have posted this in the wrong forum: this might be more college/university level. Feel free to move it over - moderators.
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  2. #2
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    Quote Originally Posted by lostnumber View Post
    If I have a binomial distribution, can I work out the confidence interval simply by summing up the probabilities of each set of outcomes until I reach 95%?

    e.g. n = 70, p(success) = 0.25. I know that 95% of the distribution falls between 11 and 24.

    Can I take this range as the 95% confidence interval or do I need to approximate to a normal distribution and do a z-test? The interval I have selected is evenly distributed +/-6.5 of the mean.

    The mean of the data is 17.5, SD is 3.62 using this site

    Binomial Distribution Calculator

    (and if you put "Between 11 and 24" you will see that the probability is 0.9480 ~= 95%)

    Here is a sample of my data if you wish to do some rough calculations

    0 0.0000
    1 0.0000
    2 0.0000
    3 0.0000
    4 0.0000
    5 0.0001
    6 0.0003
    7 0.0010
    8 0.0026
    9 0.0059
    10 0.0121
    *11 0.0219
    *12 0.0360
    *13 0.0535
    *14 0.0726
    *15 0.0903
    *16 0.1035
    *17 0.1096
    *18 0.1075
    *19 0.0981
    *20 0.0834
    *21 0.0662
    *22 0.0491
    *23 0.0342
    *24 0.0223
    25 0.0137
    26 0.0079
    27 0.0043
    28 0.0022
    29 0.0011
    30 0.0005
    31 0.0002
    32 0.0001
    33 0.0000

    The thing here is I'm using a discrete variable so I don't think it would be right to approximate this to a normal distribution and then do a z-test.

    Thanks.

    PS: I think I might have posted this in the wrong forum: this might be more college/university level. Feel free to move it over - moderators.
    Your calculation looks OK to me.

    The normal approximation would be valid here (why?) - perhaps you should use it just to see what happens.
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