Width of a confidence interval

Width is what you trade against confidence: raising the confidence level raises the critical value and widens the interval, while a larger sample lowers the standard error and narrows it. Because the standard error carries a $\sqrt{n}$, the width is roughly proportional to $1/\sqrt{n}$, so cutting the width in half takes four times as much data. For example, the interval 12 to 18 has width $18 - 12 = 6$ and margin of error 3, and moving from n = 100 to n = 400 would shrink that width to about 3. A narrow interval only helps if the method is sound, since a biased sample gives you a tight interval around the wrong value.