FRM Part I · FRM Exam Part I · Sample Moments
Returns are i.i.d. with population variance 0.0400 (standard deviation 20%). A researcher uses a sample of 25 observations. What is the standard error of the sample mean?
The standard error of the sample mean is 4.0%. For i.i.d. data it equals the population standard deviation divided by the square root of the sample size: 20% divided by 5. Dividing by 25 instead of its square root would wrongly give 0.80%.
- A0.80%
- B4.0%Correct
- C20.0%
- D0.16%
Explanation
Standard error = sigma/sqrt(n) = 20%/sqrt(25) = 20%/5 = 4.0%. The 0.80% option divides by n=25 instead of the square root. The 20% option ignores the sample size entirely.
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