Width of Confidence Intervals
The width of a confidence interval based on a sample statistic depends partly on its standard error, and therefore on both the standard deviation, and sample size. It also depends on the degree of “confidence” that we wish to associate with the resulting interval.
The sample size affects the size of the standard error and in turn affects the width of the confidence interval. Reducing the sample size leads to less precision and an increase in width of the confidence interval. Similarly, increasing the sample size leads to greater precision and a reduction in width of the confidence interval.
Note: Confidence intervals only convey the effects of sampling variation on the precision of estimated statistics and cannot control for non-sampling errors like biases in design, conduct, or analysis.