Answer: Use of non-independent data.

## Explanation Bootstrapping is ineffective when using **non-independent data**. The bootstrapping method relies on the assumption that observations in the data are **independent and identically distributed (i.i.d.)**. This means: - Each observation must be independent of all other observations - All observations must follow the same probability distribution **Why non-independent data breaks bootstrapping:** - If data are correlated or dependent, the resampling process (sampling with replacement) cannot accurately capture the original data's structure and dependencies - The resulting bootstrap samples would not be representative of the original data - This leads to inaccurate estimates of the sampling distribution **Why other options are incorrect:** - **B: Sampling with replacement** - This is actually a fundamental aspect of bootstrapping, not a limitation - **C: If there are no outliers in the data** - Bootstrapping doesn't make assumptions about outliers and can handle datasets with or without them - **D: Re-sampling from regression residuals** - This can be an effective use of bootstrapping for testing hypotheses about regression coefficients or constructing confidence intervals Bootstrapping is particularly vulnerable to violations of the independence assumption because it treats each observation as interchangeable, which isn't valid when observations are correlated.

Author: Tanishq Prabhu