All possible samples of a particular size are selected from a population that is approximately Normal with a mean of 30 and a standard deviation of 10. Which sample size will produce the smallest standard deviation of the sampling distribution of the sample mean?

The standard deviation of the sampling distribution of the sample mean is the standard error, calculated as the population standard deviation divided by the square root of the sample size: 10/√n. As n increases, this value decreases. Among the choices, n = 50 is largest, so it produces the smallest standard deviation.

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