Which method uses repeated samples with replacement to estimate a statistic's sampling distribution?

Which method uses repeated samples with replacement to estimate a statistic's sampling distribution?

• A. Jackknife
• B. Bootstrap
• C. Permutation test
• D. Monte Carlo simulation

Answer: (B)

Bootstrap is the method that uses repeated samples with replacement to estimate a statistic's sampling distribution. By drawing many bootstrap samples from the observed data, each time selecting observations with replacement, some data points appear multiple times while others may be left out. Calculating the statistic for each sample produces an empirical distribution that approximates how the statistic would vary across repeated samples from the population, enabling estimation of standard errors, bias, and confidence intervals without assuming a specific population distribution. The other options involve different ideas: jackknife uses leave-one-out samples without replacement to assess bias and variance; permutation tests create a null distribution by shuffling labels rather than resampling with replacement; Monte Carlo simulation draws samples from a specified model or distribution, not necessarily via resampling the observed data.

Bootstrap is the method that uses repeated samples with replacement to estimate a statistic's sampling distribution. By drawing many bootstrap samples from the observed data, each time selecting observations with replacement, some data points appear multiple times while others may be left out. Calculating the statistic for each sample produces an empirical distribution that approximates how the statistic would vary across repeated samples from the population, enabling estimation of standard errors, bias, and confidence intervals without assuming a specific population distribution. The other options involve different ideas: jackknife uses leave-one-out samples without replacement to assess bias and variance; permutation tests create a null distribution by shuffling labels rather than resampling with replacement; Monte Carlo simulation draws samples from a specified model or distribution, not necessarily via resampling the observed data.