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  1. #1
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    For a sample size of  n = 10 I simulated the roll of a dice with  k = 200 replications.

    My sample mean and variance of the mean were  \bar{x} = 1.131, \ \ s_{\bar{x}}^{2} = 1.28

    And  \mu = 3.5, \ \ \sigma^{2} = 2.917, \ \ \ \frac{\sigma^2}{10} = 0.2917 .

     s_{\bar{x}}^{2} > 0.2917 . Is this because my sample size  n = 10 was too small, and thats why they differ by a lot?
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  2. #2
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    Quote Originally Posted by heathrowjohnny View Post
    For a sample size of  n = 10 I simulated the roll of a dice with  k = 200 replications.

    My sample mean and variance of the mean were  \bar{x} = 1.131, \ \ s_{\bar{x}}^{2} = 1.28

    And  \mu = 3.5, \ \ \sigma^{2} = 2.917, \ \ \ \frac{\sigma^2}{10} = 0.2917 .

     s_{\bar{x}}^{2} > 0.2917 . Is this because my sample size  n = 10 was too small, and thats why they differ by a lot?
    It is not clear what your experiment was from what you write.

    What is the outcome of a replication? what are your  \bar{x} and s_{\bar{x}}^{2} mean and variance of?

    RonL
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  3. #3
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    Basically I simulated the rolling of a dice 30 times, and repeated this 200 times.  \bar{x} is the average of the averages from each replication.  s_{\bar{x}}^{2} is the variance of those averages
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  4. #4
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    Quote Originally Posted by heathrowjohnny View Post
    Basically I simulated the rolling of a dice 30 times, and repeated this 200 times.  \bar{x} is the average of the averages from each replication.  s_{\bar{x}}^{2} is the variance of those averages

    Suppose you have a fair die, and you roll it 10 times and compute the mean of the rolls.

    On a single roll the mean is 3.5 and the sd is ~1.708. So for the mean of 10 rolls the mean is 3.5 and the se of that mean is ~1.708/sqrt(10) ~=0.540

    Now you conduct 200 replications, and the grand mean will be 3.5 and the se of such a grand mean will be ~=0.540/sqrt(200) ~=0.0382.

    Therefore if the die is fair the mean of your sample of 200 means should be in the interval [3.42, 3.58] ~95% or the time (200 being large enough for us to use a normal approximation). Your grand mean is not in this interval so we may conclude that it is likley that the die is not fair.

    You can also compare the experimental variance 1.28 with the fair die prediction of (0.540)^2~=0.292 using the F test.

    RonL
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