CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst has a random sample of 25 observations with a standard error of the mean of 2.0. To cut the standard error to 0.5 with the same population, the analyst must most likely increase the sample size to:
The sample size must rise to 400. Standard error falls with the square root of n, so cutting it to one quarter requires sixteen times as many observations: 25 multiplied by 16 equals 400.
- A100
- B200
- C400Correct
Explanation
Standard error = s/√n, so s = 2.0×5 = 10. For 0.5, √n = 10/0.5 = 20, so n = 400. Answer 100 results from assuming a fourfold cut in standard error needs a fourfold rise in n.
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