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Math Help - Precision of estimator

  1. #1
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    Hypothesis testing question

    In a large city the distribution of incomes per family has a standard deviation of 2500.
    For a random sample of 400 families, what is the probability that the sample mean per family is within 500 of the actual income per family?
    Attached Thumbnails Attached Thumbnails Precision of estimator-sdsdsd.jpg  
    Last edited by bluebiro; August 31st 2009 at 07:29 AM.
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  2. #2
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     <br />
\mu = 0 <br />

     <br />
E\left(\frac{1}{n}\sum x_i^2\right) = \sigma^2 <br />

     <br />
Var\left(\frac{1}{n}\sum x_i^2\right) = E\left[\left(\frac{1}{n}\sum x_i^2 - \sigma^2\right)^2\right]  = ... = \frac{2\sigma^4}{n}<br />

    This should get you started, I hope...

    I'm on my way to work, so I don't have much time, but let me know if you need help with (...)
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  3. #3
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    Quote Originally Posted by temp View Post
     <br />
\mu = 0 <br />

     <br />
E\left(\frac{1}{n}\sum x_i^2\right) = \sigma^2 <br />

     <br />
Var\left(\frac{1}{n}\sum x_i^2\right) = E\left[\left(\frac{1}{n}\sum x_i^2 - \sigma^2\right)^2\right] = ... = \frac{2\sigma^4}{n}<br />

    This should get you started, I hope...

    I'm on my way to work, so I don't have much time, but let me know if you need help with (...)
    Yes please

    1) How do you know that E(the function) is \sigma^2?
    2) How did you calculate the variance?

    thank you!
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  4. #4
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    see Estimation with applications to tracking and navigation By Yaakov Bar-Shalom, Xiao-Rong Li, Thiagalingam Kirubarajan p.106

    Available on books.google.com

    Reference courtesy of physicsforum.com
    Last edited by temp; August 17th 2009 at 04:41 PM.
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