1. The problem asks to identify which statement about confidence intervals for a population proportion $p$ is NOT correct. 2. Recall the key concepts about confidence intervals for a population proportion: - The population proportion $p$ is fixed but unknown. - The sample proportion $\hat{p}$ varies from sample to sample. - A confidence interval is constructed from sample data and varies with each sample. - The confidence level (e.g., 95%) represents the long-run proportion of such intervals that will contain $p$. - For a given interval, $p$ either lies inside or outside it, but we do not know which. 3. Analyze each statement: A. "The endpoints of the interval can vary with each new sample." This is true because each sample produces a different interval. B. "The probability that $p$ is in the interval is equal to the level of confidence for the interval." This is NOT correct. The confidence level is the probability that the method produces intervals containing $p$ in the long run, not the probability that $p$ is in a specific interval. C. "Whether the interval captures $p$ is not known with certainty." This is true; we do not know if the specific interval contains $p$. D. "The population proportion $p$ is fixed, but the sample proportion $\hat{p}$ can vary from sample to sample." This is true. E. "The interval either does or does not capture $p$." This is true; $p$ is either inside or outside the interval. 4. Therefore, the incorrect statement is B. **Final answer:** Statement B is not correct.