What is the recommended method if 20 x < 40 with Non-Gaussian distribution?

• A. Robust with 90% CI of reference limits - must also include histogram, mean or median, and minimum and maximum; alternatively, a table of all reference values can be provided along with the histogram
• B. Parametric with 90% CI
• C. Nonparametric with 90% CI
• D. Robust with 95% CI

Answer: (B)

When the data don’t follow a normal shape but you have a reasonably large sample, the central limit theorem lets the distribution of the sample mean be approximately normal. That means you can use a parametric confidence interval for the mean even with non-Gaussian data, as long as the sample size is around forty or more. For a 90% confidence interval, you’d use the standard normal critical value (about 1.645) in the interval mean ± z × (SD/√n). This approach is preferred here because it leverages the normal-approximation of the mean’s sampling distribution given a sufficient n, providing a straightforward, interpretable CI without needing nonparametric reshaping of the data. If the sample were much smaller or the data extremely skewed, nonparametric or robust methods would be more appropriate, but with a non-Gaussian distribution and a sample size around forty, a parametric 90% CI is the most suitable choice.