The upper and lower limits of a confidence interval are:

The upper and lower limits of a confidence interval are not random variables; rather, they are determined values based on the sample data and the chosen confidence level. Therefore, the correct understanding involves recognizing that the limits are influenced by the specifics of the data collected and the desired confidence level.

In the context of confidence intervals, if we consider fixed constants, the limits can vary based on the sample being analyzed but are calculated to provide a range where the true population parameter is expected to lie with a certain degree of confidence. The confidence coefficient does indeed play a role, as different confidence levels (such as 90%, 95%, or 99%) change the width of the interval, effectively adjusting the limits based on the required certainty. This reflects how the confidence coefficient directly influences both the calculated limits.

Furthermore, the limits are not always equal; they will generally differ unless the point estimate is the same for both the upper and lower bounds, which is uncommon.

By recognizing that the upper and lower limits depend on statistical calculations that include the sample data, standard deviations, and the selected confidence coefficient, one can better understand the nature of confidence intervals in statistical analysis.