Step 1 :The estimated margin of error is calculated as the difference between the upper limit and the lower limit divided by 2. In this case, the upper limit is 79.3 and the lower limit is 48.1. So, the margin of error is \((79.3 - 48.1) / 2\).
Step 2 :The sample mean in a confidence interval is the midpoint of the interval, which is the average of the upper limit and the lower limit. So, the sample mean is \((79.3 + 48.1) / 2\).
Step 3 :By calculating, we get the estimated margin of error as \(15.6\) and the sample mean as \(63.7\).
Step 4 :Final Answer: The estimated margin of error is \(\boxed{15.6}\) and the sample mean is \(\boxed{63.7}\).