Step 1 :Given the confidence interval (13.8, 21.0), we can find the sample mean \(\bar{x}\) by calculating the midpoint of the interval, and the margin of error \(E\) by calculating half the width of the interval.
Step 2 :Calculate the sample mean: \(\bar{x} = \frac{{13.8 + 21.0}}{2} = 17.4\)
Step 3 :Calculate the margin of error: \(E = \frac{{21.0 - 13.8}}{2} = 3.6\)
Step 4 :Final Answer: The sample mean is \(\boxed{17.4}\) and the margin of error is \(\boxed{3.6}\)