IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A 95% confidence interval for a normal mean with known variance has width 6 using a sample of size 36. Keeping the same confidence level and standard deviation, what sample size gives an interval of width 3?
The required sample size is 144. Interval width is proportional to one over the square root of n, so halving the width requires quadrupling the sample size, and 4 times 36 equals 144.
- A72
- B108
- C144Correct
- D216
- 54
Explanation
Width is proportional to 1/√n. Halving the width needs √n to double, so n must be multiplied by 4: 36 × 4 = 144. Choosing 72 wrongly assumes width is proportional to 1/n.
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