To determine which statement accurately represents a 95% confidence level, let's evaluate each option carefully:
1. The probability that the true population parameter is in the confidence interval is 0.95.
This statement is slightly misleading. The confidence interval either contains the true population parameter or it does not. Therefore, the correct interpretation is about the method that generates the interval.
2. We are 95% confident that the population parameter is the midpoint of the confidence interval.
This statement is incorrect. The 95% confidence level refers to the entire interval, not its midpoint. The population parameter could plausibly lie anywhere within the interval, not necessarily at the midpoint.
3. In repeated sampling of size n, the CI will capture the true population parameter 95% of the time.
This statement is accurate. Over many samples of the same size, we expect 95% of the resulting confidence intervals to contain the true population parameter. This aligns correctly with the concept of a confidence level.
Thus, the accurate interpretation of a 95% confidence level is:
In repeated sampling of size n, the CI will capture the true population parameter 95% of the time.
