What happens to the confidence interval if the sample size is increased while keeping the confidence level constant?

When the sample size increases while keeping the confidence level constant, the confidence interval becomes narrower. This occurs because a larger sample size typically provides more accurate estimates of the population parameters, resulting in a reduced margin of error.

The margin of error is influenced by the standard error, which is calculated as the standard deviation divided by the square root of the sample size. As the sample size increases, the standard error decreases, leading to a narrower confidence interval. This reflects greater precision in the estimate, as the range of values representing the confidence interval constricts around the sample estimate.

In practical terms, a narrower confidence interval means that we have a better estimate of the population parameter, enhancing the reliability of our conclusions based on the data collected. Therefore, increasing the sample size contributes to more defined and reliable results in statistical analysis.