CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
Holding the confidence level and the sample standard deviation constant, an analyst quadruples the sample size when estimating a population mean. The width of the confidence interval will most likely:
The width of the interval is proportional to one over the square root of the sample size. Quadrupling the sample size doubles the square root, so the interval width is halved, assuming the confidence level and standard deviation stay constant.
- Abe halvedCorrect
- Bbe reduced to one-quarter of its original width
- Cremain unchanged because the confidence level is constant
Explanation
Width is proportional to s/sqrt(n). Quadrupling n multiplies sqrt(n) by 2, so the width falls by half. It is not quartered, because the relation involves the square root of n.
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