What does a smaller margin of error indicate about the confidence interval?

A smaller margin of error indicates that the confidence interval is more narrow. This is because the margin of error determines the range of values above and below the sample estimate that is included in the confidence interval. When the margin of error decreases, the difference between the upper and lower bounds of the interval becomes smaller, resulting in a narrower range. This typically implies a more precise estimate of the parameter being measured.

Additionally, a smaller margin of error often reflects either an increase in sample size or a lower level of variability in the data, both of which contribute to more accurate estimates. However, it’s important to note that while a narrower interval may suggest greater precision, it does not necessarily mean that the interval is more likely to contain the true parameter. The confidence level associated with the interval remains constant regardless of the width, and this does not change with the margin of error alone.