CFA Level IQuantitative MethodsMedium
An analyst samples 50 bond mutual funds and finds a mean annual return of 6.2%. The population standard deviation of fund returns is known to be 2.5%. What is the 95% confidence interval for the true mean return of all bond funds?
- A4.90% to 7.50%
- B5.51% to 6.89%
- C5.20% to 7.20%
- D5.80% to 6.60%
Show answer & explanationAnswer & explanation
Correct answer: B. 5.51% to 6.89%
Since the population standard deviation is known, use the z-distribution: SE = 2.5/√50 = 0.3536. Margin of error = 1.96 × 0.3536 ≈ 0.693. CI = 6.2% ± 0.693% = (5.51%, 6.89%).
Why the other options are wrong
- A. Overstates the margin of error, possibly using an incorrect critical value or SE.
- C. Uses too wide a margin, inconsistent with the correct standard error.
- D. Margin too narrow; does not match the correct z×SE calculation.
Confidence Interval (Known Population Variance)
An interval estimate for a population mean when the population standard deviation is known, using the z-distribution critical values.
- CI = sample mean ± z × (σ/√n)
- 95% confidence uses z = 1.96
- Use t-distribution instead if population variance is unknown and n is small
Memory trick: Known sigma? Grab the z! Unknown sigma? Reach for t!