IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
Ten paired observations of claim costs before and after a process change give differences (before minus after) with mean 12 and sample standard deviation 9.49. Using t(9) at 97.5% = 2.262, which is the 95% confidence interval for the mean difference?
The standard error of the mean difference is 9.49 divided by root 10, which is 3.0. The margin is 2.262 x 3.0 = 6.79, so the interval is 12 ± 6.79, giving (5.2, 18.8).
- A(3.0, 21.0)
- B(5.2, 18.8)Correct
- C(7.5, 16.5)
- D(4.0, 20.0)
- (1.2, 22.8)
Explanation
SE = 9.49/sqrt(10) = 3.0011. Margin = 2.262 x 3.0011 = 6.788. Interval = 12 ± 6.79 = (5.21, 18.79). A distractor using the two-sample unpaired formula would give a different width.
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