IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A sample of n = 11 observations from a normal population has sample variance s^2 = 25. For chi-square with 10 degrees of freedom, the 2.5% point is 3.247 and the 97.5% point is 20.48. What is the 95% confidence interval for sigma^2?
The interval is (12.21, 77.00). Multiply s squared by the degrees of freedom to get 250, then divide by the upper chi-square point 20.48 for the lower limit and by the lower point 3.247 for the upper limit.
- A(12.21, 77.00)Correct
- B(9.77, 62.00)
- C(1.22, 7.70)
- D(12.21, 20.48)
- (2.50, 20.48)
Explanation
Interval is ((n-1)s^2/20.48, (n-1)s^2/3.247). (n-1)s^2 = 250. Lower = 250/20.48 = 12.21; upper = 250/3.247 = 77.00. Option (1.22, 7.70) divides 25 rather than 250, ignoring the factor n-1.
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