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

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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.
Being $$ 95\% $$ confident means that: - $$ 95\% $$ of the confidence intervals calculated from many samples will contain the true parameter. - $$ 95\% $$ refers to the percentage of all possible samples where the confidence interval includes the parameter. These statements are correct.

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