FRM Part I · FRM Exam Part I · Hypothesis Testing
A sample of 100 daily P&L observations has a mean of 1.50 (in USD thousands) and a sample standard deviation of 10.0. Using a large-sample normal approximation, what is the 95% confidence interval for the population mean (use 1.96)?
The 95% confidence interval is -0.46 to 3.46. The standard error is 10 divided by 10, which is 1.0, and the margin of error is 1.96 times that. Adding and subtracting 1.96 from the 1.50 mean gives the interval.
- A-0.46 to 3.46Correct
- B-18.10 to 21.10
- C0.52 to 2.48
- D-0.46 to 3.00
Explanation
SE = 10/sqrt(100) = 1.0. Margin = 1.96 x 1.0 = 1.96. Interval = 1.50 ± 1.96 = -0.46 to 3.46. Using the standard deviation instead of the standard error gives the much wider interval of -18.10 to 21.10.
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