CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
Compared with the standard deviation of individual observations in a population, the standard error of the mean of a random sample of 100 observations is most likely:
The standard error is one-tenth of the population standard deviation. It equals σ divided by the square root of the sample size, and the square root of 100 is 10. The variance of the mean is divided by 100, but the standard deviation is divided by 10.
- Aequal to it, because the mean is unbiased
- Bone-tenth of it, because it is divided by the square root of the sample sizeCorrect
- Cone-hundredth of it, because it is divided by the sample size
Explanation
The standard error of the mean is σ/√n, and √100 = 10, so it is one-tenth of the population standard deviation. Unbiasedness concerns the center of the distribution, not its spread, and division by n applies to variance, not standard deviation.
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