The larger confidence interval is more likely to have the true value of the mean. Also how precise the estimate is also effective onthe size of margin of error. If it's not precise, the margin of error would be large. 3 margin of error which means that the mean of the data can be within a 6 point spread centered around the mean. The larger the sample size the smaller the margin of error.
Several factors can determine the size of the margin of error.
The larger the confidence level and the larger the variation is of a population,the larger the margin of error is. The more trials done, the smaller the margin of error is. The margin of error associated with a certain confidence level by increasing as the confidence level increases. This is because a shorter confidence intercal is more informative than a longer one. The size of a margin of error can be determined by the size of the sample collected and also whether or not sigma is known.