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IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions

A random sample X1, ..., Xn is drawn from a population with mean 50 and variance 64. Which of the following is the standard deviation of the sample mean when n = 16?

The standard deviation of the sample mean is 2. The variance of the mean equals the population variance divided by n, which is 64/16 = 4, and the square root of 4 is 2. The value 4 is the variance, not the standard deviation.

  1. A0.5
  2. B2Correct
  3. C4
  4. D8
  5. 16

Explanation

Var(sample mean) = sigma^2/n = 64/16 = 4, so the standard deviation is 2. Choosing 4 gives the variance instead of the standard deviation. Choosing 8 ignores the sample size.

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