How do i know the require sample size needed to get a specific std. dev. value for the mean and median?
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Suppose X_1, ... , X_n are independent random variables each with a N(0,1) distribution. How large a sample is required for the standard deviation of the sample mean to be 1/10? And likewise large a sample is required for the standard deviation of the sample median to be 1/10? this question confuses me because i dont have a sample mean to use
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Answer:
The sum of X_1 + ... + X_n will have standard deviation sqrt(n) * 1 =sqrt(n). If you divide by n to have a mean, the standard deviation will be sqrt(n)/n = 1/sqrt(n). So if n = 100, the standard deviation of the mean is 1/10. For the median, should be around the same, hopefully....
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