FRM Part I · FRM Exam Part I · Hypothesis Testing
A sample of 100 monthly excess returns on a fund has a mean of 0.80% and a sample standard deviation of 4.00%. Using the normal approximation with a critical value of 1.96, what is the 95% confidence interval for the true mean monthly excess return?
The standard error is 4%/10 = 0.40%, so the margin of error is 1.96 times 0.40%, about 0.784%. Adding and subtracting this from the 0.80% sample mean gives an interval of roughly 0.016% to 1.584%.
- A0.016% to 1.584%Correct
- B-0.30% to 1.90%
- C0.00% to 1.60%
- D-0.58% to 2.18%
Explanation
SE = 4.00/sqrt(100) = 0.40%. Margin = 1.96 x 0.40% = 0.784%. Interval = 0.80% ± 0.784% = 0.016% to 1.584%. Using the standard deviation 4% instead of the SE would give a far wider interval, and 0.00%-1.60% is a rounding of margin to 0.80%, which is wrong.
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