In A/B testing, what does a narrow confidence interval indicate?

In A/B testing, a narrow confidence interval indicates a high degree of precision and certainty in the estimated results. A confidence interval is a range of values within which the true population parameter (e.g., the true click-through rate) is likely to fall, with a certain level of confidence (e.g., 95%). A narrow confidence interval suggests that the sample data provides a precise estimate of the true population parameter, meaning that the results are less susceptible to random variation. This typically occurs when the sample size is large and the variability within the data is low. Conversely, a wide confidence interval indicates less precision and greater uncertainty. For example, a narrow confidence interval of [2.4%, 2.6%] for the click-through rate of headline A suggests a more reliable estimate than a wide confidence interval of [2.0%, 3.0%].