How do you construct a confidence interval?

To construct a confidence interval, the correct process involves calculating the sample mean and adding or subtracting the margin of error. This method allows for the estimation of the range within which the true population parameter (such as the mean) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).

The sample mean serves as the central point of the confidence interval, representing the estimated population mean based on the sampled data. The margin of error accounts for the variability in the data and is calculated using the standard error of the mean, which is derived from the sample's standard deviation and the sample size. Adding and subtracting this margin from the sample mean provides the upper and lower boundaries of the confidence interval.

This approach is fundamental in statistics because it incorporates both the central tendency of the sample (the mean) and the precision of that estimate (the margin of error), thereby offering a clearer picture of where the true population parameter lies.

In contrast, calculating the mode does not provide a measure of central tendency that reflects the average of the sample, and setting arbitrary limits does not yield a statistically informed interval. Using only the sample variance to determine limits fails to account for the sample mean and does not consider the distribution of the