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Quick question about means/confidence intervals Watch

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    If I am given the standard deviation, the mean and the number of observations of a random variable, how do I work out the confidence level of the true mean being within 10% of the mean. i.e. the confidence that the true mean = estimated_mean \pm 0.1*estimated_mean

    Help would be appreciated.

    EDIT: click here for new thread, this one has too much unnecessary info in it.
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    (Original post by The Racist Dragon)
    If I am given the standard deviation, the mean and the number of observations of a random variable, how do I work out the confidence level of the true mean being within 10% of the mean. i.e. the confidence that the true mean = estimated_mean \pm 0.1*estimated_mean

    Help would be appreciated.
    It depends on the sample size.

    A large sample size you can use the normal distribution, a small one and you use the t-distribution.

    For instance, for a normal distribution, the confidence interval is:
    [\bar{x} \pm Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt n}]

    For a t-distribution, the confidence interval is:
    [\bar{x} \pm t_{n-1}(\frac{\alpha}{2}) \times \frac{\sigma}{\sqrt n}]

    \alpha being the significance level, i.e. in this case, 0.1.
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    (Original post by CTArsenal)
    It depends on the sample size.

    A large sample size you can use the normal distribution, a small one and you use the t-distribution.

    For instance, for a normal distribution, the confidence interval is:
    [\bar{x} \pm Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt n}]

    For a t-distribution, the confidence interval is:
    [\bar{x} \pm t_{n-1}(\frac{\alpha}{2}) \times \frac{\sigma}{\sqrt n}]

    \alpha being the significance level, i.e. in this case, 0.1.
    The confidence level is what I'm calculating, I want to know the confidence level that the true mean is within 10% of the estimated mean, i don't want the 10% confidence interval of the estimated mean.

    I know it's a little confusing, I had to read the question a few times myself...!

    So far I have calculated that:

    Z_\frac{\alpha}{2} = \frac{0.1*mean*\sqrt{n}}{stdev}

    But I don't know how to find \alpha from that, I'd probably need some crazy formula...

    I think I should make a new thread asking how to find alpha when I already know what Z is, this thread has too much unnecessary info in it.
 
 
 
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