CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
A sample of 64 monthly returns has a mean of 1.20% and a sample standard deviation of 4.00%. Using a z-value of 1.96, the 95% confidence interval for the population mean return is closest to:
The standard error is 4%/8 = 0.5%. The margin of error is 1.96 x 0.5% = 0.98%. The 95% confidence interval is therefore 1.20% plus or minus 0.98%, or 0.22% to 2.18%.
- A0.22% to 2.18%Correct
- B0.52% to 1.88%
- C0.82% to 1.58%
Explanation
Standard error = 4.00/sqrt(64) = 0.50%. Margin = 1.96 x 0.50 = 0.98%. Interval = 1.20 ± 0.98 = 0.22% to 2.18%. Using 4.00% as the standard error would be wrong, and 0.52 to 1.88 uses a margin of 0.68, which is not correct.
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