What is the recommended method if 40 ≤ n < 120 with Gaussian distribution?

• A. Robust with 90% CI of reference limits (preferred, do not require assumption of normality but do better when data is symmetrical)
• B. Nonparametric with 90% CI of reference limits
• C. Parametric with 90% CI of reference limits
• D. Bootstrap with 90% CI of reference limits

Answer: (D)

When you have a moderate sample size (40 to 120) and the data are Gaussian, bootstrapping the reference limits offers a practical and reliable way to construct 90% confidence intervals. Bootstrap resampling repeatedly draws samples with replacement from the observed data, recalculates the lower and upper reference limits, and uses the distribution of those replicated limits to form the 90% CI. This approach is distribution-free and tends to give accurate interval estimates at this sample size without relying on complex normal-theory formulas for percentiles.

Nonparametric methods need larger samples to pin down the tails with precision, so the CIs tend to be wide when n is in this range. Parametric methods would derive CIs from normal theory for the percentile limits, which is feasible with Gaussian data but can be sensitive to finite-sample behavior and is less flexible. Robust methods are advantageous when symmetry or non-normality is a concern, but with Gaussian data their advantage is limited. Bootstrap strikes a good balance by providing reliable, distribution-free CIs for reference limits in this n range.