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Math Help - Confidence interval: Normal or T-Student?

  1. #1
    Newbie noname's Avatar
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    Confidence interval: Normal or T-Student?

    Hi, I have a doubt.

    I have a sample N = 20, sample mean = 1.1 and the standard deviation of the population = 0.3. No other assumptions are made.
    I need to find a confidence interval.

    The sample is small, but the standard deviation of the population is not unknown.

    Which quantiles should I use?

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by noname View Post
    Hi, I have a doubt.

    I have a sample N = 20, sample mean = 1.1 and the standard deviation of the population = 0.3. No other assumptions are made.
    I need to find a confidence interval.

    The sample is small, but the standard deviation of the population is not unknown.

    Which quantiles should I use?

    Thanks
    The problem is that both the T- and Normal distribution methods require that the sample be drawn from a normal population (if the variance or standard deviation is known then we use the normal distribution method, if it is estimated from the sampel then we use the T-distribution method).

    Without further information the normality or not of the population is an unknown so neither method strictly applicable.

    If the sample does not look normal-ish I would use the bootstrap.

    CB
    Last edited by CaptainBlack; September 28th 2009 at 03:49 AM.
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  3. #3
    Newbie noname's Avatar
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    Thanks for your help CaptainBlack

    Now I think that I am required to just assume that the population is normal.
    We don't study the bootstrapping.. I don't have even the sample values.

    Assuming that it is normal, should I use the t-student?
    I'm not sure because the sample is small but I know the standard deviation of the population...
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by noname View Post
    Thanks for your help CaptainBlack

    Now I think that I am required to just assume that the population is normal.
    We don't study the bootstrapping.. I don't have even the sample values.

    Assuming that it is normal, should I use the t-student?
    I'm not sure because the sample is small but I know the standard deviation of the population...
    No, you have a known standard deviation, so you use the normal.

    CB
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