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Math Help - confidence interval

  1. #1
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    confidence interval

    Let X1, X2,....,Xn be a random sample of size n from the normal distribution N(\mu, \sigma^{2}). Calculate the expected length of a 95% confidence interval for \mu assuming that n=5 and the variance is:

    a. known
    b. unknown

    Thank you for any help!
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  2. #2
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    Quote Originally Posted by redpack View Post
    Let X1, X2,....,Xn be a random sample of size n from the normal distribution N(\mu, \sigma^{2}). Calculate the expected length of a 95% confidence interval for \mu assuming that n=5 and the variance is:

    a. known
    b. unknown

    Thank you for any help!
    let  \bar{X}=\frac{1}{n}(\sum_{k=1}^n X_k) . If X_k independent with other, then we have  \bar{X} ~  N(\mu, \sigma^2/\sqrt{n}).
    In the case \sigma is known
    we use  \frac{\bar{X}-\mu}{\sigma/ \sqrt{n}} ~N(0,1).
    In the case \sigma is unknown
    we use  \frac{\bar{X}-\mu}{s/ \sqrt{n}} ~t-distribution.
    From here, we get the confident interval.
    Many book talk about this.
    Last edited by mr fantastic; May 29th 2009 at 04:38 AM. Reason: Fixed some latex
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