IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A 95% confidence interval for a mean is calculated from a sample with known sigma. If the sample size is multiplied by 4 and the confidence level and sigma are unchanged, what happens to the expected width of the interval?
The width is halved. The interval width is proportional to one over the square root of the sample size, so quadrupling n doubles the square root and halves the width.
- AIt is halvedCorrect
- BIt is quartered
- CIt is unchanged
- DIt is doubled
- It is reduced to one third
Explanation
Width = 2 z sigma/sqrt(n). Multiplying n by 4 multiplies sqrt(n) by 2, so the width is divided by 2. Quartering would require n to be 16 times larger.
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