Answer: can be used to estimate the standard error of a population median.

## Explanation **Correct Answer: B** **Analysis of each option:** **A. repeatedly draws samples without replacement.** - **Incorrect** - Bootstrap resampling actually draws samples **with replacement** from the original dataset. This is a fundamental characteristic of the bootstrap method. **B. can be used to estimate the standard error of a population median.** - **Correct** - Bootstrap resampling is particularly useful for estimating standard errors of statistics that don't have simple analytical formulas, such as the median, quantiles, or other complex estimators. By repeatedly resampling from the original data and calculating the statistic of interest each time, we can estimate its sampling distribution and standard error. **C. relies on an analytical formula to estimate the distribution of estimators.** - **Incorrect** - The bootstrap method is a **computational** approach that doesn't rely on analytical formulas. Instead, it uses resampling to empirically estimate the sampling distribution of a statistic. **Key Concepts:** 1. **Bootstrap resampling** involves drawing samples **with replacement** from the original dataset. 2. Each bootstrap sample is the same size as the original dataset. 3. The statistic of interest is calculated for each bootstrap sample. 4. The distribution of these bootstrap statistics approximates the sampling distribution of the original statistic. 5. This method is especially valuable for complex statistics where analytical formulas for standard errors are not available or are difficult to derive. **Why B is correct:** The bootstrap method is commonly used to estimate standard errors for statistics like medians, quantiles, and other robust estimators that don't have simple analytical standard error formulas.

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