FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk manager estimates the mean of a return series and obtains a 95% confidence interval whose half-width is 1.20% based on 50 observations. Holding the sample standard deviation and critical value constant, approximately how many observations are needed to reduce the half-width to 0.40%?
About 450 observations are needed. The half-width falls with the square root of the sample size, so cutting it to one-third requires nine times as many observations. Nine times 50 equals 450, not 150.
- A150
- B450Correct
- C100
- D300
Explanation
Half-width is proportional to 1/sqrt(n). Reducing it by a factor of 3 requires sqrt(n) to rise by 3, so n rises by 9: 50 x 9 = 450. Tripling n to 150 is wrong because it ignores the square root relationship.
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