Based upon the Central Limit Theorem How does the mean of th

Based upon the Central Limit Theorem

How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

How does the standard deviation of the sample distribution of all possible means from a population compare to the standard deviation of the population?

Solution

How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

They are equal, that is, u = u(X).

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How does the standard deviation of the sample distribution of all possible means from a population compare to the standard deviation of the population?

They are related by the equation sigma(X) = sigma/sqrt(n).

Thus, the standard deviation of the sampling distribution is smaller by a factor of 1/sqrt(n).