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Math Help - 95% confidence intervals

  1. #1
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    95% confidence intervals

    I have data that is very right skew where I know the sample mean, the sample standard deviation and the sample size. I have calculated a 95% confidence interval for the mean using the following method:
    (mean-1.96xESE, mean+1.96xESE) where ESE is estimated standard error.
    The question then asks why it doesn't matter whether the distribution of the population is or isn't normal?

    Does anyone know the answer? Thanks.
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  2. #2
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    Re: 95% confidence intervals

    The central limit theorem states that when taking samples from a distribution with mean \mu and variance \sigma^2 the distribution of the sample tends toward a normal distribution with mean \mu and variance \frac{\sigma^2}{n} as sample size n increases. In the limit as n tends to infinity the sample mean is exactly normally distributed. For large sample sizes (n>30 or n>50) we often assume that the distribution is normal.
    Central limit theorem - Wikipedia, the free encyclopedia
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