1 Multiple Answer 2 points What does it mean to be \( 95 \% \) confident when referencing confidence intervals? Select all that apply. The \( 95 \% \) is a success rate of the process of computing the confidence interval that contain the parameter. The \( 95 \% \) refers to the percentage of ALL possible samples resulting in a confidence interval that contains the parameter. It is a range of values between which all values of the variable will lie. This is the probability that the parameter lies in the confidence interval. Then

To understand what it means to be \( 95\% \) confident when referencing confidence intervals, let's analyze each statement: 1. **The \( 95\% \) is a success rate of the process of computing the confidence interval that contains the parameter.** - This statement is true. The \( 95\% \) confidence level indicates that if we were to take many samples and compute a confidence interval from each sample, approximately \( 95\% \) of those intervals would contain the true population parameter. 2. **The \( 95\% \) refers to the percentage of ALL possible samples resulting in a confidence interval that contains the parameter.** - This statement is also true. It emphasizes that out of all possible samples, \( 95\% \) of the confidence intervals constructed from those samples would include the true parameter. 3. **It is a range of values between which all values of the variable will lie.** - This statement is false. A confidence interval does not imply that all values of the variable will lie within that range. Instead, it suggests that we are \( 95\% \) confident that the true parameter lies within that range. 4. **This is the probability that the parameter lies in the confidence interval.** - This statement is misleading. Once a confidence interval is calculated from a specific sample, the parameter either lies within that interval or it does not. The \( 95\% \) confidence level does not refer to the probability of the parameter lying in that specific interval; rather, it refers to the long-term success rate of the method used to construct the interval. Based on this analysis, the correct answers are: - The \( 95\% \) is a success rate of the process of computing the confidence interval that contains the parameter. - The \( 95\% \) refers to the percentage of ALL possible samples resulting in a confidence interval that contains the parameter.