CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst draws 25 observations from a normally distributed population with unknown variance. The sample mean is 8.0% and the sample standard deviation is 5.0%. The t-value for 24 degrees of freedom at 95% confidence is 2.064. The confidence interval for the population mean is closest to:
With unknown population variance and a normal population, use the t-distribution. Standard error is 5%/5 = 1%, and the margin is 2.064 x 1% = 2.064%. The interval is 8.0% plus or minus 2.064%, which is about 5.94% to 10.06%.
- A5.94% to 10.06%Correct
- B6.00% to 10.00%
- C3.55% to 12.45%
Explanation
Standard error = 5.0/sqrt(25) = 1.0%. Margin = 2.064 x 1.0 = 2.064%. Interval = 8.0 ± 2.064 = 5.94% to 10.06%. Using z of 1.96 gives 6.04 to 9.96 (not the key). The 3.55 to 12.45 option wrongly uses the standard deviation of 5.0 as the standard error multiplied by... roughly 0.89 of the t-value, a standard-error mistake.
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