What does it mean to say that the confidence interval methods for the mean are robust against departures from normality? Choose the correct answer below. A. The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme. B. The confidence interval methods for the mean are robust against departures from normality, meaning they don't work well with distributions that aren't normal. C. The confidence interval methods for the mean are robust against departures from normality, meaning they only work with distributions that aren't normal. D. The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are extreme.

A. The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme. Imagine you’re baking a cake and you’re short on flour, but only a little! Luckily, that won’t ruin your masterpiece. Confidence interval methods act similarly by allowing for some variation in the data distribution without completely derailing your conclusions. Of course, if you start running low on every ingredient (i.e., face extreme non-normality), that might be a cake to rethink! In the real world, you often deal with data that doesn’t follow perfect normality—like income distribution or user engagement metrics. The robustness of confidence intervals means you can use them confidently, even when your data has a few quirks. Just remember, mild deviations from normal are usually just fine, but major departures might need more nuanced statistical strategies!