CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
A portfolio manager has a sample of 25 observations and wants the standard error of the sample mean to fall to half its current value, holding the sample standard deviation constant. The sample size needed is closest to:
The sample size must be about 100. Standard error falls with the square root of n, so halving it requires the square root of n to double, which means n must quadruple from 25 to 100. Simply doubling the sample to 50 reduces the error only by about 29%.
- A50
- B100Correct
- C625
Explanation
Standard error is proportional to 1/√n. Halving it requires √n to double, so n must quadruple: 25 × 4 = 100. Doubling to 50 gives a reduction of only about 29%, and 625 would be 25 squared.
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