Bootstrap resampling involves...

• A. Resampling without replacement from the observed data to estimate sampling distribution.
• B. Generating new data from a specified theoretical distribution.
• C. Repeating sampling with replacement from the observed data to estimate the sampling distribution and confidence intervals.
• D. Discarding outliers before resampling.

Answer: (C)

Bootstrap resampling works by repeatedly drawing samples from the observed data with replacement, calculating the statistic of interest for each resample, and using the resulting distribution of statistics to approximate the sampling distribution. This approach lets us estimate standard errors and build confidence intervals without assuming a specific population distribution. The replacement is the crucial part: it creates variability among the bootstrap samples similar to what we’d see if we could sample from the population, since some observations can appear more than once while others may not appear at all. If we sampled without replacement, we wouldn’t capture the same type of sampling variability, and generating data from a theoretical distribution would be a different, model-based approach. Discarding outliers beforehand isn’t part of bootstrap and would distort the empirical representation of the population.